Graph structure and homophily for label propagation in Graph Neural Networks

Graph Neural Networks work under the assumption of homophily, where similar nodes are more likely to be connected together. We evaluate the relation between graph homophily and various aspects of a graph: node scores derived from the graph structure (notably PageRank and SALSA), node labels, and local neighborhood. These aspects are then used to build label propagation mechanisms, and we evaluate their relative efficiency in the context of node classification for graph data. We find that the local topology of graph datasets has a much greater impact than such score-based propagation mechanisms. We highlight this by proposing two simple mechanisms, label homophily and unanimity, that show interesting properties and a relation with homophily. In particular, we argue that label homophily could be further used in more elaborate Graph Neural Network algorithms.