Emergent Behaviors over Signed Random Networks in Dynamical Environments

TL;DR

This paper investigates how nodes in a dynamically changing signed network develop behaviors over time, considering positive and negative interactions, and identifies conditions for convergence, divergence, or clustering of their states.

Contribution

It introduces a comprehensive analysis of emergent behaviors in signed random networks with time-varying interactions, including new insights into negative recommendation effects.

Findings

Conditions for almost sure convergence established

Divergence and clustering scenarios characterized

Differences between types of negative recommendations analyzed

Abstract

We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Positive recommendations follow the standard consensus update while two types of negative recommendations, each modeling a different type of antagonistic or malicious interaction, are considered. Nodes may weigh positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to the positive and negative recommendations. Various conditions for almost sure convergence, divergence, and clustering of the node states are established. Some fundamental similarities and differences are established for the two notions of negative recommendations.