Estimation of Graphlet Statistics
Abstract
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small graphs. Most previous work has focused on exact algorithms, however, it is often too expensive to compute graphlets exactly in massive networks with billions of edges, and finding an approximate count is usually sufficient for many applications. In this work, we propose an unbiased graphlet estimation framework that is (a) fast with significant speedups compared to the stateoftheart, (b) parallel with nearly linearspeedups, (c) accurate with <1% relative error, (d) scalable and spaceefficient for massive networks with billions of edges, and (e) flexible for a variety of realworld settings, as well as estimating macro and microlevel graphlet statistics (e.g., counts) of both connected and disconnected graphlets. In addition, an adaptive approach is introduced that finds the smallest sample size required to obtain estimates within a given userdefined error bound. On 300 networks from 20 domains, we obtain <1% relative error for all graphlets. This is significantly more accurate than existing methods while using less data. Moreover, it takes a few seconds on billion edge graphs (as opposed to days/weeks). These are by far the largest graphlet computations to date.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.01772
 Bibcode:
 2017arXiv170101772R
 Keywords:

 Computer Science  Social and Information Networks;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Mathematics  Combinatorics;
 Statistics  Machine Learning