Abstract

In this paper we present a self-avoiding walk-jump (SAWJ) algorithm for finding a maximum degree node on a large assortative graph. We offer two contributions: i) we use the theory of absorbing Markov chains to effectively approximate the required search time as a function of the number of nodes, the edge density, and the assortativity, and ii) we measure the performance of our algorithm against competing algorithms (including star sampling) from the literature on the class of assortative Erdos-Renyi (AER) random graphs, and on six real-world large graphs from the Stanford SNAP dataset. In most cases SAWJ significantly outperforms the competing algorithms.

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