Fuzzy modularity and fuzzy community structure in networks |
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Authors: | Jian Liu |
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Affiliation: | 1.LMAM and School of Mathematical Sciences, Peking University,Beijing,P.R. China |
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Abstract: | To find the fuzzy community structure in a complex
network, in which each node has a certain probability of belonging
to a certain community, is a hard problem and not yet satisfactorily
solved over the past years. In this paper, an extension of
modularity, the fuzzy modularity is proposed, which can provide a
measure of goodness for the fuzzy community structure in networks.
The simulated annealing strategy is used to maximize the fuzzy
modularity function, associating with an alternating iteration based
on our previous work. The proposed algorithm can efficiently
identify the probabilities of each node belonging to different
communities with random initial fuzzy partition during the cooling
process. An appropriate number of communities can be automatically
determined without any prior knowledge about the community
structure. The computational results on several artificial and
real-world networks confirm the capability of the algorithm. |
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Keywords: | |
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