Mean first-passage time for random walks on the T-graph

Abstract

For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks using the famous T-graph, linking this important quantity to the resistance distance in electronic networks. We obtain an exact formula for the MFPT that is confirmed by extensive numerical calculations. This interesting quantity is derived through the recurrence relations resulting from the self-similar structure of the T-graph. The obtained closed-form expression shows that the MFPT increases approximately as a power-law function of the number of nodes, with the exponent lying between 1 and 2. Our research may further a deeper understanding of random walks on the T-graph. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.