Geodesic
The maximum likelihood method for detecting communities in communication networks
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 3, pp. 200-214

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The community detection in social and communication networks is an important problem in many applied fields: biology, sociology, social networks. This is especially true for networks that are represented by large graphs. In this paper, we propose a method for community detection based on the maximum likelihood method for the random formation of a network with given parameters of the tightness of connections within the community and between different communities. A numerical algorithm for finding the maximum of the objective function over all possible network partitions is described. The algorithm is implemented and tested on real networks of small dimension.
Keywords: network communities, detecting communities in a network, maximum likelihood method, Gibbs sampling. 
@article{VSPUI_2018_14_3_a1,
     author = {V. V. Mazalov and N. N. Nikitina},
     title = {The maximum likelihood method for detecting communities in communication networks},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {200--214},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2018_14_3_a1/}
}
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V. V. Mazalov; N. N. Nikitina. The maximum likelihood method for detecting communities in communication networks. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 3, pp. 200-214. http://geodesic.mathdoc.fr/item/VSPUI_2018_14_3_a1/