Reconstructing topological properties of complex networks using the fitness model

TL;DR

This paper introduces a method to reconstruct key topological features of complex networks using limited node information and an intrinsic fitness property, enabling analysis of privacy-restricted systems.

Contribution

The novel approach uses node fitness and partial connection data to generate representative network ensembles for estimating topological properties.

Findings

Robust reconstruction of network density, assortativity, and clustering.

Effective on both synthetic and real economic networks.

Maintains accuracy with limited calibration data.

Abstract

A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this paper we investigate a novel method to reconstruct global topological properties of a complex network starting from limited information. This method uses the knowledge of an intrinsic property of the nodes (indicated as fitness), and the number of connections of only a limited subset of nodes, in order to generate an ensemble of exponential random graphs that are representative of the real systems and that can be used to estimate its topological properties. Here we focus in particular on reconstructing the most basic properties that are commonly used to describe a network: density of links, assortativity, clustering. We test the method on both benchmark synthetic networks and real economic and financial systems, finding a remarkable robustness with respect to the number of nodes used for calibration. The method thus represents a valuable tool for gaining insights on privacy-protected systems.