Identifying Communities and Key Vertices by Reconstructing Networks from Samples

TL;DR

This paper introduces a sampling and reconstruction method using random walks and probabilistic coalescing to uncover community structures and key vertices in networks, aiding in epidemic control.

Contribution

It presents a novel network reconstruction approach from samples that effectively identifies communities and influential nodes for immunization strategies.

Findings

Reconstructed networks preserve community structures well.

Key vertices identified can significantly reduce infection spread.

Method approximates original network properties effectively.

Abstract

Sampling techniques such as Respondent-Driven Sampling (RDS) are widely used in epidemiology to sample "hidden" populations, such that properties of the network can be deduced from the sample. We consider how similar techniques can be designed that allow the discovery of the structure, especially the community structure, of networks. Our method involves collecting samples of a network by random walks and reconstructing the network by probabilistically coalescing vertices, using vertex attributes to determine the probabilities. Even though our method can only approximately reconstruct a part of the original network, it can recover its community structure relatively well. Moreover, it can find the key vertices which, when immunized, can effectively reduce the spread of an infection through the original network.