Palla Gergely, Derényi Imre, Farkas Illés, Vicsek Tamás
Biological Physics Research Group of the Hungarian Academy of Sciences, Pázmány P. stny. 1A, H-1117 Budapest, Hungary.
Nature. 2005 Jun 9;435(7043):814-8. doi: 10.1038/nature03607.
Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.
自然界和社会中的许多复杂系统都可以用网络来描述，这些网络捕捉了构成它们的单元之间错综复杂的联系网络。一个关键问题是如何将此类网络的全局组织解释为与其结构亚单元（群落）的共存，这些亚单元与联系更为紧密的部分相关联。识别这些先验未知的构建模块（如功能相关的蛋白质、工业部门和人群）对于理解网络的结构和功能特性至关重要。用于大型网络的现有确定性方法会找到分离的群落，而大多数实际网络是由高度重叠的凝聚节点组构成的。在此，我们介绍一种分析重叠群落交织集主要统计特征的方法，这朝着揭示复杂系统的模块化结构迈出了一步。在为群落统计定义了一组新的特征量之后，我们应用一种有效的技术来大规模探索重叠群落。我们发现重叠是显著的，并且我们引入的分布揭示了网络的普遍特征。我们对合作、词关联和蛋白质相互作用图的研究表明，群落网络具有非平凡的相关性和特定的标度性质。
