Graph regularization centrality

This paper introduces a novel centrality for the nodes of a graph. Our centrality is based on the graph regularization, a tool of graph signal processing theory. For this reason, it is called graph regularization centrality (GRC). In order to define the centrality of a node, a delta signal centered on this node is defined and a new smooth signal is generated by the graph regularization of the delta signal. The transformation of the delta signal into the new smooth signal strongly depends on the position of the node in the graph. Our centrality takes advantage of this feature to define a centrality for each node of the graph. Synthetic and real-world graphs are used to demonstrate the effectiveness of our centrality that combines local and global positioning of nodes in one measure. Furthermore, it is compared against classical centralities and graph Fourier transform centrality, which is also based on graph signal processing theory. We conclude with a discussion of the main features of GRC and a proposal for potential future work.(c) 2023 Elsevier B.V. All rights reserved.