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Entropy 2018, 20(12), 916; https://doi.org/10.3390/e20120916

Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures

1
Institute of Computer Science, Poznań University of Technology, 60-965 Poznań, Poland
2
Center for Artificial Intelligence and Machine Learning CAMIL, Poznan University of Technology, 60-965 Poznań, Poland
3
Department of Computational Intelligence, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
*
Author to whom correspondence should be addressed.
Received: 5 September 2018 / Revised: 8 November 2018 / Accepted: 27 November 2018 / Published: 30 November 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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Abstract

Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randić energy, Laplacian energy, distance energy, and many others. Although theoretical properties of various graph energies have been investigated in the past in the areas of mathematics, chemistry, physics, or graph theory, these explorations have been limited to relatively small graphs representing chemical compounds or theoretical graph classes with strictly defined properties. In this paper we investigate the usefulness of the concept of graph energy in the context of large, complex networks. We show that when graph energies are applied to local egocentric networks, the values of these energies correlate strongly with vertex centrality measures. In particular, for some generative network models graph energies tend to correlate strongly with the betweenness and the eigencentrality of vertices. As the exact computation of these centrality measures is expensive and requires global processing of a network, our research opens the possibility of devising efficient algorithms for the estimation of these centrality measures based only on local information. View Full-Text
Keywords: graph energy; Randić energy; Laplacian energy; egocentric network; vertex centrality measures graph energy; Randić energy; Laplacian energy; egocentric network; vertex centrality measures
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Morzy, M.; Kajdanowicz, T. Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures. Entropy 2018, 20, 916.

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