Classical and quantum random-walk centrality measures in multilayer networks

• URL: http://arxiv.org/abs/2012.07157v2
• Date: Sun, 25 Apr 2021 06:28:18 GMT
• Title: Classical and quantum random-walk centrality measures in multilayer networks
• Authors: Lucas B\"ottcher and Mason A. Porter
• Abstract summary: Classifying the importance of nodes and node-layers is an important aspect of the study of multilayer networks. It is common to calculate various centrality measures, which allow one to rank nodes and node-layers according to a variety of structural features. We apply our framework to a variety of synthetic and real-world multilayer networks, and we identify marked differences between classical and quantum centrality measures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multilayer network analysis is a useful approach for studying the structural properties of entities with diverse, multitudinous relations. Classifying the importance of nodes and node-layer tuples is an important aspect of the study of multilayer networks. To do this, it is common to calculate various centrality measures, which allow one to rank nodes and node-layers according to a variety of structural features. In this paper, we formulate occupation, PageRank, betweenness, and closeness centralities in terms of node-occupation properties of different types of continuous-time classical and quantum random walks on multilayer networks. We apply our framework to a variety of synthetic and real-world multilayer networks, and we identify marked differences between classical and quantum centrality measures. Our computations also give insights into the correlations between certain random-walk-based and geodesic-path-based centralities.

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