Towards influence centrality: where to not add an edge in the network?

TL;DR

This paper analyzes how adding or removing edges in a network affects the influence of stubborn agents on group opinions, using the Friedkin-Johnsen model and signal flow graphs to identify impactful modifications.

Contribution

It introduces a method to determine which network edges to modify to increase an influencer's control over opinions, revealing conditions for influence change and redundancy.

Findings

Edge modifications can increase an influencer's control

Some edge changes have no effect on influence centrality

Provided conditions for effective network modifications

Abstract

In this work, we consider a strongly connected group of individuals involved in decision-making. The opinions of the individuals evolve using the Friedkin-Johnsen (FJ) model. We consider that there are two competing `influencers' (stubborn agents) vying for control over the final opinion of the group. We investigate the impact of modifying the network interactions on their respective control over the final opinions (influence centrality). We use signal flow graphs (SFG) to relate the network interactions with the influence that each `influencer' exerts on others. We present the sufficient conditions on the edge modifications which lead to the increase of the influence of an `influencer' at the expense of the other. Interestingly, the analysis also reveals the existence of redundant edge modifications that result in no change in the influence centrality of the network. We present several numerical examples to illustrate these results.