Reactive random walkers on complex networks

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.

References in corpus (38)

• Assortative mixing in networks
• Maps of random walks on complex networks reveal community structure
• The structure of scientific collaboration networks
• Mixing patterns in networks
• Self-similar community structure in organisations
• Dynamical and correlation properties of the Internet
• Community Structure in Jazz
• Random walks and diffusion on networks
• Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems
• Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
• Turing patterns in network-organized activator-inhibitor systems
• Turing patterns on networks
• Remote synchronization reveals network symmetries and functional modules
• Entropy Rate of Diffusion Processes on Complex Networks
• Localization of maximal entropy random walk
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Network dynamics of innovation processes
• A measure of individual role in collective dynamics
• Exploring complex networks by walking on them
• Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
• Maximal-entropy random walks in complex networks with limited information
• Effective Distances for Epidemics Spreading on Complex Networks
• Multiscale mixing patterns in networks
• Characteristic times of biased random walks on complex networks
• Generalized Master Equations for Non-Poisson Dynamics on Networks
• Mean-field diffusive dynamics on weighted networks
• Incoherence-Mediated Remote Synchronization
• Efficient exploration of multiplex networks
• Centrality measures and thermodynamic formalism for complex networks
• Uncovering the community structure associated with the diffusion dynamics of networks
• Topologically biased random walk with application for community finding in networks
• Diffusion geometry unravels the emergence of functional clusters in collective phenomena
• Mean first-passage time for maximal-entropy random walks in complex networks
• Pattern Formation on Networks with Reactions: A Continuous Time Random Walk Approach
• Hopping in the crowd to unveil network topology
• Motion-induced synchronization in metapopulations of mobile agents
• Impact of network structure on a model of diffusion and competitive interaction
• Random Walks on Complex Networks

Cited by in corpus (9)

• Random walks on hypergraphs
• Diffusive behavior of multiplex networks
• Extreme events in stochastic transport on networks
• Reactive explorers to unravel network topology
• Chaos in Nonlinear Random Walks with Non-Monotonic Transition Probabilities
• Amplitude death and restoration in networks of oscillators with random-walk diffusion
• On the dual nature of adoption processes in complex networks
• Effects of topological structure and destination selection strategies on agent dynamics in complex networks
• Smart Walkers in Discrete Space