Metropolis-Hastings Random Walk with a Reduced Number of Self-Loops

The random walk (RW) is one of the effective sampling methods for large-scale networks such as the Internet and social networks. While a simple RW method tends to visit nodes with high degrees, the Metropolis-Hastings random walk (MHRW) algorithm has ready-to-use characteristics, wherein the nodes visited by the algorithm distribute uniformly. However, because the MHRW algorithm conducts many self-looping operations and the spread of its crawler is slow, it requires many samples in order to secure sufficient accuracy. This study proposes a RW that requires less self-looping than MHRW did while maintaining the ready-to-use characteristics. The ready-to-use characteristics are achieved by appropriately changing the adaption probability of MHRW and choice probability of neighboring nodes. Our experiments demonstrated that the proposed RW required less self-loop operations than MHRW did. Moreover, the cost of the proposed algorithm is discussed keeping applications to real networks in mind.