Graph Size Estimation

TL;DR

This paper introduces a novel, efficient method for estimating the size of large, partially known graphs using random walk sampling, significantly reducing the number of samples needed compared to existing techniques.

Contribution

It presents IE, an efficient estimator based on induced edges, and SafetyMargin, a correction method for dependence in random walk samples, combined to improve graph size estimation.

Findings

IE with SafetyMargin requires at least 10 times fewer samples than previous methods.

The approach is effective on real-world networks like Facebook.

The combined method reduces sample complexity substantially.

Abstract

Many online networks are not fully known and are often studied via sampling. Random Walk (RW) based techniques are the current state-of-the-art for estimating nodal attributes and local graph properties, but estimating global properties remains a challenge. In this paper, we are interested in a fundamental property of this type - the graph size N, i.e., the number of its nodes. Existing methods for estimating N are (i) inefficient and (ii) cannot be easily used with RW sampling due to dependence between successive samples. In this paper, we address both problems. First, we propose IE (Induced Edges), an efficient technique for estimating N from an independence sample of graph's nodes. IE exploits the edges induced on the sampled nodes. Second, we introduce SafetyMargin, a method that corrects estimators for dependence in RW samples. Finally, we combine these two stand-alone techniques to obtain a RW-based graph size estimator. We evaluate our approach in simulations on a wide range of real-life topologies, and on several samples of Facebook. IE with SafetyMargin typically requires at least 10 times fewer samples than the state-of-the-art techniques (over 100 times in the case of Facebook) for the same estimation error.