Abstract
Community detection is one of the most interesting problems in the study of social networks. Most recent studies have focused on the design of algorithms to determine communities without knowing the number of communities in advance. This paper defines the k-path graph and generalizes Newman’s modularity as a weighted modularity, and provides a detailed discussion on the relationship between eigenvalues and the maximum modularity of the network. It is proved that the maximum modularity of the weighted graphs depend on both the maximum eigenvalue and a relative parameter.
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Acknowledgements
This work is supported by Natural Science Foundation of China (71471106) and Specialized Research Fund for the Doctoral Program of Higher Education (20133704110003).
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Ma, YH., Wang, WQ. (2016). Weighted Modularity on a k-Path Graph. In: Hussain, A. (eds) Electronics, Communications and Networks V. Lecture Notes in Electrical Engineering, vol 382. Springer, Singapore. https://doi.org/10.1007/978-981-10-0740-8_48
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DOI: https://doi.org/10.1007/978-981-10-0740-8_48
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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-10-0740-8
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