摘要
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science1, 2, 3. Recent studies suggest that networks often exhibit hierarchical organization, in which vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases the groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks or genetic regulatory networks) or communities in social networks4, 5, 6, 7. Here we present a general technique for inferring hierarchical structure from network data and show that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients and short path lengths. We further show that knowledge of hierarchical structure can be used to predict missing connections in partly known networks with high accuracy, and for more general network structures than competing techniques8. Taken together, our results suggest that hierarchy is a central organizing principle of complex networks, capable of offering insight into many network phenomena.
摘要译文
网络在最近几年成为一个宝贵的工具，用于描述和量化复杂系统科学的许多分支SUP 1 / SUP SUP 2 / SUP SUP 3 / SUP。最近的研究表明，网络通常呈现分层组织的，其顶点分组进一步细分为基的基团，等等在多个尺度。在许多情况下，被发现的基团为对应于已知的功能单元，如生态位中的食物链，模块中的生化网络（蛋白相互作用网络，在社交网络中的代谢网络和基因调控网络）或社区SUP 4 / SUP SUP 5 / SUP SUP 6 / SUP SUP 7 / SUP。从网络数据环层次结构，并显示该层次结构的存在，可以同时解释和定量重现网络的许多常用观察到的拓扑性质，如右偏度分布，高集群系数和短路径长度。我们进一步显示分级结构的知识可以被用来预测缺少连接的部分已知的网络具有精度高，和比同类技术SUP 8 / SUP更一般的网络结构。总之，我们的研究结果表明，层次结构复杂的网络的核心组织原则，能够提供洞察到许多网络现象。
Aaron Clauset[1][3]; Cristopher Moore[1][2][3]; M. E. J. Newman[3][4];. Hierarchical structure and the prediction of missing links in networks[J]. Nature; London, 2008,453(7191): 98-101