Random walks in time-varying networks with memory

TL;DR

This paper investigates how individual memory influences random walk dynamics on time-varying networks, revealing that memory increases degree fluctuation and delays node visitation, with analytical and empirical validation.

Contribution

It introduces a model incorporating individual memory into activity-driven networks and derives analytical solutions for stationary distribution and MFPT, highlighting memory's impact on network dynamics.

Findings

Memory increases degree distribution fluctuations.

Memory delays mean first-passage time.

Results validated on real and artificial networks.

Abstract

Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's memory has been proved to be important to affect network evolution and dynamical processes unfolding on the network. In this manuscript, we study the random-walk process on extended activity driven network model by taking account of individual's memory. We analyze how individual's memory affects random-walk process unfolding on the network when the timescales of the processes of the random walk and the network evolution are comparable. Under the constraints of long-time evolution, we derive analytical solutions for the distribution of stationary state Wa and the mean first-passage time (MFPT) of the random-walk process. We find that, compared with the memoryless activity-driven model, individual's memory enhances the fluctuation of degree distribution, which reduces the capability of gathering walkers for nodes, especially with large activity and delays the mean first-passage time. The results on real networks also support the theoretical analysis with artificial networks.