Complex networks renormalization: Flows and fixed points
Complex networks renormalization: Flows and fixed points
复制标题
DOI：
10.1103/physrevlett.101.148701
复制
发表时间：
2008-10-03
影响因子：
8.6
通讯作者：
Fortunato, Santo
中科院分区：
文献类型：
--
作者：
Radicchi, Filippo;Ramasco, Jose J.;Fortunato, Santo
最近，有人声称，一些复杂的网络是自相似的一个方便的重整化过程。我们提出了一种研究图中重整化流的一般方法。我们发现一些变量在重整化下的行为，如节点的最大连接数，服从简单的标度律，其特征在于临界指数。这对于任何类型的图都是正确的，从随机到无标度网络，从格子到层次图。因此，图的重整化流与自旋系统的重整化类似。经典的重正化渗流和伊辛模型的晶格上的分析证实了这一类比。临界指数和标度函数可用于对普适类中的图进行分类，并揭示标准分析无法访问的图之间的相似性。
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.