Copy-Spread-Annihilate Dynamics in Degree-Assortative Networks

TL;DR

This paper introduces a minimal broadcasting model to study how degree correlations affect signal lifetime in networks, revealing that assortativity optimally balances amplification and annihilation for signal persistence.

Contribution

It presents the Copy-Spread-Annihilate dynamics, demonstrating non-monotonic effects of assortativity on signal lifetime and applying the framework to brain networks.

Findings

Signal lifetime peaks near neutral assortativity.

Assortativity influences robustness and spreading in networks.

Application to mouse connectome suggests structural control of signal persistence.

Abstract

In many systems, communication proceeds by broadcasting rather than single source-target routing, but network structures that maximize signal lifetime are not well understood. Degree correlations are known to influence robustness and spreading, yet their effect on signal persistence has remained unclear. Here we introduce Copy-Spread-Annihilate dynamics, a minimal synchronous broadcasting model with annihilation. We show that signal lifetimes vary non-monotonically with assortativity and are maximized near neutral assortativity, where hub-driven amplification is strong but annihilation via short cycles is still limited. Applying this framework to the mouse connectome suggests assortativity as a structural control parameter for broadcast signal persistence in brain-like and other complex networks.