Scalable Estimation of Network Average Degree

Abstract

In massive networked systems, it is an important problem to obtain a certain kind of network statistic such as average degree or clustering coefficient. In this paper, we propose a one-shot scalable average degree estimation algorithm, which allows a monitoring node outside of the target network obtains the average degree with o(n) message complexity. The proposed algorithm is based on the method by Goldreich and Ron (GR), which is well-known in the context of property testing. In this sense our algorithm is a “network version” of it. While the original GR algorithm can be regarded as a pull-based scheme in the sense that the monitoring node can get information only from randomly chosen nodes, our algorithm utilizes push-based schemes, that is, each node in the target network can actively send information to the monitoring server. The primary contribution of this paper is that such push-based schemes actually yield better message complexity.