Network community detection from the perspective of time series

We present a quasi-isometric mapping to transform complex networks into time series, which enables the network distance to be strictly preserved and allows to solve the network clustering problem from the perspective of its time series. In order to reconstruct the network distance characteristics exactly, we weight the network links in several ways and then convert the weighted networks into time series via classical multidimensional scaling (CMDS). Given such a transformation framework, we utilize the criterion of relative eigenvalue gap (REG) to estimate the number of communities of a network. Further, we enunciate that the distributions of two time series from two isomorphic networks are identical. We then apply the distance-based k-means algorithm to the generated time series to detect the community structures of complex networks with success. The results of diverse simulated and real networks demonstrate the superiority of quasi-isometry-based time series in network community detection.