| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
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A Unifying Modularity in Networks |
| HAO Jun-Jun1, CAI Shui-Ming2, HE Qin-Bin1,3, LIU Zeng-Rong1,2**
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1Institute of System Biology, Shanghai University, Shanghai 200444
2Department of Mathematics, Shanghai University, Shanghai 200444
3Department of Mathematics, Taizhou University, Linhai 317000
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| Cite this article: |
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HAO Jun-Jun, CAI Shui-Ming, HE Qin-Bin et al 2010 Chin. Phys. Lett. 27 128901 |
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Abstract We propose a new modularity criterion in complex networks, called the unifying modularity q which is independent of the number of partitions. It is shown that, for a given network, the relationship between the upper limit of Q and the number of the partitions, k, is sup(Qk)=(k−1)/k. Since the range of Q for each partition number is inconsistent, we try to extend the concept Q to unifying modularity q, which is independent of the number of partitions. Subsequently, we indicate that it is more accurately to determine the number of partitions by using unifying modularity q than Q.
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| Keywords:
89.75.Hc
87.23.Ge
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Received: 13 June 2010
Published: 23 November 2010
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| PACS: |
89.75.Hc
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(Networks and genealogical trees)
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87.23.Ge
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(Dynamics of social systems)
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