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Enforcing Katz and PageRank Centrality Measures in Complex Networks

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arxiv 2409.02524 v2 pith:432UA57R submitted 2024-09-04 physics.soc-ph cs.NAmath.NA

Stefano Cipolla , Fabio Durastante , Beatrice Meini This is my paper · ORCID
classification physics.soc-phcs.NAmath.NA
keywords centralitynetworkcomplexedgesenforcingkatznetworksnodes
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We investigate the problem of enforcing a desired centrality measure in complex networks, while still keeping the original pattern of the network. Specifically, by representing the network as a graph with suitable nodes and weighted edges, we focus on computing the smallest perturbation on the weights required to obtain a prescribed PageRank or Katz centrality index for the nodes. Our approach relies on optimization procedures that scale with the number of modified edges, enabling the exploration of different scenarios and altering network structure and dynamics.

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  1. Changing the ranking in eigenvector centrality of a weighted graph by small perturbations

    math.NA 2025-01 conditional novelty 6.0 of 10

    A two-level gradient-flow algorithm computes the minimal Frobenius-norm perturbation that makes the top m eigenvector-centrality entries coalesce.

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