Measuring Fundamental Properties of Real-World Complex Networks

TL;DR

This paper introduces a practical method to assess whether measurements of real-world complex networks are reliable, by analyzing how network properties evolve with increasing sample size, thereby improving network modeling accuracy.

Contribution

It proposes the first practical approach to determine the reliability of network property measurements based on their evolution with sample size.

Findings

The method effectively distinguishes reliable from misleading measurements.

Some network properties are easier to evaluate in practice.

The approach is validated on representative complex network datasets.

Abstract

Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these procedures eventually lead to samples large enough to be representative of the whole, at least concerning some key properties. This has crucial impact on network modeling and simulation, which rely on these properties. Recent contributions proved that this approach may be misleading, but no solution has been proposed. We provide here the first practical way to distinguish between cases where it is indeed misleading, and cases where the observed properties may be trusted. It consists in studying how the properties of interest evolve when the sample grows, and in particular whether they reach a steady state or not. In order to illustrate this method and to demonstrate its relevance, we apply it to data-sets on complex network measurements that are representative of the ones commonly used. The obtained results show that the method fulfills its goals very well. We moreover identify some properties which seem easier to evaluate in practice, thus opening interesting perspectives.