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Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called Simple Random Walk with re-weighting (SRW-rw) and Metropolis-Hastings (MH) algorithm have been popular in the literature for such unbiased graph sampling. However, an unavoidable downside of their core random walks-slow diffusion over the space, can cause poor estimation accuracy. In particular, a remarkable feature of the MHDA is its applicability for any non-uniform node sampling like the MH algorithm, but ensuring better sampling efficiency than the MH algorithm. The authors also provide simulation results to confirm their theoretical findings.
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