Network Analysis Based on Statistical-Thermodynamics Formalism
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- Takaguchi Taro TAKAGUCHI Taro
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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- Ejima Kei EJIMA Kei
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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- Miyazaki Syuji MIYAZAKI Syuji
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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Author(s)
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- Takaguchi Taro TAKAGUCHI Taro
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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- Ejima Kei EJIMA Kei
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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- Miyazaki Syuji MIYAZAKI Syuji
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
Abstract
Random walk on a real social networking service consisting of 2271 nodes is analyzed on the basis of the statistical-thermodynamics formalism to find phase transitions in network structure. Each phase can be related to a characteristic local structure of the network such as a cluster or a hub. For this purpose, the generalized transition matrix is introduced, whose largest eigenvalue yields statistical structure functions. The weighted visiting frequency related to the Gibbs probability measure, which is useful for extracting characteristic local structures, is obtained from the products of the right and left eigenvectors corresponding to the largest eigenvalue. An algorithm to extract the characteristic local structure of each phase is also suggested on the basis of this weighted visiting frequency.
Journal
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- Progress of theoretical physics
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Progress of theoretical physics 124(1), 27-52, 2010-07-25
Publication Office, Progress of Theoretical Physics
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- Network Analysis Based on Statistical-Thermodynamics Formalism
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MIYAZAKI Syuji , TAKAGUCHI Taro
形の科学会誌 = Bulletin of the Society for Science on Form 25(2), 204-205, 2010-11-01
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