How zealots affect the energy cost for controlling complex social networks

TL;DR

This paper investigates how stubborn agents, called zealots, influence the energy required to control complex social networks, revealing that their impact depends on various network parameters and behaviors.

Contribution

It introduces the effect of zealots on control energy in social networks and analyzes how their beliefs and configurations alter control costs under different dynamics.

Findings

Zealots alter control energy at a quadratic rate based on their beliefs.

The impact of zealots depends on network parameters and dynamics.

Contrarian zealots can reduce control energy in non-conformist networks.

Abstract

The controllability of complex networks may be applicable for understanding how to control a complex social network, where members share their opinions and influence one another. Previous works in this area have focused on controllability, energy cost, or optimization under the assumption that all nodes are compliant, passing on information neutrally without any preferences. However, the assumption on nodal neutrality should be reassessed, given that in networked social systems, some people may hold fast to their personal beliefs. By introducing some stubborn agents, or zealots, who hold steadfast to their beliefs and seek to influence others, the control energy is computed and compared against those without zealots. It was found that the presence of zealots alters the energy cost at a quadratic rate with respect to their own fixed beliefs. However, whether or not the zealots' presence increases or decreases the energy cost is affected by the interplay between different parameters such as the zealots' beliefs, number of drivers, final control time regimes, network effects, network dynamics, and number and configurations of neutral nodes influenced by the zealots. For example, when a network dynamics is linear but does not have conformity behavior, it could be possible for a contrarian zealot to assist in reducing control energy. With conformity behavior, a contrarian zealot always negatively affects network control by increasing energy cost. The results of this paper suggest caution when modeling real networked social systems with the controllability of networked linear dynamics since the system dynamical behavior is sensitive to parameter change.