dgl.edge_homophily

dgl.edge_homophily(graph, y)

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