Analysis of directed networks via the matrix exponential
Analysis of directed networks via the matrix exponential
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DOI：
10.1016/j.cam.2019.01.015
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发表时间：
2019-08-01
影响因子：
2.4
通讯作者：
Reichel, Lothar
中科院分区：
文献类型：
--
作者：
Cabrera, Omar De la Cruz;Matar, Mona;Reichel, Lothar
矩阵指数已被确定为分析无向网络的有用工具，它对给定网络的重要方面进行建模的能力具有良好的理论依据。然而，它在定向网络中的应用尚不成熟，迄今为止也不太成功。在本文中，我们讨论了使用矩阵指数来识别有向网络中重要节点的一些方法，考虑到重要性的概念会发生变化，无论我们是考虑沿边缘方向的给定节点的影响（下游影响），还是考虑指向它的有向路径对它的影响（上游影响）。此外，我们引入了一系列基于计数行走的重要性度量，这些行走被允许在有限次数内逆转其方向，从而捕获由于影响相同节点或受到相同节点的影响而产生的关系，而不会牺牲有关边缘方向的信息。这些措施提供了有关分支点的信息。(C) 2019 Elsevier B.V.版权所有
The matrix exponential has been identified as a useful tool for the analysis of undirected networks, with sound theoretical justifications for its ability to model important aspects of a given network. Its use for directed networks, however, is less developed and has been less successful so far. In this article we discuss some methods to identify important nodes in a directed network using the matrix exponential, taking into account that the notion of importance changes whether we consider the influence of a given node along the edge directions (downstream influence) or how it is influenced by directed paths that point to it (upstream influence). In addition, we introduce a family of importance measures based on counting walks that are allowed to reverse their direction a limited number of times, thus capturing relationships arising from influencing the same nodes, or being influenced by the same nodes, without sacrificing information about edge direction. These measures provide information about branch points. (C) 2019 Elsevier B.V. All rights reserved.