Centrality Graph Shift Operators for Graph Neural Networks

Yassine ABBAHADDOU, Fragkiskos D. Malliaros, Johannes F. Lutzeyer, Michalis Vazirgiannis

Keywords: Graph Neural Networks, Graph Shift Operators, Centrality

TL;DR: We propose and study Centrality Graph Shift Operators (CGSOs), which normalize adjacency matrices by global centrality metrics. We furthermore outline how CGSOs can act as message passing operators in any Graph Neural Network.

Abstract: Graph Shift Operators (GSOs), such as the adjacency and graph Laplacian matrices, play a fundamental role in graph theory and graph representation learning. Traditional GSOs are typically constructed by normalizing the adjacency matrix by the degree matrix, a local centrality metric. In this work, we instead propose and study Centrality GSOs (CGSOs), which normalize adjacency matrices by global centrality metrics such as the PageRank, $k$-core or count of fixed length paths. We study spectral properties of the CGSOs, allowing us to get an understanding of their action on graph signals. We confirm this understanding by defining and running the spectral clustering algorithm based on different CGSOs on several synthetic and real-world datasets. We furthermore outline how our CGSO can act as the message passing operator in any Graph Neural Network and in particular demonstrate strong performance of a variant of the Graph Convolutional Network and Graph Attention Network using our CGSOs on several real-world benchmark datasets.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 10202