Zlatić Vinko, Stefancić Hrvoje
Theoretical Physics Division, Rudjer Bosković Institute, HR-10002 Zagreb, Croatia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 2):016117. doi: 10.1103/PhysRevE.80.016117. Epub 2009 Jul 28.
Reciprocal edges represent the lowest-order cycle possible to find in directed graphs without self-loops. Representing also a measure of feedback between vertices, it is interesting to understand how reciprocal edges influence other properties of complex networks. In this paper, we focus on the influence of reciprocal edges on vertex degree distribution and degree correlations. We show that there is a fundamental difference between properties observed on the static network compared to the properties of networks, which are obtained by simple evolution mechanism driven by reciprocity. We also present a way to statistically infer the portion of reciprocal edges, which can be explained as a consequence of feedback process on the static network. In the rest of the paper, the influence of reciprocal edges on a model of growing network is also presented. It is shown that our model of growing network nicely interpolates between Barabási-Albert (BA) model for undirected and the BA model for directed networks.
互惠边代表在无自环的有向图中可能找到的最低阶循环。由于它也表示顶点之间的反馈度量，因此了解互惠边如何影响复杂网络的其他属性很有意思。在本文中，我们专注于互惠边对顶点度分布和度相关性的影响。我们表明，在静态网络上观察到的属性与通过互惠驱动的简单演化机制获得的网络属性之间存在根本差异。我们还提出了一种统计推断互惠边比例的方法，这可以解释为静态网络上反馈过程的结果。在本文的其余部分，还介绍了互惠边对增长网络模型的影响。结果表明，我们的增长网络模型很好地插补了无向巴拉巴西-阿尔伯特（BA）模型和有向网络的BA模型之间的情况。
