Weighted edge sampling for static graphs

Graph sampling provides an efficient yet inexpensive solution for analysing large graphs. The purpose of sampling a graph is to extract a small representative subgraph from a big graph so that the sample can be used in place of the big graph for studying and analysing it. In this paper, we propose a new sampling method called weighted edge sampling. In this method, we give equal weight to all the edges in the beginning. During the sampling process, we sample an edge with the probability proportional to its weight. When an edge is sampled, we increase the weight of its neighbouring edges and this increases their probability to be sampled. Our method extracts the neighbourhood of a sampled edge more efficiently than previous approaches. We evaluate the efficacy of our sampling approach empirically using several real-world datasets. We find that our method produces better samples than the previous approaches. Our results show that our samples better estimate the degree and path length of the original graphs whereas our samples are less efficient in estimating the clustering coefficient of a graph.