Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,0]
node 2: [1,1]
node 3: [1,1]
node 4: [0,1]
node 5: [1,0]
node 6: [0,0]
The edges are: (0,6) (0,5) (1,4) (2,6) (2,4) (2,5) (3,4) (3,5) (4,6)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [5,6]
node 1: [3,2]
node 2: [8,8]
node 3: [6,5]
node 4: [4,6]
node 5: [3,2]
node 6: [5,3]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 12, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [0,1]
node 2: [1,1]
node 3: [1,1]
node 4: [0,1]
node 5: [0,0]
node 6: [1,1]
node 7: [1,1]
node 8: [0,0]
node 9: [0,0]
node 10: [1,0]
node 11: [0,1]
node 12: [0,1]
The edges are: (0,5) (0,11) (1,10) (1,3) (2,8) (3,6) (3,5) (3,11) (4,12) (5,12) (5,8) (5,11) (5,9) (6,12) (7,12) (7,9) (8,11) (9,12) (9,11)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [4,4]
node 1: [1,4]
node 2: [1,2]
node 3: [7,7]
node 4: [2,3]
node 5: [7,13]
node 6: [3,6]
node 7: [3,6]
node 8: [4,4]
node 9: [6,8]
node 10: [2,1]
node 11: [5,12]
node 12: [4,10]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,0]
node 1: [0,0]
node 2: [0,0]
node 3: [0,1]
node 4: [1,0]
node 5: [0,1]
node 6: [1,0]
node 7: [1,1]
node 8: [1,0]
node 9: [0,1]
The edges are: (0,5) (0,2) (1,5) (2,4) (3,7) (3,8) (4,7) (4,9) (4,8) (5,7) (5,6) (6,7) (7,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,1]
node 1: [2,1]
node 2: [2,3]
node 3: [5,4]
node 4: [7,4]
node 5: [4,6]
node 6: [5,3]
node 7: [9,8]
node 8: [7,5]
node 9: [2,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [1,0]
node 3: [0,1]
node 4: [0,1]
node 5: [1,0]
node 6: [1,1]
node 7: [0,0]
The edges are: (0,6) (0,4) (1,5) (1,4) (2,3) (2,7) (3,4) (4,5) (4,6) (5,7) (6,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [4,5]
node 1: [3,4]
node 2: [4,2]
node 3: [3,4]
node 4: [4,7]
node 5: [7,5]
node 6: [7,6]
node 7: [1,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,0]
node 2: [0,1]
node 3: [0,1]
node 4: [0,1]
node 5: [0,0]
The edges are: (0,5) (0,4) (1,5) (1,3) (2,3) (3,4) (4,5)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,2]
node 1: [3,3]
node 2: [1,2]
node 3: [1,3]
node 4: [3,4]
node 5: [1,3]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,1]
node 2: [0,0]
node 3: [1,0]
node 4: [1,0]
node 5: [1,0]
node 6: [0,1]
node 7: [0,0]
node 8: [1,0]
node 9: [0,0]
node 10: [1,0]
node 11: [1,0]
node 12: [0,1]
node 13: [1,0]
The edges are: (0,13) (1,11) (1,10) (1,9) (1,5) (2,4) (2,12) (3,11) (3,7) (4,8) (5,8) (6,12) (8,11) (8,13) (9,10) (10,11) (10,13) (11,12)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,0]
node 1: [11,5]
node 2: [2,1]
node 3: [5,2]
node 4: [5,1]
node 5: [7,0]
node 6: [1,1]
node 7: [1,0]
node 8: [10,3]
node 9: [6,1]
node 10: [12,3]
node 11: [12,2]
node 12: [5,4]
node 13: [8,1]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,0]
node 2: [1,1]
node 3: [0,1]
node 4: [0,0]
node 5: [1,0]
node 6: [1,1]
node 7: [0,1]
node 8: [0,1]
node 9: [1,1]
The edges are: (0,7) (1,5) (1,9) (2,4) (3,4) (3,6) (4,9) (5,8) (5,9) (5,6) (6,8) (7,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [1,2]
node 1: [5,3]
node 2: [2,3]
node 3: [3,5]
node 4: [3,1]
node 5: [7,5]
