Random Walk on a Graph with Vicinity Avoidance

Abstract

Random walk on a graph is a mathematical mobility model that extends random walk to a graph. In recent years, studies have investigated various aspects of a random walk on a graph, such as analyses of the mathematical properties of a discrete random walk on a graph and their applications to large-scale network exploration. A random walk on a graph has strong locality; therefore, a mobile agent is likely to visit the same node multiple times in a short period. If the locality of the random walk on a graph can be mitigated, the properties of the random walk (e.g., average first passage time and average cover time) can be improved. Toward this end, the present study proposes Vicinity-Avoiding Random Walk (VA-RW), a mobility model based on a random walk with less locality without requiring a large amount of memory in the mobile agent. In addition, we investigate the extent to which VA-RW reduces the average first passage time and average cover time, both of which are typical measures of a random walk, compared with those of a simple random walk and the non-backtracking random walk through simulations. We also analytically investigate the effectiveness of VA-RW in terms of the average first passage time in a graph with a community structure.