具有度相关的广义组态模型及其逾渗分析
A Generalized Configuration Model with Degree Correlations and Its Percolation Analysis
摘要：
在本文中，我们提出了一个推广的经典配置模型。与经典配置模型一样，广义配置模型允许用户指定任意的度分布。在我们的广义配置模型中，我们将配置模型中的存根划分为大小相等的b个块，并为这些块选择置换函数h。在每个块中，我们随机指定与q个存根成比例的数量作为类型1存根，其中q是范围[0; 1]中的参数。其他存根被指定为2类存根。要构建一个网络，随机选择一个未连接的存根。假设这个存根在块i中。如果它是一个类型1存根，将这个存根连接到块h（i）中随机选择的未连接的类型1存根。如果它是2型存根，将其连接到随机选择的未连接的2型存根。我们重复这个过程，直到所有的存根都连接起来。在一定的假设条件下，我们得到了所构造图中两个随机邻点的联合度分布的一个封闭形式。基于这个联合度分布，我们证明了对于任何固定的b，Pearson度相关函数在q中是线性的。通过适当地选择h，我们表明，我们的构造算法可以创建独立网络以及独立网络。我们提出了这个模型的渗流分析。我们通过广泛的计算机模拟验证了我们的结果。
英文摘要：
In this paper we present a generalization of the classical configuration model. Like the classical configuration model, the generalized configuration model allows users to specify an arbitrary degree distribution. In our generalized configuration model, we partition the stubs in the configuration model into b blocks of equal sizes and choose a permutation function h for these blocks. In each block, we randomly designate a number proportional to q of stubs as type 1 stubs, where q is a parameter in the range [0; 1]. Other stubs are designated as type 2 stubs. To construct a network, randomly select an unconnected stub. Suppose that this stub is in block i. If it is a type 1 stub, connect this stub to a randomly selected unconnected type 1 stub in block h(i). If it is a type 2 stub, connect it to a randomly selected unconnected type 2 stub. We repeat this process until all stubs are connected. Under an assumption, we derive a closed form for the joint degree distribution of two random neighboring vertices in the constructed graph. Based on this joint degree distribution, we show that the Pearson degree correlation function is linear in q for any fixed b. By properly choosing h, we show that our construction algorithm can create assortative networks as well as disassortative networks. We present a percolation analysis of this model. We verify our results by extensive computer simulations.
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