node 6: [6,6]
node 7: [2,3]
node 8: [5,7]
node 9: [7,7]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,0]
node 1: [1,0]
node 2: [1,0]
node 3: [1,0]
node 4: [0,1]
node 5: [0,0]
node 6: [1,1]
The edges are: (0,6) (0,5) (0,2) (1,3) (1,4) (1,2) (3,5) (3,4) (5,6)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,1]
node 1: [4,1]
node 2: [4,2]
node 3: [6,2]
node 4: [3,2]
node 5: [3,2]
node 6: [4,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [0,1]
node 2: [1,1]
node 3: [1,0]
node 4: [1,0]
node 5: [0,0]
node 6: [1,1]
node 7: [0,1]
node 8: [0,1]
node 9: [1,0]
node 10: [0,1]
node 11: [0,0]
node 12: [0,1]
node 13: [1,1]
node 14: [0,1]
The edges are: (0,6) (0,5) (0,12) (0,7) (1,6) (1,11) (1,3) (1,2) (2,8) (2,10) (3,5) (3,11) (3,12) (4,7) (5,14) (6,9) (6,12) (6,10) (7,13) (7,12) (8,13) (9,13) (10,14) (12,13)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [7,13]
node 1: [2,10]
node 2: [7,7]
node 3: [8,9]
node 4: [2,3]
node 5: [1,6]
node 6: [11,14]
node 7: [5,11]
node 8: [1,6]
node 9: [2,7]
node 10: [1,8]
node 11: [3,4]
node 12: [5,15]
node 13: [9,11]
node 14: [3,5]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [0,0]
node 2: [0,0]
node 3: [1,0]
node 4: [1,1]
The edges are: (0,3) (0,1) (0,2) (1,4) (1,3) (2,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [6,1]
node 1: [2,0]
node 2: [2,0]
node 3: [6,1]
node 4: [3,1]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [1,0]
node 3: [1,1]
node 4: [1,1]
node 5: [1,0]
node 6: [1,0]
node 7: [0,1]
node 8: [1,0]
node 9: [0,1]
node 10: [0,1]
The edges are: (0,2) (0,10) (1,3) (1,5) (1,7) (1,8) (2,5) (2,4) (4,10) (4,8) (4,6) (5,9) (6,9) (7,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [5,4]
node 1: [3,3]
node 2: [5,3]
node 3: [3,2]
node 4: [7,8]
node 5: [8,4]
node 6: [5,1]
node 7: [4,4]
node 8: [7,3]
node 9: [2,3]
node 10: [4,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,0]
node 2: [1,1]
node 3: [0,1]
node 4: [1,0]
node 5: [1,1]
node 6: [1,0]
node 7: [0,1]
node 8: [0,1]
The edges are: (0,5) (0,6) (1,5) (1,2) (2,7) (2,3) (2,5) (2,4) (3,8) (5,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [4,4]
node 1: [6,6]
node 2: [9,10]
node 3: [3,4]
node 4: [3,3]
node 5: [9,8]
node 6: [2,1]
node 7: [6,6]
node 8: [1,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,0]
node 2: [1,1]
node 3: [0,1]
node 4: [0,0]
node 5: [0,1]
node 6: [0,0]
node 7: [0,0]
node 8: [1,1]
node 9: [1,1]
The edges are: (0,6) (0,2) (0,5) (1,6) (2,7) (2,8) (3,4) (3,6) (4,8) (5,7) (5,9) (7,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,6]
node 1: [1,2]
node 2: [4,6]
node 3: [2,4]
node 4: [1,1]
node 5: [3,6]
node 6: [1,2]
node 7: [3,5]
node 8: [4,7]
node 9: [1,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [0,1]
node 2: [1,0]
node 3: [1,0]
node 4: [0,0]
node 5: [1,1]
node 6: [0,1]
The edges are: (0,3) (0,2) (0,6) (1,3) (1,2) (2,5) (2,6) (3,4) (3,5) (5,6)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [7,6]
node 1: [4,5]
node 2: [9,3]
node 3: [7,2]
node 4: [2,2]
node 5: [7,6]
node 6: [6,5]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,1]
node 2: [0,0]
node 3: [1,0]
node 4: [1,0]
