Work

Ranking Edges by Their Impact on the Spectral Complexity of Information Diffusion over Networks

Year: 2024

Type: article

Abstract: . Despite the numerous ways now available to quantify which parts or subsystems of a network are most important, there remains a lack of centrality measures that are related to the complexity of information flows and are derived directly from entropy measures. Here, we introduce a ranking of edges based on how each edge’s removal would change a system’s von Neumann entropy (VNE), which is a spectral-entropy measure that has been adapted from quantum information theory to quantify the complexity of information dynamics over networks. We show that a direct calculation of such rankings is computationally inefficient (or unfeasible) for large networks, since the possible removal of [Formula: see text] edges requires that one compute all the eigenvalues of [Formula: see text] distinct matrices. To overcome this limitation, we employ spectral perturbation theory to estimate VNE perturbations and derive an approximate edge-ranking algorithm that is accurate and has a computational complexity that scales as [Formula: see text] for networks with [Formula: see text] nodes. Focusing on a form of VNE that is associated with a transport operator [Formula: see text], where [Formula: see text] is a graph Laplacian matrix and [Formula: see text] is a diffusion timescale parameter, we apply this approach to diverse applications including a network encoding polarized voting patterns of the 117th U.S. Senate, a multimodal transportation system including roads and metro lines in London, and a multiplex brain network encoding correlated human brain activity. Our experiments highlight situations where the edges that are considered to be most important for information diffusion complexity can dramatically change as one considers short, intermediate, and long timescales [Formula: see text] for diffusion.

Source: Multiscale Modeling and Simulation

DOI: 10.1137/22m153135x

Authors: Jeremy Kazimer, Manlio De Domenico, Peter J. Mucha, Dane Taylor