Optimal map of the modular structure of complex networks
Optimal map of the modular structure of complex networks
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DOI：
10.1088/1367-2630/12/5/053009
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发表时间：
2010-05-06
影响因子：
3.3
通讯作者：
Zamora-Lopez, G.
中科院分区：
文献类型：
--
作者：
Arenas, A.;Borge-Holthoefer, J.;Zamora-Lopez, G.
模块化结构在自然科学、社会科学和技术科学中观察到的许多复杂的相互作用网络中普遍存在。它的研究揭示了复杂系统的结构与功能之间的关系。一般来说，模块是由高度连接的节点组成的岛，这些节点被相对较少的链接分开。每个模块都可以有来自网络中任何节点的链接的贡献。挑战在于理清这些贡献，以了解模块化结构是如何构建的。主要的问题是，分析一个特定的模块划分，原则上，涉及的数据与模块数量乘以节点数量一样多。为了应对这一挑战，我们首先定义了贡献矩阵，这个数学对象包含了关于感兴趣分区的所有信息，然后我们使用截断奇异值分解来提取这个矩阵在平面上的最佳表示。对这种投射的分析使我们能够仔细检查模块结构的骨架，揭示各个模块的结构及其相互关系。
The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.