大型网络中的社区结构：自然集群规模和大型明确集群的缺乏
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters
摘要：
大量的工作致力于界定和确定社会和信息网络中的集群或社区。我们从一个新的角度探讨了在大型社会和信息网络中识别有意义社区的几个问题，并得出了几个引人注目的结论。我们采用近似算法的图形划分问题的特征作为一个函数的大小的统计和结构特性的分区的图形，可以解释为社区。特别是，我们定义了网络社区配置文件图，它的特点是“最好的”可能的社区-根据电导措施-在很大范围内的大小尺度。我们研究了100多个大型的真实世界的社交和信息网络。我们的研究结果表明，一个显着更精细的图片社区结构在大型网络比以前已经赞赏。特别是，我们观察到，在非常小的规模上，紧密的社区几乎不与网络的其他部分相连;而规模较大的社区逐渐“融入”网络的扩展器样核心，从而变得不那么“社区样”。“这种行为甚至在定性层面上都无法用任何常用的网络生成模型来解释。此外，这与人们根据扩展图、低维或流形图以及作为社区发现算法测试平台的小型社交网络的直觉所期望的完全相反。我们已经发现，生成图模型，其中通过迭代的“森林火灾”燃烧过程添加新的边缘，能够生成显示网络社区配置文件图的图，类似于我们在网络数据集中观察到的。
英文摘要：
A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. We employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, we define the network community profile plot, which characterizes the "best" possible community--according to the conductance measure--over a wide range of size scales. We study over 100 large real-world social and information networks. Our results suggest a significantly more refined picture of community structure in large networks than has been appreciated previously. In particular, we observe tight communities that are barely connected to the rest of the network at very small size scales; and communities of larger size scales gradually "blend into" the expander-like core of the network and thus become less "community-like." This behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models. Moreover, it is exactly the opposite of what one would expect based on intuition from expander graphs, low-dimensional or manifold-like graphs, and from small social networks that have served as testbeds of community detection algorithms. We have found that a generative graph model, in which new edges are added via an iterative "forest fire" burning process, is able to produce graphs exhibiting a network community profile plot similar to what we observe in our network datasets.
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