Eigenvector centrality for multilayer networks with dependent node importance

Area of Science:

• Network Science
• Graph Theory
• Computational Social Science

Background:

• Eigenvector centrality is a key metric for identifying influential nodes in networks.
• Multilayer networks, composed of interconnected layers, require specialized centrality measures.
• Existing methods for multilayer eigenvector centrality have limitations in handling inter-layer constraints.

Purpose of the Study:

• To introduce a novel approach for computing eigenvector centrality in multilayer networks.
• To address inter-layer constraints on node importance.
• To provide an efficient computational method for these complex networks.

Main Methods:

• Defined a multilayer network model with distinct layers and inter-layer constraints on node importance.
• Formulated layer-specific eigenvector centrality using independent and dependent pseudo-eigenvalue problems.
• Developed an interleaved power iteration algorithm for efficient computation.

Main Results:

• The proposed method effectively computes constrained, layer-specific eigenvector centrality values.
• The interleaved power iteration algorithm provides an efficient solution.
• An R package is available for practical implementation.

Conclusions:

• This novel approach extends eigenvector centrality to multilayer networks with inter-layer constraints.
• The computational method is efficient and practical for complex network analysis.
• The R package facilitates the application of this method in research.