Steady state and mean recurrence time for random walks on stochastic temporal networks

Abstract

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of random walks on temporal networks. Here we theoretically study two types of event-driven random walks on a stochastic temporal network model that produces arbitrary distributions of interevent-times. In the so-called active random walk, the interevent-time is reinitialized on all links upon each movement of the walker. In the so-called passive random walk, the interevent-time is only reinitialized on the link that has been used last time, and it is a type of correlated random walk. We find that the steady state is always the uniform density for the passive random walk. In contrast, for the active random walk, it increases or decreases with the node's degree depending on the distribution of interevent-times. The mean recurrence time of a node is inversely proportional to the degree for both active and passive random walks. Furthermore, the mean recurrence time does or does not depend on the distribution of interevent-times for the active and passive random walks, respectively.

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References in corpus (16)

• Emergence of scaling in random networks
• Maps of random walks on complex networks reveal community structure
• Temporal Networks
• The origin of bursts and heavy tails in human dynamics
• Search in Power-Law Networks
• Modeling bursts and heavy tails in human dynamics
• Optimal network topologies for local search with congestion
• Memory in network flows and its effects on spreading dynamics and community detection
• Causality-Driven Slow-Down and Speed-Up of Diffusion in Non-Markovian Temporal Networks
• Random walks and search in time-varying networks
• Temporal networks: slowing down diffusion by long lasting interactions
• Quantifying the effect of temporal resolution on time-varying networks
• Temporal Heterogeneities Increase the Prevalence of Epidemics on Evolving Networks
• Generalized Master Equations for Non-Poisson Dynamics on Networks
• Burstiness and spreading on temporal networks
• Random walk centrality for temporal networks

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