Communicability betweenness in complex networks
Communicability betweenness in complex networks
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DOI：
10.1016/j.physa.2008.11.011
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发表时间：
2009-03-01
影响因子：
3.3
通讯作者：
Hatano, Naomichi
中科院分区：
文献类型：
--
作者：
Estrada, Ernesto;Higham, Desmond J.;Hatano, Naomichi
介数度量提供了定量工具，可以从大型复杂网络提供的大量交互数据中挑选出精细的细节。它们使我们能够研究信息在网络中传递时节点参与的程度。介数高的节点可以被视为具有高度活跃作用的关键参与者。在一个极端，介数是通过考虑仅通过节点对之间的最短路径传递的信息来定义的。在另一个极端，通过考虑任意长度的所有可能的行走来定义另一种类型的中间性。在这项工作中，我们提出了介于这两种对立观点之间的介数度量。我们允许信息通过所有可能的路线，但引入缩放，以便更长的步行变得不那么重要。这个新定义与网络中节点对的可通信性原理相似，由 Estrada 和 Hatano [E.埃斯特拉达，N.波多野，物理学家。修订版 E 77 (2008) 36111]。定义了这种新的可通信性介数度量后，我们证明它可以用邻接矩阵的指数来巧妙地表征。我们还表明，该度量与矩阵指数的 Frechet 导数密切相关。这使我们得出结论，当给定节点的边缘受到无限小的扰动时，它还描述了网络敏感性。使用说明性的合成网络和现实生活网络，我们表明新的中介度量的行为与现有版本不同，特别是我们表明它从蛋白质-蛋白质相互作用网络中恢复了有意义的生物信息。 (c) 2008 Elsevier B.V. 保留所有权利。
Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano [E. Estrada, N. Hatano, Phys. Rev. E 77 (2008) 36111]. Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Frechet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a protein-protein interaction network. (c) 2008 Elsevier B.V. All rights reserved.