2018/09/30 by Mikołaj Morzy, Tomasz Kajdanowicz
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Betweenness centrality #Bioinformatics and Genomic Networks #Butterfly graph #Centrality #Combinatorics #Complex Network Analysis Techniques #Computation #Computer science #Graph #Graph energy #Graph property #Graph theory and applications #Laplacian matrix #Line graph #Mathematics #Matrix representation #Null graph #Physics #Quantum mechanics #Theoretical computer science #Vertex (graph theory) #Voltage graph #cs.SI #physics.soc-ph
paper · pdf · doi:10.3390/e20120916
published as Entropy 2018, 20(12), 916
arxiv created 2018/11/12 · openalex publication_date 2018/11/30 · arxiv updated 2019/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.