Estimating the size and average degree of online social networks at the extreme

Given the increasingly limiting nature of online social networks (OSNs), studying their structural characteristics under a limited data access model becomes important. In this study, we propose estimators for network size and average degree characteristics of OSNs. We sample an OSN graph using random neighbor API calls. A random neighbor API call returns only the id of a randomly selected neighbor of a given user. Although the existing estimators give good accuracy estimations for a given sample size, they are not applicable under the extremely limited data access model considered here. We conduct experiments on real world graphs to measure the performance of the proposed estimators.