A Measurement Framework for Directed Networks

TL;DR

This paper introduces a novel framework for measuring characteristics of directed networks using a personalized PageRank-based sampling method and an importance sampling estimator, addressing bias correction and applicability to large complex networks.

Contribution

It presents a new two-step sampling and estimation framework specifically designed for directed networks, including a PageRank-based sampling algorithm and a bias-correcting estimator.

Findings

The estimator is asymptotically unbiased even with poor PageRank approximation.

The framework effectively corrects sampling bias in directed networks.

Empirical results validate the theoretical properties of the estimator.

Abstract

Partially-observed network data collected by link-tracing based sampling methods is often being studied to obtain the characteristics of a large complex network. However, little attention has been paid to sampling from directed networks such as WWW and Peer-to-Peer networks. In this paper, we propose a novel two-step (sampling/estimation) framework to measure nodal characteristics which can be defined by an average target function in an arbitrary directed network. To this end, we propose a personalized PageRank-based algorithm to visit and sample nodes. This algorithm only uses already visited nodes as local information without any prior knowledge about the latent structure of the network. Moreover, we introduce a new estimator based on the approximate importance sampling to estimate average target functions. The proposed estimator utilizes calculated PageRank value of each sampled node as an approximation for the exact visiting probability. To the best of our knowledge, this is the first study on correcting the bias of a sampling method by re-weighting of measured values that considers the effect of approximation of visiting probabilities. Comprehensive theoretical and empirical analysis of the estimator demonstrate that it is asymptotically unbiased even in situations where stationary distribution of PageRank is poorly approximated.