Node Homophiliy

[qubit0]

I made a simple (in fact I modified a graph from PyG's example):

edge_index = torch.tensor([[0, 1, 2, 3, 4,5],
                           [1, 2, 0, 4, 5,0]])
y = torch.tensor([0, 0, 0, 0, 1,1])

print(homophily(edge_index, y, method='node'))  # 0.58
print(homophily(edge_index, y, method='edge'))  # 0.66

I tried to write my own function:

#Edge homophily 
def fraction_same_label_edges(G):
    same_label_edges = 0
    total_edges = 0

    for u, v in G.edges:
        total_edges += 1
        if G.nodes[u]['label'] == G.nodes[v]['label']:
            same_label_edges += 1

    if total_edges == 0:
        return 0
    else:
        return same_label_edges / total_edges

Created a networkx graph:

# Create an empty networkx graph
G1 = nx.Graph()

# Add nodes to the graph with their corresponding labels
for i in range(len(y)):
    G1.add_node(i, label=y[i])

# Add edges to the graph using the edge index
for j in range(edge_index.shape[1]):
    u, v = edge_index[0, j].item(), edge_index[1, j].item()
    G1.add_edge(u, v)

Homophily:
fraction_same_label_edges(G1) # 0.66

This is equivalent to edge homophily given by PyG 's function.

However, for node homophily, I get something different:

#Node homophily
def count_same_label_neighbors(G, i):
    same_label_neighbors = 0

    for neighbor in G.neighbors(i):
        if G.nodes[neighbor]['label'] == G.nodes[i]['label']:
            same_label_neighbors += 1
            
    return same_label_neighbors

sum = 0
for i in G1.nodes:
    if len(list(G1.neighbors(i))) != 0:
        sum = sum + count_same_label_neighbors(G1, i)/len(list(G1.neighbors(i)))

print(sum/G1.number_of_nodes())   #0.611

If I follow the formula and do this my hand then I also get 0.611

Where am I going wrong here?

[rusty1s]

Sorry for taking so long to answer. I just ran this by myself. I think the issue is that edge_index is given as a directed graph, while you are creating an undirected nx.Graph. Running edge_index = to_undirected(edge_index) fixes this.