Centre for Computational Systems Biology, Fudan University, Shanghai 200433, People's Republic of China.
Chaos. 2011 Mar;21(1):016107. doi: 10.1063/1.3553644.
Defining the importance of nodes in a complex network has been a fundamental problem in analyzing the structural organization of a network, as well as the dynamical processes on it. Traditionally, the measures of node importance usually depend either on the local neighborhood or global properties of a network. Many real-world networks, however, demonstrate finely detailed structure at various organization levels, such as hierarchy and modularity. In this paper, we propose a multiscale node-importance measure that can characterize the importance of the nodes at varying topological scale. This is achieved by introducing a kernel function whose bandwidth dictates the ranges of interaction, and meanwhile, by taking into account the interactions from all the paths a node is involved. We demonstrate that the scale here is closely related to the physical parameters of the dynamical processes on networks, and that our node-importance measure can characterize more precisely the node influence under different physical parameters of the dynamical process. We use epidemic spreading on networks as an example to show that our multiscale node-importance measure is more effective than other measures.
定义复杂网络中节点的重要性一直是分析网络结构组织以及网络上动态过程的基本问题。传统上，节点重要性的度量通常取决于网络的局部邻域或全局属性。然而，许多现实世界的网络在各种组织层次上表现出精细的细节结构，例如层次结构和模块性。在本文中，我们提出了一种多尺度节点重要性度量方法，可以在不同的拓扑尺度上刻画节点的重要性。这是通过引入核函数来实现的，核函数的带宽决定了相互作用的范围，同时考虑了节点所涉及的所有路径的相互作用。我们证明了这里的尺度与网络上动态过程的物理参数密切相关，并且我们的节点重要性度量可以在不同的动态过程物理参数下更精确地刻画节点的影响。我们以网络上的传染病传播为例，表明我们的多尺度节点重要性度量比其他度量方法更有效。
