Information transfer pathways: signal propagation in complex global topologies

Abstract

In the real world, many dynamic behaviors can be explained by the propagation of perturbations, such as the transfer of chemical signals and the spread of infectious diseases. Previous researchers have achieved excellent results in approximating the global propagation time, revealing the mechanism of signal propagation through multiple paths. However, the known frameworks rely on the extension of physical concepts rather than mathematically rigorous derivations. As a result, they may not perfectly predict time or explain the underlying physical significance in certain specific cases. In this paper, we propose a novel method for decomposing network topology, focusing on two modules: the tree-like module and the path-module. Subsequently, we introduce a new framework for signal propagation analysis, which can be applied to estimate the propagation time for two fundamental global topology modules and provide a rigorous proof for the propagation time in global topology. Compared to previous work, our results are not only more concise, clearly defined, efficient, but also are more powerful in predicting propagation time which outperforms some known results in some cases, for example, biochemical dynamics. Additionally, the proposed framework is based on information transfer pathways, which can be also applied to other physical fields, such as network stability, network controlling and network resilience.