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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Random walks are crucial for network analysis (e.g., PageRank, information retrieval).
  • Individual memory significantly influences network evolution and dynamical processes.
  • Existing models often overlook memory effects in network dynamics.

Purpose of the Study:

  • To investigate the impact of individual memory on random walk processes.
  • To analyze random walks on an extended activity-driven network model incorporating memory.
  • To understand how memory affects walker distribution and movement when network evolution and random walk timescales are comparable.

Main Methods:

  • Developed an extended activity-driven network model with individual memory.
  • Derived analytical solutions for stationary walker distribution and mean first-passage time.
  • Validated theoretical findings with numerical simulations on artificial and real-world networks.

Main Results:

  • Individual memory increases activity fluctuations and forms small, highly active clusters.
  • Memory reduces the capacity of nodes to attract walkers, particularly high-activity nodes.
  • Mean first-passage time is delayed due to the presence of memory.

Conclusions:

  • Individual memory fundamentally changes random walk behavior in activity-driven networks.
  • The findings offer insights into network dynamics influenced by agent memory.
  • The study highlights the importance of considering memory in network models for accurate predictions.