期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2016
卷号：113
期号：45
页码：12679-12684
DOI：10.1073/pnas.1525793113
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：In directed graphs, relationships are asymmetric and these asymmetries contain essential structural information about the graph. Directed relationships lead to a new type of clustering that is not feasible in undirected graphs. We propose a spectral co-clustering algorithm called di-sim for asymmetry discovery and directional clustering. A Stochastic co-Blockmodel is introduced to show favorable properties of di-sim. To account for the sparse and highly heterogeneous nature of directed networks, di-sim uses the regularized graph Laplacian and projects the rows of the eigenvector matrix onto the sphere. A nodewise asymmetry score and di-sim are used to analyze the clustering asymmetries in the networks of Enron emails, political blogs, and the Caenorhabditis elegans chemical connectome. In each example, a subset of nodes have clustering asymmetries; these nodes send edges to one cluster, but receive edges from another cluster. Such nodes yield insightful information (e.g., communication bottlenecks) about directed networks, but are missed if the analysis ignores edge direction.
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