Boolean Gossip Networks
Bo Li, Junfeng Wu, Hongsheng Qi, Alexandre Proutiere, and Guodong Shi

TL;DR
This paper introduces a Boolean gossip model for probabilistic Boolean networks, analyzing convergence, communication classes, and the influence of network structure on dynamics, with implications for understanding complex network behaviors.
Contribution
It provides a comprehensive analysis of Boolean gossip networks, including convergence properties, communication class enumeration, and conditions for absorbing dynamics, linking network topology to Boolean dynamics.
Findings
Node states converge to a binary distribution in large networks.
Number of communication classes depends on network topology.
Most Boolean interaction rules lead to topology-independent absorption, given connectivity.
Abstract
This paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states asymptotically converge to an agreement at a binary random variable, whose distribution is characterized for large-scale networks by mean-field approximation. Using combinatorial analysis, we also successfully count the number of communication classes of the positive Boolean network explicitly in terms of the topology of the underlying interaction graph, where remarkably minor variation in local structures can drastically change the number of network communication classes. With general Boolean interaction rules, emergence of absorbing network Boolean dynamics is shown to be determined by the network structure with necessary and sufficient conditions…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGene Regulatory Network Analysis · Slime Mold and Myxomycetes Research · Cellular Automata and Applications
