Node concordance: a local homophily prediction task in graphs - Martinelli, Caio Lorenzetti (2023)
Homophily is a characteristic present in many real-world graphs, this work proposes a task to predict the local manifestation of it, the node concordance. The task is explored in benchmark datasets for node classification, using node labels to create the concordance label, and with two frameworks, one positional and one structured, for a semi-supervised version of the task are pro- posed. In those datasets, the task can be viewed as a subtask of the node classification, we want to predict if two nodes are same-class nodes, not taking into account which classes the nodes belong to. It is shown here that there is a performance advantage in tackling node concordance directly in this case. The frameworks consist of utilizing Graph Neural Networks (GNNs) and Node2Vec to generate node embeddings that are informative of the node concordance. The positional framework is trained in an unsupervised manner, actually targeting link prediction, using the graph topology as its only feature, and is shown to hold predictive power for node concordance although the relation between the link prediction and node concordance predictive powers is not direct, as is shown in this work . The structural embeddings are trained directly for node concordance, using node features and GNNs convolutional mechanisms, and generally perform better than the posi- tional framework, but are more sensitive to the number of labeled edges. It is also shown that the two frameworks can be used in combination, in an ensemble, since they contain complementary information to each other. This task can be an end in itself if one desires exactly to assess the node concordance of the nodes, or can serve as a preprocessing step, to attribute edge weights or rewire and make projections of the graph. The code of this work is made publicly available on https://github.com/caiolmart/node-concordance.