node 5: [1,0]
node 6: [1,0]
node 7: [1,1]
node 8: [0,0]
node 9: [0,1]
node 10: [1,0]
The edges are: (0,7) (0,3) (1,7) (1,8) (1,9) (1,2) (2,8) (3,7) (3,5) (3,4) (5,10) (5,6) (7,10) (8,9)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [8,4]
node 1: [7,6]
node 2: [2,4]
node 3: [10,3]
node 4: [4,2]
node 5: [7,3]
node 6: [3,0]
node 7: [9,6]
node 8: [3,4]
node 9: [2,4]
node 10: [7,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,0]
node 1: [0,0]
node 2: [0,1]
node 3: [1,0]
node 4: [1,1]
node 5: [1,1]
node 6: [0,1]
node 7: [1,1]
node 8: [1,0]
The edges are: (0,4) (0,7) (0,3) (0,2) (1,8) (2,8) (2,3) (2,6) (5,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [2,2]
node 1: [1,2]
node 2: [4,7]
node 3: [5,4]
node 4: [3,3]
node 5: [1,2]
node 6: [2,1]
node 7: [3,3]
node 8: [4,1]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [0,1]
node 2: [1,1]
node 3: [1,0]
node 4: [1,0]
node 5: [0,1]
node 6: [1,0]
node 7: [0,1]
The edges are: (0,2) (0,4) (1,5) (1,3) (1,6) (1,7) (1,4) (2,7) (3,7) (4,7) (5,6) (5,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [0,5]
node 1: [4,12]
node 2: [5,4]
node 3: [6,5]
node 4: [8,6]
node 5: [6,7]
node 6: [4,4]
node 7: [4,11]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,0]
node 2: [0,1]
node 3: [1,1]
node 4: [1,1]
node 5: [1,1]
node 6: [0,1]
node 7: [1,1]
node 8: [0,0]
node 9: [0,0]
node 10: [0,0]
node 11: [1,1]
node 12: [1,0]
node 13: [1,0]
node 14: [1,0]
The edges are: (0,12) (0,3) (0,14) (0,7) (0,11) (0,1) (1,12) (1,10) (1,7) (1,4) (1,6) (2,10) (2,14) (2,7) (2,8) (3,14) (3,7) (3,5) (4,7) (4,6) (5,9) (5,13) (5,11) (6,8) (7,8) (8,10) (9,13) (9,10) (10,12) (11,13) (11,14) (12,13)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [22,18]
node 1: [19,12]
node 2: [10,12]
node 3: [16,13]
node 4: [10,9]
node 5: [13,8]
node 6: [7,9]
node 7: [19,16]
node 8: [10,7]
node 9: [8,5]
node 10: [12,10]
node 11: [15,11]
node 12: [15,10]
node 13: [12,6]
node 14: [16,9]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,2) (1,3) (2,4) (3,4)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [0,2]
node 1: [0,2]
node 2: [1,3]
node 3: [2,3]
node 4: [0,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,0]
node 2: [1,1]
node 3: [0,1]
node 4: [1,0]
node 5: [0,1]
node 6: [1,1]
node 7: [0,0]
node 8: [1,1]
The edges are: (0,7) (0,8) (1,2) (1,8) (1,4) (2,8) (3,6) (3,7) (3,8) (3,5) (4,6) (5,6) (7,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,6]
node 1: [6,5]
node 2: [5,5]
node 3: [5,10]
node 4: [4,4]
node 5: [3,5]
node 6: [5,6]
node 7: [5,7]
node 8: [9,10]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,1]
node 2: [0,0]
node 3: [1,0]
node 4: [0,1]
node 5: [1,0]
node 6: [1,1]
node 7: [0,1]
The edges are: (0,5) (1,3) (1,5) (1,2) (2,6) (2,5) (3,5) (4,5) (4,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,2]
node 1: [8,5]
node 2: [5,2]
node 3: [5,2]
node 4: [3,3]
node 5: [9,4]
node 6: [3,2]
node 7: [1,1]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,1]
node 2: [1,1]
node 3: [0,1]
node 4: [1,0]
The edges are: (0,3) (1,4) (1,2) (1,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [2,2]
