Estimating Completeness in Streaming Graphs

Finding the completeness of a graph is important from various aspects. Considering the massive growth and dynamics of real-life networks, we readdress this problem in a streaming setting. We approach the problem of verifying the completeness of a graph by estimating the eigen values of a sketch of its adjacency matrix. Here, we provide the first approximation algorithm for estimating the completeness of a bipartite graph in the streaming model. The approach is further generalized for any arbitrary simple graph. We employ some useful recent results on ` 1 heavy eigen-hitters to construct the algorithms working in linear time and consuming sublinear space. The implementation of the algorithms have also been done and tested on a couple of networks. We illustrate the e↵ectiveness of the proposed approaches in analyzing social, biological and other real-life networks.