  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.

Physics and Society