Calculating statistics of complex networks through random walks with an application to the on-line social network Bebo

We develop a methodology with which to calculate typical network statistics by sampling a network through a random walk. By examining the statistics of degree and return times of walks which return to the same vertex, we can estimate characteristics of the giant component such as average clustering coefficient, degree distribution, degree correlations and network size. We confirm the validity of the methods using a variety of available network network data sets and then apply these methods to data collected by performing a random walk on the large on-line social networking website, Bebo. We find good agreement between our results and the results of previous studies of on-line social networks in which data collection was performed by a BFS (“snow-ball”) sampling algorithm. In particular, we find that the degree distribution exhibits a multi-scaling power-law tail and the network exhibits clustering and positive degree correlations.