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Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks.

Kai Bergermann1, Martin Stoll1

  • 1Department of Mathematics, Technische Universität Chemnitz, 09107 Chemnitz, Germany.

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Summary
This summary is machine-generated.

We introduce generalized matrix function-based centrality measures for complex multilayer networks. Our efficient numerical methods enable scalable analysis of large-scale networks, providing meaningful rankings for nodes and layers.

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Graph Theory

Background:

  • Centrality measures are crucial for identifying influential entities in complex networks.
  • Existing methods are limited in analyzing layer-coupled multiplex networks.
  • Matrix function-based centralities offer parameterized insights but face scalability challenges.

Purpose of the Study:

  • To generalize matrix function-based centrality measures to layer-coupled multiplex networks.
  • To develop efficient numerical approximation techniques for large-scale network analysis.
  • To evaluate the effectiveness of the proposed framework on diverse real-world networks.

Main Methods:

  • Utilizing the supra-adjacency matrix for multiplex network representation.
  • Adapting single-layer matrix function-based centrality definitions to the multilayer context.
  • Employing Krylov subspace methods, Gauss quadrature, and stochastic trace estimation for efficient computation.

Main Results:

  • The generalized framework effectively interpolates between degree and eigenvector centrality in multiplex networks.
  • Efficient approximation techniques demonstrate linear computational complexity, enabling scalability to large networks.
  • Meaningful rankings of nodes, layers, and node-layer pairs were achieved across transportation, communication, and collaboration networks.

Conclusions:

  • The proposed matrix function-based centrality framework provides a scalable and effective method for analyzing complex multiplex networks.
  • The numerical techniques ensure computational feasibility for networks with millions of node-layer pairs.
  • This approach enhances the understanding of influence and structure in multilayer systems.