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Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond
Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. Much effort has been put into developing efficient methods for learning on heterophilous graphs. However, there is no universally agreed-upon measure of homophily in the literature. In this work, we show that commonly used homophily measures have critical drawbacks preventing the comparison of homophily levels across different datasets. For this, we formalize desirable properties for a proper homophily measure and verify which measures satisfy which properties. In particular, we show that a measure that we call adjusted homophily satisfies more desirable properties than other popular homophily measures while being rarely used in graph machine learning literature. Then, we go beyond the homophily--heterophily dichotomy and propose a new characteristic allowing one to further distinguish different sorts of heterophily. The proposed label informativeness (LI) characterizes how much information a neighbor's label provides about a node's label. We prove that this measure satisfies important desirable properties and also observe empirically that LI better agrees with GNN performance compared to homophily measures.