Topological transition in a coupled dynamic in random networks

TL;DR

This paper investigates the topological transition in coupled node and link dynamics on random networks, revealing phase-dependent changes in network structure and modularity, and extends previous models using random geometric graphs.

Contribution

It introduces the analysis of topological transitions in associated networks using RGGs and demonstrates modularity as an effective order parameter for phase identification.

Findings

Topological transition observed in associated networks between absorbing and active phases.

Modularity effectively indicates phase changes, matching original order parameters.

Associated networks show maximum modularity in the absorbing phase and minimum in the active phase.

Abstract

In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better understand the two observed phases, so we use another network structure (the so called random geometric graph - RGG) together with other metrics borrowed from network science. We observed a topological transition on the two associated networks, which are subgraphs of the full network. As the links have two possible states (friendly and non-friendly), we defined each associated network as composed of only one type of link. The (non) friendly associated network has (non) friendly links only. This topological transition was observed from the domain distribution of each associated network between the two phases of the system (absorbing and active). We also showed that another metric from network science called modularity (or assortative coefficient) can also be used as order parameter, giving the same phase diagram as the original order parameter from the seminal work. On the absorbing phase the absolute value of the modularity for each associated network reaches a maximum value, while on the active phase they fall to the minimum value.