Network topology optimization by turning non-scale-free networks into scale-free networks using nonlinear preferential rewiring method

Feng Su,Peijiang Yuan,Shuangqian Cao,Yuanwei Liu

doi:10.1177/1550147718784477

Feng Su, Peijiang Yuan + Show 2 more

Open Access

https://doi.org/10.1177/1550147718784477

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Abstract

In practical application, the generation and evolution of many real networks always do not follow rigorous mathematical model, making network topology optimization a great challenge in the field of complex networks. In this research, we optimize the topology of non-scale-free networks by turning it into scale-free networks using a nonlinear preferential rewiring method. For different kinds of original networks generated by Watts and Strogatz model, we systematically demonstrate the optimization process and the modified networks to verify the performance of nonlinear preferential rewiring. We conduct further researches to explore the effect of nonlinear preferential rewiring’s parameters on performance. Simulation results show that various non-scale-free networks with different network topologies generated by WS model, including random networks and various networks between regular and random, are turned into scale-free networks perfectly by nonlinear preferential rewiring method.

Highlights

The interdisciplinary field of complex networks is a young and attractive area of scientific research
Networks generated by ER model do not capture two important properties which are generally observed in real networks: the local clustering and the formation of School of Mechanical Engineering & Automation, Beihang University, Beijing, China
In order to visually demonstrate the change in the topology between original non-scale-free networks and the networks modified by nonlinear preferential rewiring (NPR) method, the number of nodes is set relatively small

Summary

Introduction

The interdisciplinary field of complex networks is a young and attractive area of scientific research. The collaboration graph of film actors and the electrical power grid are shown to have short average path lengths as well as high clustering coefficients, which is always called ‘‘small-world’’ networks according to the six degrees of separation theory.[15,16,17] Watts and Strogatz (WS) model is proposed to generate graphs with small-world properties. WS model is used to generate non-scale-free networks here.[17] There are three critical parameters in WS model: the desired number of nodes (N), the mean degree (K, assumed to be an even integer), and rewiring probability b (0 b 1). In order to generate a complex network with scale-free degree distribution, the processes 1, 2, and 3 should be repeated several times till a termination condition is satisfied. The global information is introduced into topology optimization process using the cumulative sum of sorted node degree. If these processes are repeated M iterations, we would get a series of modified networks

X N X N

Conclusion and discussion