Community detection, with lower time complexity, using coupled Kuramoto oscillators
Authors: 
João E. M. de Oliveira, Marcos G. Quiles, Marcos D. N. Maia, Elbert E. N. MacauAuthors Info & Claims
João E. M. de Oliveira, Marcos G. Quiles, Marcos D. N. Maia, Elbert E. N. MacauAuthors Info & ClaimsPages 1160 - 1166
Abstract
For about two decades, the research topic of Complex Networks has been presented ubiquitously. As a simple and effective framework to express agents and their relationships, several fields of study, from Physics to Sociology, have taken advantage of the powerful representation provided by complex networks. A particular feature inherited by almost any real world network is the presence of densely connected groups of vertices, named modules, clusters or communities. The majority of the proposed techniques does not take advantage of specific features commonly encountered on real networks, such as the power law distribution of vertices' degree (presence of hubs) and its dynamic nature, i.e. vertices, edges and communities normally does not persist invariant regarding to time. Aiming to take into account these two important features, an another ubiquitous phenomenon is applied on detecting communities: synchronization, expressed by coupled Kuramoto oscillators. Here, we extend the Kuramoto's model by introducing a negative coupling between hubs in the network. Moreover, two adjacency lists are used to represent, efficiently, the network structure. Tests have been performed in real network benchmarks, with consistent results achieved.
References
[1]
R. Albert, H. Jeong, and A.-L. Barabási. Diameter of the world wide web. Nature, 401:130--131, 1999.
[2]
A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou. Synchronization in complex networks. Physics Reports, 469:93--153, 2008.
[3]
A.-L. Barabási. Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life. Plume, New York City, NY, USA, 1st edition, 2003.
[4]
J. A. Bondy and U.S. R. Murty. Graph Theory. Graduate Texts in Mathematics, Vol. 244. Springer, New York City, NY, USA, 2008.
[5]
L. Danon, A. Díaz-Guilera, J. Duch, and A. Arenas. Comparing Community Structure Identification. Journal of Statistical Mechanics: Theory and Experiments., P09008:1--10, 2005.
[6]
P. Erdős and A. Rényi. On the Evolution of Random Graphs. Sociometry., 32:425--443, 1969.
[7]
L. Euler. Solutio problematis ad geometriam situs pertinentis. Comment. Acad. Sci. U. Petrop., 8:128--140, 1736.
[8]
S. Fortunato. Community detection in graphs. Physics Reports, 486(3--5):75--174, 2010.
[9]
M. Girvan and M. E. J. Newman. Community Structure in Social and Biological Networks. Journal of Statistical Mechanics: Theory and Experiments., P09008:1--10, 2002.
[10]
D. Greene, D. Doyle, and P. Cunningham. Tracking the evolution of communities in dynamic social networks. Advances in Social Networks Analysis and Mining (ASONAM)., pages 176--183, 2010.
[11]
Y. Kuramoto and H. Araki. International symposium on mathematical problems in theoretical physics. Lecture Notes in Physics., 39:420, 1975.
[12]
D. Li, I. Leyva, J. Almendral, I. Sendiña-Nadal, J. Buldú, S. Havlin, and S. Boccaletti. Synchronization interfaces and overlapping communities in complex networks. Phys. Rev. Lett., 101:168701, 2008.
[13]
D. Lusseau, K. Schneider, O. J. Boisseau, P. Haase, E. Slooten, and S. M. Dawson. The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behavioral Ecology and Sociobiology, pages 396--405, 2003.
[14]
E. Massaro, F. Bagnoli, A. Guazzini, and P. Lió. Information Dynamics Algorithm for Detecting Communities in Networks. Communications in Nonlinear Science and Numerical Simulation, 17:4294--4303, 2012.
[15]
S. Milgram and J. Travers. An experimental study of the small world problem. Publications of the Mathematical Institute of the Hungarian Academy of Sciences., 5(4):17--61, 1960.
[16]
M. E. J. Newman. Finding and Evaluating Community Structure in Networks. Physical Review E., 69:026113:1--15, 2004.
[17]
M. E. J. Newman. Modularity and Community Structure in Networks. Proceedings of the National Academy of Sciences of the United States of America, 23(103):8577--8696, 2006.
[18]
M. E. J. Newman. Networks: An Introduction. Oxford University Press, Oxford, UK, 1st edition, 2010.
[19]
A. Pikovsky, M. Rosenblum, and J. Kurths. Synchronization: a universal concept in nonlinear sciences. The Cambridge nonlinear science series. Cambridge University Press, Cambridge, 2001.
[20]
S. M. Porto and M. G. Quiles. A methodology for generating time-varying complex networks with community structure. ICCSA 2014., pages 344--359, 2014.
[21]
H.-W. Shen, X.-Q. Cheng, and B.-X. Fang. Covariance, correlation matrix, and the multiscale community structure of networks. Physical Review, (016114), 2010.
[22]
D. J. Watts and S. H. Strogatz. Collective Dynamics of 'Small-World' Networks. Nature, 393:440--442, 1998.
[23]
A. T. Winfree. Biological rhythms and the behavior of populations of coupled oscillators. J. Theor. Biol., 16(15):15--42, 1967.
[24]
J. Wu, L. Jiao, C. Jin, F. Liu, M. Gong, R. Shang, and W. Chen. Overlapping community detection via network dynamics. Physical Review., E85(016115):17--61, 2012.
[25]
J. Wu and Y. Jiao. Clustering dynamics of complex discrete-time networks and its application in community detection. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24(033104), 2014.
[26]
W. W. Zachary. An information flow model for conflict and fission in small groups. Journal of Anthropological Research, pages 452--473, 1977.
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April 2015
2418 pages
ISBN:9781450331968
DOI:10.1145/2695664
- Conference Chairs:
- Roger L. Wainwright,
- Juan Manuel Corchado,
- Program Chairs:
- Alessio Bechini,
- Jiman Hong
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Published: 13 April 2015
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