Abstract
Community structure is an important topological property of complex networks, which has great significance for understanding the function and organization of networks. Generally, community detection can be formulated as a single-objective or multi-objective optimization problem. Most existing optimization-based community detection algorithms are only applicable to disjoint community structure. However, it has been shown that in most real-world networks, a node may belong to multiple communities implying overlapping community structure. In this paper, we propose a multi-objective evolutionary algorithm for identifying overlapping community structure in complex networks based on the framework of non-dominated sorting genetic algorithm. Two negatively correlated evaluation metrics of community structure, termed as negative fitness sum and unfitness sum, are adopted as the optimization objectives. In our algorithm, link-based adjacency representation of overlapping community structure and a population initialization method based on local expansion are proposed. Extensive experimental results on both synthetic and real-world networks demonstrate that the proposed algorithm is effective and promising in detecting overlapping community structure in complex networks.
Similar content being viewed by others
References
Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97
Arenas A, Fernández A, Gomez S (2008) Analysis of the structure of complex networks at different resolution levels. N J Phys 10:053039
Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
Chen J, Wan Z, Cho YJ (2013) Nonsmooth multiobjective optimization problems and weak vector quasi-variational inequalities. Comput Appl Math 32:291–301
Clauset A, Newman MEJ, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70:066111
Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197
Deb K (2014) Multi-objective optimization. Search methodologies. Springer, New York
Duch J, Arenas A (2005) Community detection in complex networks using extremal optimization. Phys Rev E 72:027104
Fortunato S (2010) Community detection in graphs. Phys Rep 486:75–174
Fortunato S, Barthélemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci USA 104:36–41
Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99:7821–7826
Gong M, Fu B, Jiao L (2011) Memetic algorithm for community detection in networks. Phys Rev E 84:056101
Gong M, Ma L, Zhang Q, Jiao L (2012) Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Phys A 391:4050–4060
Gong M, Chen X, Ma L, Zhang Q, Jiao L (2013) Identification of multi-resolution network structures with multi-objective immune algorithm. Appl Soft Comput 13:1705–1717
Gregory S (2010) Finding overlapping communities in networks by label propagation. N J Phys 12:103018
Kumpula J, Saramäki J, Kaski K, Kertész J (2007) Limited resolution and multiresolution methods in complex network community detection. In: Proceddings of SPIE 4th international symposium on fluctuations and noise, pp 660116–660116
Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78:046110
Lancichinetti A, Fortunato S, Kertesz J (2009) Detecting the overlapping and hierarchical community structure in complex networks. N J Phys 11:033015
Lee C, Reid F, McDaid A, Hurley N (2010) Detecting highly overlapping community structure by Greedy clique expansion. In: Proceedings of international workshop on social network mining and analysis (SNAKDD 2010), Washington DC, pp 33–42
Li Z, Zhang S, Wang RS, Zhang XS, Chen L (2008) Quantitative function for community detection. Phys Rev E 77:036109
Lusseau D (2003) The emergent properties of a dolphin social network. Proc R Soc Lond B 270:S1860–1888
Martin R, Carl TB (2007) An information-theoretic framework for resolving community structure in complex networks. Proc Natl Acad Sci USA 104:7327–7331
Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256
Newman MEJ (2004a) Detecting community structure in networks. Eur Phys J B 38:321–330
Newman MEJ (2004b) Fast algorithm for detecting community structure in networks. Phys Rev E 69:066133
Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74:036104
Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113
Nicosia V, Mangioni G, Carchiolo V, Malgeri M (2009) Extending the definition of modularity to directed graphs with overlapping communities. J Stat Mech 3:P03024
Palla G, Derényi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435:814–818
Park YJ, Song MS (1989) A genetic algorithm for clustering problems. In: Proceedings of the 3rd annual conference on genetic algorithms, pp 2–9
Pizzuti C (2008) GA-Net: A genetic algorithm for community detection in social networks. In: Rudolph G, Jansen T, Beume N, Lucas S, Poloni C (eds) Parallel problem solving from nature (PPSN), Springer, Berlin, pp. 1081–1090
Pizzuti C (2009) Overlapped community detection in complex networks. In: Preceedings of 2009 genetic and evolutionary computation conference (GECCO’09), Montral Qubec, pp 859–866
Pizzuti C (2012) A multiobjective genetic algorithm to find communities in complex networks. IEEE Trans Evol Comput 16:418–430
Psorakis I, Roberts S, Ebden M, Sheldon B (2011) Overlapping community detection using bayesian non-negative matrix factorization. Phys Rev E 83:066114
Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Defining and identifying communities in networks. Proc Natl Acad Sci USA 101:2658–2663
Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76:036106
Salazar FJT, Macau EEN, Winter OC (2015) Pareto Frontier for the time-energy cost vector to an Earth–Moon transfer orbit using the patched-conic approximation. Comput Appl Math 34:461–475. doi:10.1007/s40314-014-0154-7
Shang R, Bai J, Jiao L, Jin C (2013) Community detection based on modularity and an improved genetic algorithm. Phys A 392:1215–1231
Shi C, Yan ZY, Cai YN, Wu B (2012) Multi-objective community detection in complex networks. Appl Soft Comput 12:850–859
Shi C, Yu PS, Cai Y, Yan Z, Wu B (2011) On selection of objective functions in multi-objective community detection. In: Proceedings of the 20th ACM international conference on information and knowledge management (CIKM’11), Glasgow, Scotland, pp 2301–2304
Strogatz SH (2001) Exploring complex networks. Nature 410:268–276
Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393:440–442
Xie J, Szymanski BK (2012) Towards linear time overlapping community detection in social networks. In: Proceedings of the Pacific-Asia conference on knowledge discovery and data mining (PAKDD), Kuala Lumpur, pp 25–36
Zachary WW (1997) An information flow model for conflict and fission in small groups. J Anthropol Res 33:452–473
Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731
Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Proceedings of evolutionary methods for design optimization and control with applications to industrial problems. Greece, Athens, p 95C100
Acknowledgments
This research work is funded by the National Science Foundation of China (61271316), Shanghai Key Laboratory of Integrated Administration Technologies for Information Security, and Chinese National Engineering Laboratory for Information Content Analysis Technology.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Geraldo Nunes Silva.
Rights and permissions
About this article
Cite this article
Yuxin, Z., Shenghong, L. & Feng, J. Overlapping community detection in complex networks using multi-objective evolutionary algorithm. Comp. Appl. Math. 36, 749–768 (2017). https://doi.org/10.1007/s40314-015-0260-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40314-015-0260-1
Keywords
- Complex network
- Community detection
- Overlapping community structure
- Optimization problem
- Multi-objective evolutionary algorithm