研究网络节点演化的可扩展位置分析
Scalable Positional Analysis for Studying Evolution of Nodes in Networks
摘要：
在社会网络分析中，位置概念背后的基本思想是发现具有相似结构特征的参与者。社交网络的位置分析涉及到使用等价的概念，捕捉演员之间的关系结构的演员划分成不相交的集。位置分析的经典方法，如正则等价和公平划分，在对参与者进行分组时过于严格，并且经常导致现实世界网络中参与者的琐碎划分。图的Epperly Equitable Partition（EEP）在精神上类似于随机块模型，是对结构等价概念的有用放松，从而导致有意义的演员划分。在本文中，我们提出并实现了一个新的可扩展的分布式算法的基础上MapReduce方法来找到一个图的EEP。随机幂律图的实证研究表明，我们的算法是高度可扩展的稀疏图，从而使我们能够研究非常大规模的网络上的位置分析。我们还提出了我们的算法上的facebook和flickr社交图的时间演变快照的结果。结果表明，位置分析的重要性，大型动态网络。
英文摘要：
In social network analysis, the fundamental idea behind the notion of position is to discover actors who have similar structural signatures. Positional analysis of social networks involves partitioning the actors into disjoint sets using a notion of equivalence which captures the structure of relationships among actors. Classical approaches to Positional Analysis, such as Regular equivalence and Equitable Partitions, are too strict in grouping actors and often lead to trivial partitioning of actors in real world networks. An Epsilon Equitable Partition (EEP) of a graph, which is similar in spirit to Stochastic Blockmodels, is a useful relaxation to the notion of structural equivalence which results in meaningful partitioning of actors. In this paper we propose and implement a new scalable distributed algorithm based on MapReduce methodology to find EEP of a graph. Empirical studies on random power-law graphs show that our algorithm is highly scalable for sparse graphs, thereby giving us the ability to study positional analysis on very large scale networks. We also present the results of our algorithm on time evolving snapshots of the facebook and flickr social graphs. Results show the importance of positional analysis on large dynamic networks.
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