A Fast Method to Calculate Hitting Time Distribution for a Random Walk on Connected Undirected Graph
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With the advent of increasingly larger graphs, we need to find a quick and reliable method to measure the distance between a pair of nodes. There are already algorithms for measuring this distance using the concept of random walk on graphs. However, the implementation of that algorithm is expensive due to the use of Monte Carlo simulations. Here, we propose an alternative measure of the distance between any two nodes that are connected to each other via a path on the graph, a distance which we call the hitting time of random walks on graph. We also give an analytical solution to the hitting time of a random walk on a connected and undirected graph. This analytical solution, which can be conveniently implemented using numerical linear algebra packages, is more time-saving and more accurate than the Monte Carlo simulation results. It is further noted that the hitting times also provide a glimpse of the community structure of a graph.
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