Controlling centrality in complex networks

TL;DR

This paper investigates how small groups of nodes in a network can manipulate spectral centrality scores by adjusting their outgoing links, revealing potential vulnerabilities in network influence measures.

Contribution

It introduces the concept of controlling sets that can assign any centrality values, showing that many real-world networks have small controlling sets, thus highlighting manipulation risks.

Findings

Small controlling sets can influence entire network centralities

Many real-world networks have controlling sets less than 10% of nodes

Spectral centrality measures are susceptible to manipulation

Abstract

Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network crucially depends on the entire pattern of connections, so that the usual approach is to compute the node centralities once the network structure is assigned. We face here with the inverse problem, that is, we study how to modify the centrality scores of the nodes by acting on the structure of a given network. We prove that there exist particular subsets of nodes, called controlling sets, which can assign any prescribed set of centrality values to all the nodes of a graph, by cooperatively tuning the weights of their out-going links. We show that many large networks from the real world have surprisingly small controlling sets, containing even less than 5-10% of the nodes. These results suggest that rankings obtained from spectral centrality measures have to be considered with extreme care, since they can be easily controlled and even manipulated by a small group of nodes acting in a coordinated way.