Konini S, Janse van Rensburg E J
Mathematics & Statistics, York University, Toronto, Ontario, M3J 1P3, Canada.
PLoS One. 2017 Dec 22;12(12):e0189866. doi: 10.1371/journal.pone.0189866. eCollection 2017.
The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms include the Barabási-Albert algorithm. Later algorithms, such as the Duplication-Divergence algorithm, the Solé algorithm and the iSite algorithm, were inspired by biological processes underlying the evolution of protein networks, and the networks they produce differ essentially from networks grown by the Barabási-Albert algorithm. In this paper the mean field analysis of these algorithms is reconsidered, and extended to variant and modified implementations of the algorithms. The degree sequences of scale-free networks decay according to a powerlaw distribution, namely P(k) ∼ k-γ, where γ is a scaling exponent. We derive mean field expressions for γ, and test these by numerical simulations. Generally, good agreement is obtained. We also found that some algorithms do not produce scale-free networks (for example some variant Barabási-Albert and Solé networks).
在分子生物学中，无标度网络的采样通常是通过使用递归算法从一个种子开始生长网络来实现的，这些算法的基本操作包括节点和键的添加与删除。这些算法包括巴拉巴西 - 阿尔伯特算法。后来的算法，如复制 - 发散算法、索勒算法和iSite算法，是受蛋白质网络进化背后的生物学过程启发而产生的，它们所生成的网络与通过巴拉巴西 - 阿尔伯特算法生长的网络本质上有所不同。本文重新考虑了这些算法的平均场分析，并将其扩展到算法的变体和修改实现。无标度网络的度序列根据幂律分布衰减，即P(k) ∼ k-γ，其中γ是一个标度指数。我们推导了γ的平均场表达式，并通过数值模拟对其进行检验。总体而言，得到了良好的一致性。我们还发现一些算法不会产生无标度网络（例如一些变体的巴拉巴西 - 阿尔伯特网络和索勒网络）。
