X-distribution: Retraceable Power-law Exponent of Complex Networks

Abstract

Network modeling has been explored extensively by means of theoretical analysis as well as numerical simulations for Network Reconstruction (NR). The network reconstruction problem requires the estimation of the power-law exponent ( γ ) of a given input network. Thus, the effectiveness of the NR solution depends on the accuracy of the calculation of γ . In this article, we re-examine the degree distribution-based estimation of γ , which is not very accurate due to approximations. We propose X -distribution, which is more accurate as compared to degree distribution. Various state-of-the-art network models, including CPM, NRM, RefOrCite2, BA, CDPAM, and DMS, are considered for simulation purposes, and simulated results support the proposed claim. Further, we apply X -distribution over several real-world networks to calculate their power-law exponents, which differ from those calculated using respective degree distributions. It is observed that X -distributions exhibit more linearity (straight line) on the log-log scale as compared to degree distributions. Thus, X -distribution is more suitable for the evaluation of power-law exponent using linear fitting (on the log-log scale). The MATLAB implementation of power-law exponent ( γ ) calculation using X -distribution for different network models, and the real-world datasets used in our experiments are available here: https://github.com/Aikta-Arya/X-distribution-Retraceable-Power-Law-Exponent-of-Complex-Networks.git