  In many important graph data processing applications the acquired information
includes both node features and observations of the graph topology. Graph
neural networks (GNNs) are designed to exploit both sources of evidence but
they do not optimally trade-off their utility and integrate them in a manner
that is also universal. Here, universality refers to independence on homophily
or heterophily graph assumptions. We address these issues by introducing a new
Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR
weights so as to jointly optimize node feature and topological information
extraction, regardless of the extent to which the node labels are homophilic or
heterophilic. Learned GPR weights automatically adjust to the node label
pattern, irrelevant on the type of initialization, and thereby guarantee
excellent learning performance for label patterns that are usually hard to
handle. Furthermore, they allow one to avoid feature over-smoothing, a process
which renders feature information nondiscriminative, without requiring the
network to be shallow. Our accompanying theoretical analysis of the GPR-GNN
method is facilitated by novel synthetic benchmark datasets generated by the
so-called contextual stochastic block model. We also compare the performance of
our GNN architecture with that of several state-of-the-art GNNs on the problem
of node-classification, using well-known benchmark homophilic and heterophilic
datasets. The results demonstrate that GPR-GNN offers significant performance
improvement compared to existing techniques on both synthetic and benchmark
data.
