Enforcing Katz and PageRank Centrality Measures in Complex Networks

TL;DR

This paper presents an optimization-based method to minimally modify network edge weights to enforce specific Katz and PageRank centrality measures while preserving the original network structure.

Contribution

It introduces a scalable optimization approach for adjusting network weights to achieve desired centrality scores, balancing structural integrity and targeted centrality enforcement.

Findings

Effective algorithms for minimal weight perturbations

Ability to control centrality measures in complex networks

Scalable solutions for large network modifications

Abstract

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.