Abstract
Measuring graph similarities is an important topic with numerous applications. Early algorithms often incur quadratic time or higher, making it unpractical to use for graphs of very large scales. We present in this paper the first-known linear-time algorithm for solving this problem. Our algorithm, called Random Walker Termination (RWT), is based on random walkers and time series. Three major graph models, that is, the Erdős-Renyi random graphs, the Watts-Strogatz small world graphs, and the Barabasi-Albert preferential attachment graphs are used to generate graphs of different sizes. We show that the RWT algorithm performs well for all three graph models. Our experiment results agree with the actual similarities of generated graphs. Built on stochastic process, RWT is sufficiently stable to generate consistent results. We use the graph edge rerouting test and the cross model test to demonstrate that RWT can effectively identify structural similarities between graphs.
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