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 than 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 than 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 at https://github.com/Aikta-Arya/X-distribution-Retraceable-Power-Law-Exponent-of-Complex-Networks.git.

通过理论分析和网络重建（NR）的数值模拟，网络建模得到了广泛的探索。网络重构问题需要估计给定输入网络的幂律指数 (γ)。因此，NR解的有效性取决于γ计算的准确性。在本文中，我们重新审视基于度分布的 γ 估计，由于近似，该估计不是很准确。我们提出X分布，它比度分布更准确。各种最先进的网络模型，包括 CPM、NRM、RefOrCite2、BA、CDPAM 和 DMS，均被考虑用于模拟目的，模拟结果支持所提出的主张。此外，我们在几个现实世界的网络上应用X分布来计算它们的幂律指数，这与使用各自的度分布计算的幂律指数不同。据观察，X分布在双对数尺度上比度分布表现出更多的线性（直线）。因此，X分布更适合使用线性拟合（在对数尺度上）评估幂律指数。使用不同网络模型的X分布进行幂律指数 (γ) 计算的 MATLAB 实现以及我们实验中使用的真实世界数据集可在 https://github.com/Aikta-Arya/X-distribution-Retraceable 上找到-复杂网络的幂律指数.git。