2016/09/28 by Shreyas Sundaram, Sundaram, Shreyas
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Physical sciences #Opinion Dynamics and Social Influence #Opportunistic and Delay-Tolerant Networks #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #cs.DM #cs.SI #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.1609.08768
Preprint of paper to appear at the 55th IEEE Conference on Decision and Control, 2016
arxiv created 2016/09/28 · openalex publication_date 2016/09/28 · arxiv updated 2016/09/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We consider a class of opinion dynamics on networks where at each time-step, each node in the network disregards the opinions of a certain number of its most extreme neighbors and updates its own opinion as a weighted average of the remaining opinions. When all nodes disregard the same number of extreme neighbors, previous work has shown that consensus will be reached if and only if the network satisfies certain topological properties. In this paper, we consider the implications of allowing each node to have a personal threshold for the number of extreme neighbors to ignore. We provide graph conditions under which consensus is guaranteed for such dynamics. We then study random networks where each node's threshold is drawn from a certain distribution, and provide conditions on that distribution, together with conditions on the edge formation probability, that guarantee that consensus will be reached asymptotically almost surely.