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arXiv · 0910.3545

Random walks on networks: cumulative distribution of cover time

Nikola Zlatanov·Ljupco Kocarev
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Abstract

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of O(2n), is also presented. The approximation is numerically tested only for graphs with n<=1000 nodes.

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Nikola Zlatanov, Ljupco Kocarev. 2009-10-19. Random walks on networks: cumulative distribution of cover time. https://doi.org/10.1103/physreve.80.041102

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