Threshold-based network structural dynamics

The interest in dynamic processes on networks is steadily rising recent years. In this paper, we consider the (α,β)-Threshold Network Dynamics ((α,β)-Dynamics), where α≤β, which only structural dynamics (edge of network) are allowed, guided by local threshold rules executed each node. particular, discrete round t, active pair nodes u and v, computes a value E(u,v) (the potential pair) as function structure network at t around two nodes. If E(u,v)<α then link (if it exists) between v removed; if α≤E(u,v)<β an existing among maintained; β≤E(u,v) established not already present. New cannot be inserted result protocol, removed. microscopic (α,β)-Dynamics appears to simple, so that able rigorously argue about it, but still flexible, design meaningful give rise interesting macroscopic behaviors. Our goals following: a) investigate properties b) show expressive enough solve complex problems networks. contribution these directions twofold. We exhibit claim expressiveness (α,β)-Dynamics, both designing simple protocol provably k-core well showing fact Turing-Complete. Second most important, construct general tools for proving stabilization work subclass prove speed convergence restricted setting.