Accelerating consensus on co-evolving networks: the effect of committed individuals

TL;DR

This study examines how homophily-driven network evolution impedes consensus formation and demonstrates that committed individuals can significantly accelerate consensus, with effects depending on interaction rules.

Contribution

It introduces a simulation-based analysis of opinion dynamics on evolving networks, highlighting the role of committed agents in speeding up consensus.

Findings

Homophilic rewiring delays consensus exponentially with network size.

Committed individuals reduce consensus time to logarithmic growth beyond a critical fraction.

Interaction rule variations affect the scaling of consensus time, but the benefit of committed agents remains consistent.

Abstract

Social networks are not static but rather constantly evolve in time. One of the elements thought to drive the evolution of social network structure is homophily - the need for individuals to connect with others who are similar to them. In this paper, we study how the spread of a new opinion, idea, or behavior on such a homophily-driven social network is affected by the changing network structure. In particular, using simulations, we study a variant of the Axelrod model on a network with a homophilic rewiring rule imposed. First, we find that the presence of homophilic rewiring within the network, in general, impedes the reaching of consensus in opinion, as the time to reach consensus diverges exponentially with network size $N$. We then investigate whether the introduction of committed individuals who are rigid in their opinion on a particular issue, can speed up the convergence to consensus on that issue. We demonstrate that as committed agents are added, beyond a critical value of the committed fraction, the consensus time growth becomes logarithmic in network size $N$. Furthermore, we show that slight changes in the interaction rule can produce strikingly different results in the scaling behavior of $T_c$. However, the benefit gained by introducing committed agents is qualitatively preserved across all the interaction rules we consider.