Average degree estimation under ego-centric sampling design

Abstract

Estimating the structural characteristics of large graphs from a sample is a classical problem. In this study, we propose asymptotically unbiased estimators for the average degree characteristic of a network under ego-centric sampling. In this sampling design, we first sample a number of vertices called ego vertices from the underlying graph and then obtain their ego-centric graph. Ego-centric graph of a sampled vertex is defined as the subgraph induced by the vertices within 1-hop neighborhood of the sampled ego vertex. We compare the proposed estimators with the estimator that do not utilize the neighborhood information using both real-world and synthetic large-scale graphs. The results show that utilization of the neighborhood information does not always increase the estimation accuracy depending on the sampling budget usage and the structure of the underlying graph.