Emergent Behaviors over Signed Random Networks in Dynamical Environments

Guodong Shi (1) , Alexandre Proutière (1, 2) , Mikael Johansson (1) , John. S. Baras (3) , Karl H. Johansson (1)

1 KTH - KTH Royal Institute of Technology [Stockholm]
2 DYOGENE - Dynamics of Geometric Networks
3 ECE - University of Maryland - Department of Electrical and Computer Engineering [Univ. of Maryland]

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.

Mots clés: Random graphs; Signed networks; Consensus dynamics; Belief clustering

Domaines: Réseaux sociaux et d'information [cs.SI]; Physique et Société [physics.soc-ph]

Guodong Shi, Alexandre Proutière, Mikael Johansson, John. S. Baras, Karl H. Johansson. Emergent Behaviors over Signed Random Networks in Dynamical Environments. 2013. ⟨hal-00920073⟩