Using a Bayesian approach to reconstruct graph statistics after edge sampling

TL;DR

This paper introduces a Bayesian methodology to accurately reconstruct key network properties, such as degree distribution and triangle count, from uniformly edge-sampled networks, addressing challenges posed by data collection limitations.

Contribution

It presents a novel Bayesian approach for recovering fundamental network statistics from edge-sampled data without relying on assumptions about the original network.

Findings

Effective recovery of degree distribution and triangle counts demonstrated.

Method performs well on synthetic and real datasets with diverse properties.

No assumptions about original network needed for prior construction.

Abstract

Often, due to prohibitively large size or to limits to data collecting APIs, it is not possible to work with a complete network dataset and sampling is required. A type of sampling which is consistent with Twitter API restrictions is uniform edge sampling. In this paper, we propose a methodology for the recovery of two fundamental network properties from an edge-sampled network: the degree distribution and the triangle count (we estimate the totals for the network and the counts associated with each edge). We use a Bayesian approach and show a range of methods for constructing a prior which does not require assumptions about the original network. Our approach is tested on two synthetic and three real datasets with diverse sizes, degree distributions, degree-degree correlations and triangle count distributions.