Affinity-based Homophily: Can we measure homophily of a graph without using node labels?

Indranil Ojha, Kushal Bose, Swagatam Das

Keywords: Graphs, Convolutio, Homophily, Heterophily, Affinity

TL;DR: The paper deals with desiging a technique to measure homophily ratio of the graphs without having knowledge of node labels

Abstract: The homophily (heterophily) ratio in a graph represents the proportion of edges connecting nodes with similar (dissimilar) class labels. Existing methods for estimating the homophily ratio typically rely on knowing the class labels of each node in the graph. While several algorithms address both homophilic and heterophilic graphs, they necessitate prior knowledge of the homophily ratio to choose the appropriate one. To address this limitation, we propose a novel metric for measuring homophily ratio without information about node labels. In our approach, we define learnable affinity vectors for each node, characterizing the expected feature relationships with its neighbors. Our method, Affinity-based Homophily, derives the homophily ratio using these affinity vectors, eliminating the need for prior node label information. We conducted experiments on various benchmark homophilic and heterophilic graphs, demonstrating the commendable performance of our homophily measure.

Submission Number: 150