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New models for multi-class networks
Journal of Computational and Applied Mathematics ( IF 2.4 ) Pub Date : 2021-03-26 , DOI: 10.1016/j.cam.2021.113567
Omar De la Cruz Cabrera , Jiafeng Jin , Lothar Reichel

Many complex phenomena can be modeled by networks, that is, by a set of nodes connected by edges. Networks are represented by graphs, and several algebraic and analytical methods have been developed for their study. However, in order to obtain a more useful representation of a system, it is often appropriate to include more information about the nodes and/or edges, and those additions make it necessary to adapt or modify such methods of study.

Multi-class networks, in which the set of nodes and/or the set of edges are partitioned in two or more classes, are useful when different nodes and edges can play fundamentally distinct roles in the system. In this article we introduce new models and methods for multi-class networks, based on how the adjacency matrix is formed.

We apply this approach to obtain measures of node importance or centrality, in particular using the Perron eigenvector. Perturbation results shed light on how the relative importance of a node changes by the addition of a single edge, and experiments with both synthetic and real data sets illustrate features of the methods discussed.



中文翻译:

多类别网络的新模型

许多复杂的现象可以通过网络来建模,即通过边缘连接的一组节点来建模。网络用图形表示,并且已经研究了几种代数和分析方法。但是,为了获得系统的更有用的表示形式,通常宜包含有关节点和/或边缘的更多信息,并且这些增加使得有必要调整或修改此类研究方法。

当不同的节点和边缘可以在系统中起根本不同的作用时,将一组节点和/或一组边缘划分为两个或多个类别的多类网络很有用。在本文中,根据邻接矩阵的形成方式,我们介绍了用于多类网络的新模型和方法。

我们应用这种方法来获得节点重要性或中心性的度量,特别是使用Perron特征向量。摄动的结果揭示了节点的相对重要性如何通过添加单个边来改变,并且使用合成数据集和真实数据集进行的实验都说明了所讨论方法的特征。

更新日期:2021-04-09
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