node 1: [4,4]
node 2: [2,2]
node 3: [2,3]
node 4: [2,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,0]
node 1: [1,0]
node 2: [1,0]
node 3: [0,0]
node 4: [1,0]
The edges are: (0,4) (0,2) (1,2) (1,3) (2,4)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,0]
node 1: [3,0]
node 2: [4,0]
node 3: [1,0]
node 4: [4,0]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,1]
node 2: [0,0]
node 3: [0,1]
node 4: [1,1]
node 5: [0,1]
node 6: [1,1]
node 7: [0,0]
node 8: [1,0]
node 9: [0,0]
node 10: [0,0]
node 11: [1,0]
node 12: [1,0]
node 13: [1,0]
node 14: [1,1]
The edges are: (0,7) (0,8) (1,2) (1,10) (1,5) (2,9) (3,6) (3,9) (3,8) (4,7) (5,14) (6,8) (7,10) (7,8) (8,12) (11,14) (13,14)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [6,3]
node 1: [4,4]
node 2: [0,2]
node 3: [4,4]
node 4: [3,1]
node 5: [2,2]
node 6: [5,3]
node 7: [5,3]
node 8: [8,3]
node 9: [3,2]
node 10: [3,2]
node 11: [2,1]
node 12: [3,2]
node 13: [2,1]
node 14: [4,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 6, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [0,1]
node 2: [0,0]
node 3: [1,0]
node 4: [0,1]
node 5: [1,1]
node 6: [0,0]
The edges are: (0,3) (0,1) (0,2) (0,5) (0,6) (1,4) (1,5) (2,3) (2,6) (4,6)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [2,9]
node 1: [2,5]
node 2: [2,5]
node 3: [3,3]
node 4: [1,5]
node 5: [3,5]
node 6: [3,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,0]
node 1: [0,0]
node 2: [1,0]
node 3: [0,0]
node 4: [1,0]
The edges are: (0,3) (0,2) (0,1) (2,3) (2,4)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [2,0]
node 1: [1,0]
node 2: [3,0]
node 3: [2,0]
node 4: [1,0]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,0]
node 2: [0,1]
node 3: [0,1]
node 4: [1,1]
node 5: [0,0]
node 6: [0,0]
node 7: [1,0]
node 8: [1,1]
node 9: [0,0]
node 10: [0,1]
node 11: [0,0]
The edges are: (0,1) (0,3) (0,7) (0,6) (0,10) (0,2) (1,3) (1,11) (1,7) (1,8) (2,4) (4,5) (4,11) (4,10) (6,11) (6,7) (6,9) (8,11) (10,11)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [13,4]
node 1: [10,6]
node 2: [2,5]
node 3: [5,5]
node 4: [8,6]
node 5: [0,2]
node 6: [7,6]
node 7: [7,5]
node 8: [6,5]
node 9: [2,0]
node 10: [5,8]
node 11: [8,5]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,1]
node 2: [1,0]
node 3: [0,1]
node 4: [0,1]
node 5: [1,0]
node 6: [0,1]
node 7: [1,1]
node 8: [1,1]
node 9: [1,0]
node 10: [0,0]
The edges are: (0,2) (0,6) (0,4) (1,2) (2,5) (2,4) (3,10) (3,8) (3,4) (4,9) (4,7) (5,7) (8,9)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [5,7]
node 1: [2,3]
node 2: [7,6]
node 3: [4,5]
node 4: [6,10]
node 5: [3,4]
node 6: [1,2]
node 7: [5,4]
node 8: [2,4]
node 9: [4,4]
node 10: [1,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,1]
node 2: [1,0]
node 3: [1,0]
node 4: [0,1]
node 5: [0,0]
The edges are: (0,2) (0,3) (0,5) (1,2) (1,3) (2,4) (3,5)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,6]
node 1: [2,5]
node 2: [5,0]
node 3: [5,1]
node 4: [1,3]
node 5: [3,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,1]
node 2: [0,0]
node 3: [1,0]
node 4: [1,1]
node 5: [1,1]
node 6: [0,0]
node 7: [1,0]
node 8: [0,1]
