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2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM) (2016)
San Francisco, CA, USA
Aug. 18, 2016 to Aug. 21, 2016
ISBN: 978-1-5090-2847-4
pp: 41-48
Zhefeng Wang , School of Computer Science and Technology, University of Science and Technology of China, Hefei, China
Lingyang Chu , School of Computing Science, Simon Fraser University, Burnaby, Canada
Jian Pei , School of Computing Science, Simon Fraser University, Burnaby, Canada
Abdullah Al-Barakati , King Abdulaziz University, Jeddah, Saudi Arabia
Enhong Chen , School of Computer Science and Technology, University of Science and Technology of China, Hefei, China
ABSTRACT
Extracting dense subgraphs is an important step in many graph related applications. There is a challenging struggle in exploring the tradeoffs between density and size in subgraphs extracted. More often than not, different methods aim at different specific tradeoffs between the two factors. To the best of our knowledge, no existing method can allow a user to explore the full spectrum of the tradeoffs using a single parameter. In this paper, we investigate this problem systematically. First, since the existing studies cannot find highly compact dense subgraphs, we formulate the problem of finding very dense but relatively small subgraphs. Second, we connect our problem with the existing methods and propose a unified framework that can explore the tradeoffs between density and size of dense subgraphs extracted using a hyper-parameter. We give theoretical upper and lower bounds on the hyper-parameter so that the range where the unified framework can produce non-trivial subgraphs is determined. Third, we develop an efficient quadratic programming method for the unified framework, which is a generalization and extension to the existing methods. We show that optimizing the unified framework is essentially a relaxation of the maximization of a family of density functions. Last, we report a systematic empirical study to verify our findings.
INDEX TERMS
Quadratic programming, Density functional theory, Linear programming, Electronic mail, Social network services, Bioinformatics, Mathematical programming
CITATION

Z. Wang, L. Chu, J. Pei, A. Al-Barakati and E. Chen, "Tradeoffs between density and size in extracting dense subgraphs: A unified framework," 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), San Francisco, CA, USA, 2016, pp. 41-48.
doi:10.1109/ASONAM.2016.7752211
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