dgl.edge_homophily

dgl.edge_homophily(graph, y)[source]

Homophily measure from Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs

Mathematically it is defined as follows:

\[\frac{| \{ (u,v) : (u,v) \in \mathcal{E} \wedge y_u = y_v \} | } {|\mathcal{E}|},\]

where \(\mathcal{E}\) is the set of edges, and \(y_u\) is the class of node \(u\).

Parameters:

  • graph (DGLGraph) – The graph.

  • y (torch.Tensor) – The node labels, which is a tensor of shape (|V|).

Returns:

The edge homophily ratio value.

Return type:

float

Examples

>>> import dgl
>>> import torch

>>> graph = dgl.graph(([1, 2, 0, 4], [0, 1, 2, 3]))
>>> y = torch.tensor([0, 0, 0, 0, 1])
>>> dgl.edge_homophily(graph, y)
0.75