Early fragmentation in the adaptive voter model on directed networks

TL;DR

This paper investigates how directed adaptive networks influence voter dynamics, revealing a phase transition between active and fragmented states, with low out-degree nodes promoting early fragmentation through self-stabilizing structures.

Contribution

It introduces the concept of early fragmentation in directed networks and highlights the role of low out-degree nodes in destabilizing consensus.

Findings

Fragmentation occurs earlier with many low out-degree nodes.

Dense networks exhibit similar transition behavior to undirected cases.

Self-stabilizing structures nucleate fragmentation below critical points.

Abstract

We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process may be relevant for fragmentation in current political opinion formation processes.