A Strength and Sparsity Preserving Algorithm for Generating Weighted, Directed Networks with Predetermined Assortativity

TL;DR

This paper presents a novel mixed integer programming-based rewiring algorithm for weighted directed networks that preserves node strengths and sparsity while achieving desired assortativity levels.

Contribution

Introduces the SSPR algorithm, a new method for rewiring weighted networks to preserve strengths and sparsity, extending degree-preserving rewiring to weighted directed networks.

Findings

SSPR effectively preserves node strengths and sparsity.

The method can achieve targeted assortativity levels.

Applicability demonstrated on popular network models.

Abstract

Degree-preserving rewiring is a widely used technique for generating unweighted networks with given assortativity, but for weighted networks, it is unclear how an analog would preserve the strengths and other critical network features such as sparsity level. This study introduces a novel approach for rewiring weighted networks to achieve desired directed assortativity. The method utilizes a mixed integer programming framework to establish a target network with predetermined assortativity coefficients, followed by an efficient rewiring algorithm termed "strength and sparsity preserving rewiring" (SSPR). SSPR retains the node strength distributions and network sparsity after rewiring. It is also possible to accommodate additional properties like edge weight distribution with extra computational cost. The optimization scheme can be used to determine feasible assortativity ranges for an initial network. The effectiveness of the proposed SSPR algorithm is demonstrated through its application to two classes of popular network models.