node 9: [1,1]
node 10: [1,0]
node 11: [0,1]
node 12: [1,1]
node 13: [1,1]
node 14: [1,0]
The edges are: (0,12) (0,4) (1,14) (1,9) (2,6) (3,10) (3,4) (3,7) (4,5) (4,6) (5,10) (6,14) (6,8) (7,12) (7,14) (7,10) (8,12) (8,14) (8,13) (9,10) (11,14) (11,13) (12,13)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [4,5]
node 1: [4,4]
node 2: [2,2]
node 3: [10,5]
node 4: [9,6]
node 5: [6,4]
node 6: [7,7]
node 7: [11,9]
node 8: [7,11]
node 9: [6,3]
node 10: [11,4]
node 11: [3,6]
node 12: [10,8]
node 13: [7,6]
node 14: [13,7]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [0,1]
node 3: [0,0]
node 4: [0,1]
node 5: [0,1]
node 6: [1,0]
node 7: [0,1]
The edges are: (0,4) (0,5) (0,6) (1,2) (2,3) (2,6) (3,4) (3,5) (3,7) (4,7) (4,6) (5,7) (5,6) (6,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [5,9]
node 1: [1,0]
node 2: [1,10]
node 3: [6,6]
node 4: [3,13]
node 5: [3,13]
node 6: [7,8]
node 7: [5,13]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 7, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [1,1]
node 3: [0,0]
node 4: [1,0]
node 5: [1,0]
node 6: [1,1]
node 7: [1,1]
The edges are: (0,2) (0,1) (0,3) (1,4) (1,7) (1,5) (1,6) (4,7) (4,5) (4,6) (5,6) (6,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [7,5]
node 1: [11,6]
node 2: [1,1]
node 3: [1,1]
node 4: [12,6]
node 5: [11,6]
node 6: [12,7]
node 7: [11,6]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 13, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,1]
node 2: [0,1]
node 3: [0,0]
node 4: [0,0]
node 5: [0,0]
node 6: [1,0]
node 7: [1,0]
node 8: [1,1]
node 9: [1,1]
node 10: [0,1]
node 11: [0,0]
node 12: [0,0]
node 13: [0,0]
The edges are: (0,8) (1,5) (1,4) (2,5) (2,3) (3,12) (3,5) (4,9) (5,8) (5,9) (6,10) (6,7) (7,13) (7,8) (8,13) (9,11)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [2,1]
node 1: [5,6]
node 2: [3,5]
node 3: [3,4]
node 4: [0,0]
node 5: [2,2]
node 6: [3,1]
node 7: [5,3]
node 8: [8,7]
node 9: [6,7]
node 10: [1,1]
node 11: [0,0]
node 12: [0,1]
node 13: [4,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,1]
node 2: [1,0]
node 3: [0,1]
node 4: [1,1]
node 5: [0,0]
node 6: [0,0]
node 7: [1,1]
node 8: [1,0]
node 9: [0,1]
node 10: [1,0]
node 11: [0,0]
The edges are: (0,10) (0,6) (0,1) (1,10) (1,6) (1,11) (2,10) (2,3) (3,10) (3,9) (3,8) (4,11) (5,11) (5,7) (7,11)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [7,3]
node 1: [10,7]
node 2: [6,3]
node 3: [4,5]
node 4: [3,3]
node 5: [3,3]
node 6: [4,1]
node 7: [4,4]
node 8: [3,1]
node 9: [3,1]
node 10: [8,3]
node 11: [3,1]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [0,0]
node 2: [0,0]
node 3: [1,0]
node 4: [1,0]
The edges are: (0,1) (0,3) (1,3) (1,4) (1,2) (3,4)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,2]
node 1: [3,1]
node 2: [2,1]
node 3: [4,1]
node 4: [3,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 5, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [1,0]
node 2: [1,1]
node 3: [0,0]
node 4: [0,1]
node 5: [1,1]
The edges are: (0,2) (0,3) (1,2) (1,5) (1,4) (2,3) (3,5) (4,5)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [5,2]
node 1: [5,2]
