Reactive random walkers on complex networks

TL;DR

This paper presents a versatile metapopulation model of reactive random walkers on complex networks, deriving analytical equilibrium occupation probabilities that depend on local reactions and network topology, enabling new network analysis tools.

Contribution

It introduces a general analytical framework for reactive random walkers that incorporates local reactions and network structure, advancing network analysis methods.

Findings

Occupation probability depends on local reaction functions and neighbor degrees.

Reactive walkers can detect network symmetries and degree correlations.

Model enables new measures of node centrality and network classification.

Abstract

We introduce and study a metapopulation model of random walkers interacting at the nodes of a complex network. The model integrates random relocation moves over the links of the network with local interactions depending on the node occupation probabilities. The model is highly versatile, as the motion of the walkers can be fed on topological properties of the nodes, such as their degree, while any general nonlinear function of the occupation probability of a node can be considered as local reaction term. In addition to this, the relative strength of reaction and relocation can be tuned at will, depending on the specific application being examined. We derive an analytical expression for the occupation probability of the walkers at equilibrium in the most general case. We show that it depends on different order derivatives of the local reaction functions and not only on the degree of a node, but also on the average degree of its neighbours at various distances. For such a reason, reactive random walkers are very sensitive to the structure of a network and are a powerful way to detect network properties such as symmetries or degree-degree correlations. As possible applications, we first discuss how the occupation probability of reactive random walkers can be used to define novel measures of functional centrality for the nodes of a network. We then illustrate how network components with the same symmetries can be revealed by tracking the evolution of reactive walkers. Finally, we show that the dynamics of our model is influenced by the presence of degree-degree correlations, so that assortative and disassortative networks can be classified by quantitative indicators based on reactive walkers.