arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1202.4805cs.SIphysics.soc-ph
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基于聚类的大规模社交网络快速生成

Fast Generation of Large Scale Social Networks with Clustering

Joseph J. Pfeiffer, Timothy La Fond, Sebastian Moreno, Jennifer Neville

摘要:

社交网络文献中的一个关键挑战是网络生成的问题-也就是说,我们如何创建与大多数现实世界网络中传统特征相匹配的合成网络?社交网络中存在的重要特征包括幂律度分布、小直径和大量聚类;然而,大多数当前的网络生成器,如Chung Lu和Kronecker模型,在很大程度上忽略了图中存在的聚类,并选择专注于保留其他网络统计数据,如幂律分布。指数随机图模型等模型具有传递性参数,但在计算上难以学习,使得扩展到大型现实世界网络变得棘手。在这项工作中,我们提出了一个扩展的Chung Lu随机图模型,传递Chung Lu(TCL)模型,其中包括一个随机传递边的概念。也就是说,有一定的概率,它会选择连接到一个节点正好两跳远,已经介绍给一个“朋友的朋友”。在所有其他情况下,它将遵循标准的Chung Lu模型,根据给定的不变分布从图中的任何地方选择一个“随机冲浪者”。我们证明了TCL的预期度分布等于原始图的度分布,同时能够捕获网络中存在的聚类。我们的模型所需的单个参数可以在具有数百万条边的图上在几秒钟内学习,而网络可以在边数呈线性的时间内生成。我们在四个真实世界的社交网络上展示了TCL的性能,包括一个具有数十万个节点和数百万条边的电子邮件数据集,显示TCL生成的图与原始网络的度分布,聚类系数和跳点图相匹配。

英文摘要:

A key challenge within the social network literature is the problem of network generation - that is, how can we create synthetic networks that match characteristics traditionally found in most real world networks? Important characteristics that are present in social networks include a power law degree distribution, small diameter and large amounts of clustering; however, most current network generators, such as the Chung Lu and Kronecker models, largely ignore the clustering present in a graph and choose to focus on preserving other network statistics, such as the power law distribution. Models such as the exponential random graph model have a transitivity parameter, but are computationally difficult to learn, making scaling to large real world networks intractable. In this work, we propose an extension to the Chung Lu ran- dom graph model, the Transitive Chung Lu (TCL) model, which incorporates the notion of a random transitive edge. That is, with some probability it will choose to connect to a node exactly two hops away, having been introduced to a 'friend of a friend'. In all other cases it will follow the standard Chung Lu model, selecting a 'random surfer' from anywhere in the graph according to the given invariant distribution. We prove TCL's expected degree distribution is equal to the degree distribution of the original graph, while being able to capture the clustering present in the network. The single parameter required by our model can be learned in seconds on graphs with millions of edges, while networks can be generated in time that is linear in the number of edges. We demonstrate the performance TCL on four real- world social networks, including an email dataset with hundreds of thousands of nodes and millions of edges, showing TCL generates graphs that match the degree distribution, clustering coefficients and hop plots of the original networks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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