node 2: [6,6]
node 3: [4,2]
node 4: [3,4]
node 5: [7,6]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 8, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,0]
node 2: [1,0]
node 3: [0,1]
node 4: [0,0]
node 5: [0,0]
node 6: [0,0]
node 7: [1,0]
node 8: [1,1]
The edges are: (0,8) (0,6) (0,5) (1,7) (1,5) (1,3) (2,8) (4,6) (5,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,4]
node 1: [4,2]
node 2: [1,1]
node 3: [1,1]
node 4: [0,1]
node 5: [3,3]
node 6: [1,1]
node 7: [1,1]
node 8: [4,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [1,1]
node 3: [0,0]
node 4: [0,1]
node 5: [1,1]
node 6: [1,1]
node 7: [0,1]
node 8: [0,0]
node 9: [0,0]
node 10: [1,0]
The edges are: (0,9) (0,3) (0,8) (0,2) (1,6) (2,6) (2,8) (3,10) (3,9) (3,5) (4,10) (4,9) (4,5) (5,10) (6,8) (7,8) (8,9)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [9,10]
node 1: [1,1]
node 2: [5,6]
node 3: [4,6]
node 4: [3,5]
node 5: [6,5]
node 6: [6,7]
node 7: [3,4]
node 8: [5,6]
node 9: [9,8]
node 10: [6,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,0]
node 1: [0,0]
node 2: [1,0]
node 3: [0,0]
node 4: [0,1]
node 5: [0,0]
node 6: [1,0]
node 7: [1,0]
node 8: [0,1]
node 9: [0,0]
node 10: [1,0]
node 11: [0,1]
node 12: [0,1]
node 13: [0,1]
node 14: [0,1]
The edges are: (0,11) (0,6) (0,9) (1,4) (1,12) (1,14) (2,13) (2,8) (3,10) (4,6) (4,12) (4,9) (4,14) (5,7) (5,13) (5,10) (6,14) (8,9) (11,14)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,5]
node 1: [2,5]
node 2: [2,0]
node 3: [0,0]
node 4: [3,10]
node 5: [1,0]
node 6: [3,5]
node 7: [2,1]
node 8: [1,4]
node 9: [3,3]
node 10: [3,1]
node 11: [2,3]
node 12: [1,5]
node 13: [2,3]
node 14: [3,8]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 10, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,1]
node 2: [0,0]
node 3: [0,1]
node 4: [0,1]
node 5: [1,0]
node 6: [1,1]
node 7: [1,0]
node 8: [1,0]
node 9: [1,0]
node 10: [0,0]
The edges are: (0,4) (0,6) (0,9) (1,4) (1,9) (1,8) (2,6) (3,5) (4,9) (5,10) (6,8) (7,9) (9,10)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [8,6]
node 1: [8,7]
node 2: [2,1]
node 3: [0,1]
node 4: [7,6]
node 5: [3,0]
node 6: [5,5]
node 7: [3,3]
node 8: [4,2]
node 9: [10,5]
node 10: [3,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 14, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [1,1]
node 3: [1,0]
node 4: [0,0]
node 5: [1,1]
node 6: [0,0]
node 7: [0,0]
node 8: [1,0]
node 9: [1,1]
node 10: [0,0]
node 11: [1,1]
node 12: [0,0]
node 13: [1,1]
node 14: [1,1]
The edges are: (0,8) (0,10) (0,11) (0,1) (1,9) (1,7) (1,5) (1,13) (2,3) (2,12) (3,10) (4,13) (5,9) (5,14) (5,11) (6,14) (6,8) (6,12) (6,13) (7,9) (7,11) (8,14) (8,10) (10,14) (10,12) (12,14)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [12,10]
node 1: [8,7]
node 2: [3,3]
node 3: [5,2]
node 4: [0,0]
node 5: [9,8]
node 6: [6,5]
node 7: [7,7]
node 8: [11,6]
node 9: [9,9]
node 10: [9,7]
node 11: [7,6]
node 12: [10,5]
node 13: [8,7]
node 14: [14,11]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,0]
node 1: [1,1]
node 2: [1,0]
node 3: [0,0]
node 4: [1,1]
node 5: [0,0]
node 6: [1,1]
node 7: [0,0]
node 8: [0,1]
