加权超软结构模型
Weighted hypersoft configuration model
摘要：
网络的最大熵零模型有不同的风格，这取决于熵最大化的约束类型。如果约束是在度序列或分布上，我们处理的是配置模型。如果度序列是严格约束的，则具有给定度序列的随机图的微正则系综本身就是配置模型。如果度序列仅受平均约束，则具有给定期望度序列的随机图的巨典范系综是软配置模型。如果度序列不是固定的，而是从一个固定的分布中随机抽取的，那么对应的具有给定度分布的随机图的超正则系综就是超软配置模型，这是对动态现实世界网络的更充分的描述，其中度序列从来都不是固定的，但度分布通常保持稳定。在这里，我们介绍了加权网络的超软配置模型。主要贡献是一个特定版本的模型，具有幂律度和强度分布，以及强度随度的超线性缩放，模仿了一些真实世界网络的属性。作为一个副产品，我们推广的概念稀疏图子和它们的熵加权网络。
英文摘要：
Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration models. If the degree sequence is constrained exactly, the corresponding microcanonical ensemble of random graphs with a given degree sequence is the configuration model per se. If the degree sequence is constrained only on average, the corresponding grand-canonical ensemble of random graphs with a given expected degree sequence is the soft configuration model. If the degree sequence is not fixed at all but randomly drawn from a fixed distribution, the corresponding hypercanonical ensemble of random graphs with a given degree distribution is the hypersoft configuration model, a more adequate description of dynamic real-world networks in which degree sequences are never fixed but degree distributions often stay stable. Here, we introduce the hypersoft configuration model of weighted networks. The main contribution is a particular version of the model with power-law degree and strength distributions, and superlinear scaling of strengths with degrees, mimicking the properties of some real-world networks. As a byproduct, we generalize the notions of sparse graphons and their entropy to weighted networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
