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

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.