加权有向多层网络内聚系数的分类
Taxonomy of Cohesion Coefficients for Weighted and Directed Multilayer Networks
摘要：
聚类系数和封闭系数是描述网络拓扑结构中应用最广泛的指标之一。随着时间的推移，已经提出了许多不同的定义，特别是在加权网络的情况下，其中三角形权重的选择是一个关键方面。在目前的工作中，在加权有向多层网络的框架下，我们通过引入聚集系数，将经典的聚类和封闭系数推广到任何类型的不完整三角形。然后，我们组织这些系数的类在一个系统的分类在更一般的情况下，加权有向多层网络。这种内聚系数也适用于表征多层网络的不同尺度，以便从不同角度把握其结构。我们还展示了如何张量形式主义允许将新的定义，以及所有现有的文献中，在一个统一的写作，在这样一种方式，一个合适的选择所涉及的邻接张量允许获得他们中的每一个。最后，通过一些模拟网络的应用程序，我们证明了所提出的系数在捕捉不同尺度上的网络结构的不同特性的有效性。
英文摘要：
Clustering and closure coefficients are among the most widely applied indicators in the description of the topological structure of a network. Many distinct definitions have been proposed over time, particularly in the case of weighted networks, where the choice of the weight attributed to the triangles is a crucial aspect. In the present work, in the framework of weighted directed multilayer networks, we extend the classical clustering and closure coefficients through the introduction of the clumping coefficient, which generalizes them to incomplete triangles of any type. We then organize the class of these coefficients in a systematic taxonomy in the more general context of weighted directed multilayer networks. Such cohesion coefficients have also been adapted to the different scales that characterize a multilayer network, in order to grasp their structure from different perspectives. We also show how the tensor formalism allows incorporating the new definitions, as well as all those existing in the literature, in a single unified writing, in such a way that a suitable choice of the involved adjacency tensors allows obtaining each of them. Finally, through some applications to simulated networks, we show the effectiveness of the proposed coefficients in capturing different peculiarities of the network structure on different scales.
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