node 9: [0,0]
node 10: [0,1]
node 11: [0,1]
The edges are: (0,8) (0,10) (0,2) (0,11) (0,6) (1,10) (1,11) (2,5) (2,9) (3,9) (4,7) (4,11) (5,9) (6,7)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,3]
node 1: [3,3]
node 2: [4,4]
node 3: [1,0]
node 4: [4,4]
node 5: [1,0]
node 6: [4,6]
node 7: [0,1]
node 8: [2,4]
node 9: [1,0]
node 10: [2,6]
node 11: [2,7]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 9, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,0]
node 2: [0,1]
node 3: [0,1]
node 4: [1,1]
node 5: [0,1]
node 6: [1,0]
node 7: [1,0]
node 8: [1,1]
node 9: [1,0]
The edges are: (0,6) (0,1) (1,9) (1,4) (2,8) (2,3) (3,8) (3,4) (5,7) (7,9) (7,8)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [4,3]
node 1: [2,1]
node 2: [3,5]
node 3: [2,5]
node 4: [5,5]
node 5: [2,2]
node 6: [1,0]
node 7: [3,2]
node 8: [5,7]
node 9: [5,4]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [1,0]
node 2: [1,1]
node 3: [0,0]
node 4: [0,0]
The edges are: (0,1) (0,3) (2,3) (3,4)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [3,3]
node 1: [1,0]
node 2: [2,2]
node 3: [1,0]
node 4: [2,2]


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [1,1]
node 1: [0,1]
node 2: [0,1]
node 3: [1,1]
node 4: [0,1]
The edges are: (0,1) (1,4) (2,1) (2,4) (4,3)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:
Layer 1:
node 0: sum of embeddings of node 1, [0,1] = [0,1].
node 1: sum of embeddings of node 0, node 2, node 4, [1,1] + [0,1] + [0,1] = [1,3].
node 2: sum of embeddings of node 1, node 4, [0,1] + [0,1] = [0,2].
node 3: sum of embeddings of node 4, [0,1] = [0,1].
node 4: sum of embeddings of node 1, node 2, node 3, [0,1] + [0,1] + [1,1] = [1,3].

After layer 1, the node embeddings are updated to:
node 0: [0,1]
node 1: [1,3]
node 2: [0,2]
node 3: [0,1]
node 4: [1,3]

Layer 2:
node 0: sum of embeddings of node 1, [1,3] = [1,3].
node 1: sum of embeddings of node 0, node 2, node 4, [0,1] + [0,2] + [1,3] = [1,6].
node 2: sum of embeddings of node 1, node 4, [1,3] + [1,3] = [2,6].
node 3: sum of embeddings of node 4, [1,3] = [1,3].
node 4: sum of embeddings of node 1, node 2, node 3, [1,3] + [0,2] + [0,1] = [1,6].

So the answer is:
node 0: [1,3]
node 1: [1,6]
node 2: [2,6]
node 3: [1,3]
node 4: [1,6]

In an undirected graph, the nodes are numbered from 0 to 11, and every node has an embedding. (i,j) means that node i and node j are connected with an undirected edge.
Embeddings:
node 0: [0,1]
node 1: [1,1]
node 2: [1,1]
node 3: [1,0]
node 4: [1,0]
node 5: [0,0]
node 6: [1,0]
node 7: [0,0]
node 8: [1,1]
node 9: [0,0]
node 10: [0,0]
node 11: [0,0]
The edges are: (0,5) (0,10) (0,1) (1,5) (1,10) (1,4) (1,3) (2,6) (3,6) (5,11) (5,7) (6,8) (7,8) (8,10) (8,9)
In a simple graph convolution layer, each node's embedding is updated by the sum of its neighbors' embeddings.
Q: What's the embedding of each node after two layers of simple graph convolution layer?
A:

Answer:
The answer is:
node 0: [5,6]
node 1: [7,8]
node 2: [3,2]
node 3: [5,3]
node 4: [2,1]
node 5: [4,3]
node 6: [4,1]
node 7: [2,2]
node 8: [7,7]
node 9: [1,0]
node 10: [4,2]
node 11: [1,2]