Random walk with memory on complex networks
Journal
Physical Review E
Date Issued
2020-10-30
Author(s)
Kocarev, Ljupcho
Abstract
We study random walk on complex networks with transition probabilities which depend on the
current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs of nodes, for a random walk with a memory of one step. We have analyzed one particular model of random walk, where the transition probabilities depend on the number of paths to the second neighbors. The numerical experiments on paradigmatic complex networks verify the validity of the theoretical expressions, and also indicate that the flattening of the stationary occupation probability accompanies a nearly optimal random
search.
current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs of nodes, for a random walk with a memory of one step. We have analyzed one particular model of random walk, where the transition probabilities depend on the number of paths to the second neighbors. The numerical experiments on paradigmatic complex networks verify the validity of the theoretical expressions, and also indicate that the flattening of the stationary occupation probability accompanies a nearly optimal random
search.
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