Currently, all online social networks (OSNs) are considered to follow a power-law distribution. In this paper, the degree distribution for multiple OSNs has been studied. It is seen that the degree distributions of OSNs differ moderately from a power law. Lognormal distributions are an alternative to power-law distributions and have been used as best fit for many complex networks. It is seen that the degree distributions of OSNs differ massively from a lognormal distribution. Thus, for a better fit, a composite distribution combining power-law and lognormal distribution is suggested. This paper proposes an approach to find the most suitable distribution for a given degree distribution out of the six possible combinations of power law and lognormal, namely power law, lognormal, power law–lognormal, lognormal–power law, double power law, and double power law lognormal. The errors in the fitted composite distribution and the original degree distribution of the OSNs are observed. It is seen that a composite distribution fitted using the approach described in this paper is always a better fit than both power-law and lognormal distributions.

中文翻译：

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寻找 OSN 数据的最佳拟合分布

目前，所有在线社交网络 (OSN) 都被认为遵循幂律分布。在本文中，研究了多个 OSN 的度分布。可以看出，OSN 的度分布与幂律略有不同。对数正态分布是幂律分布的替代方法，已被用作许多复杂网络的最佳拟合。可以看出，OSN 的度分布与对数正态分布有很大不同。因此，为了更好地拟合，建议使用结合幂律分布和对数正态分布的复合分布。本文提出了一种方法，可以从幂律和对数正态的六种可能组合中找到最适合给定度分布的分布，即幂律、对数正态、幂律-对数正态、对数正态-幂律、双幂律，和双幂律对数正态。观察到拟合的复合分布和 OSN 的原始度分布中的误差。可以看出，使用本文描述的方法拟合的复合分布总是比幂律分布和对数正态分布更适合。