Department of Physics, Inha University, Incheon 22212, Korea.
Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS, 09200 Moulis, France.
Phys Rev E. 2019 Nov;100(5-1):052309. doi: 10.1103/PhysRevE.100.052309.
We generalize an algorithm used widely in the configuration model such that power-law degree sequences with the degree exponent λ and the number of links per node K controllable independently may be generated. It yields the degree distribution in a different form from that of the static model or under random removal of links while sharing the same λ and K. With this generalized power-law degree distribution, the critical point K_{c} for the appearance of the giant component remains zero not only for λ≤3 but also for 3<λ<λ_{l}≃3.81. This is contrasted with K_{c}=0 only for λ≤3 in the static model and under random link removal. The critical exponents and the cluster-size distribution for λ<λ_{l} are also different from known results. By analyzing the moments and the generating function of the degree distribution and comparison with those of other models, we show that the asymptotic behavior and the degree exponent may not be the only properties of the degree distribution relevant to the critical phenomena but that its whole functional form can be relevant. These results can be useful in designing and assessing the structure and robustness of networked systems.
我们推广了一种在配置模型中广泛使用的算法，使得可以生成具有独立可控幂律度序列的度指数 λ 和每个节点的链接数 K 的幂律度序列。它以与静态模型或在随机删除链接时不同的形式生成度分布，同时共享相同的 λ 和 K。使用这种广义的幂律度分布，对于 3<λ<λ_{l}≃3.81，不仅对于 λ≤3，而且对于出现巨型组件的临界点 K_{c} 仍然为零。这与静态模型中和在随机链接删除下 K_{c}=0 仅对于 λ≤3 形成对比。对于 λ<λ_{l}的临界指数和簇大小分布也与已知结果不同。通过分析度分布的矩和生成函数，并与其他模型进行比较，我们表明，渐近行为和度指数可能不是与临界现象相关的度分布的唯一属性，而是其整个函数形式可能相关。这些结果可用于设计和评估网络系统的结构和鲁棒性。
