Boguñá Marián, Pastor-Satorras Romualdo
Departament de Física Fonamental, Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036112. doi: 10.1103/PhysRevE.68.036112. Epub 2003 Sep 15.
We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.
我们研究了一类相关随机网络模型，其中顶点由控制顶点对之间边建立的隐藏变量表征。我们找到了这些模型主要拓扑性质的解析表达式，该表达式是隐藏变量分布和连接顶点概率的函数。通过一个具体例子中的数值模拟对所得表达式进行了检验。将一般模型进行扩展以描述一种生成具有先验指定相关结构随机网络的实用算法。我们还给出了该类模型的一种扩展，用于将非平衡增长网络映射到具有隐藏变量的网络，这些隐藏变量表示系统中每个顶点引入的时间。
