高阶分布与无多重连接的非增长复杂网络
Higher-order distributions and nongrowing complex networks without multiple connections
摘要：
我们研究随机过程，产生非增长的复杂网络没有自循环和多个边缘（简单的图形）。这项工作集中在理解和制定的限制，保持重新布线的随机过程中的类简单的图形。为了制定这些限制一个新的概念楔形分布（路径长度为2）的介绍和它的关系度度相关性进行了研究。分析表明，约束条件，连同边缘选择规则，甚至不允许制定一个封闭的主方程在一般情况下。我们还介绍了一个特殊的随机过程，它不包含边选择规则，但我们相信，它可以提供一些洞察简单图的复杂性。
英文摘要：
We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic processes within the class of simple graphs. To formulate these constraints a new concept of wedge distribution (paths of length 2) is introduced and its relation to degree-degree correlation is studied. The analysis shows that the constraints, together with edge selection rules, do not even allow to formulate a closed master equation in the general case. We also introduce a particular stochastic process which does not contain edge selection rules, but which, we believe, can provide some insight into the complexities of simple graphs.
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