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September  2012, 7(3): i-iii. doi: 10.3934/nhm.2012.7.3i

Preface: Mesoscales and evolution in complex networks: Applications and related topics

Regino Criado 1, , Rosa M. Benito 2, , Miguel Romance 1, and  Juan C. Losada 2,

1. 

Departamento de Matemática Aplicada, Universidad Rey Juan Carlos (URJC), C/ Tulipán s/n, 28933-Móstoles, Madrid, Spain, Spain
2. 

Departamento de Física y Mecánica, ETSI Agrónomos, Universidad Politécnica de Madrid, C/ Ciudad universitaria s/n, 28040 Madrid, Spain, Spain

Published  October 2012

The study of networks has become one of the paradigms of the science of complexity as well as a fascinating branch of research in applied mathematics, physics, engineering, sociology, biology and science in general. Different systems such as transport networks (underground, train, airline networks, road networks), communication networks (computer servers, Internet, online social networks), neural networks (neural interaction networks and brain networks), biochemical networks (metabolic, protein and genomic networks), trophic networks, social community networks, marketing and recommendation networks, other infrastructure networks (electric power grids, water supply networks) and many others (including the World Wide Web)([1],[3],[4],[7],[8],[9],[10]) are known to have behavioral and structural characteristics in common, and they can be studied by using non-linear mathematical techniques and computer modeling approaches. The interest on complex networks has certainly been promoted by the optimized rating of computing facilities, and by the availability of data on large real networks (including the World Wide Web, cortical networks, citation networks from Scientific Citation Index and online social networks). This focused section is characterized for emphasizing the latest applications of complex networks rather than the theoretical aspects, but covering several aspects as topological properties, algorithms and computation tools, models of interactions between complex systems, synchronization, control and some other related topics.

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Citation: Regino Criado, Rosa M. Benito, Miguel Romance, Juan C. Losada. Preface: Mesoscales and evolution in complex networks: Applications and related topics. Networks and Heterogeneous Media, 2012, 7 (3) : i-iii. doi: 10.3934/nhm.2012.7.3i
References:
[1]

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 0.1103/RevModPhys.74.47.

[2]

A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.

[3]

Y. Bar-Yam, "Dynamics of Complex Systems," Addison-Wesley, 1997.

[4]

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-303. doi: 10.1016/j.physrep.2005.10.009.

[5]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Resilience of the Internet to random breakdowns, Physical Review Letters, 85 (2000), 4626-4628. doi: 10.1103/PhysRevLett.85.4626.

[6]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Breakdown of the Internet under intentional attacks, Physical Review Letters, 86 (2001), 3682-3685. doi: 10.1103/PhysRevLett.86.3682.

[7]

L. Fontoura Costa, et al, "Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications,'' arXiv:0711.3199v3, [physics.soc-ph], 2006.

[8]

M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256. doi: 10.1137/S003614450342480.

[9]

M. E. J. Newman, A. L. Barabási and D. J. Watts, The structure and dynamics of networks, Princeton University Press, Princeton, NJ., 167-256, 2006.

[10]

S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. doi: 10.1038/35065725.

[11]

D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. doi: 10.1038/30918.

show all references

References:
[1]

R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 0.1103/RevModPhys.74.47.

[2]

A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-512. doi: 10.1126/science.286.5439.509.

[3]

Y. Bar-Yam, "Dynamics of Complex Systems," Addison-Wesley, 1997.

[4]

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-303. doi: 10.1016/j.physrep.2005.10.009.

[5]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Resilience of the Internet to random breakdowns, Physical Review Letters, 85 (2000), 4626-4628. doi: 10.1103/PhysRevLett.85.4626.

[6]

R. Cohen, K. Erez, D. Ben-Avraham and S. Havril, Breakdown of the Internet under intentional attacks, Physical Review Letters, 86 (2001), 3682-3685. doi: 10.1103/PhysRevLett.86.3682.

[7]

L. Fontoura Costa, et al, "Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications,'' arXiv:0711.3199v3, [physics.soc-ph], 2006.

[8]

M. E. J. Newman, The structure and function of complex networks, SIAM Review, 45 (2003), 167-256. doi: 10.1137/S003614450342480.

[9]

M. E. J. Newman, A. L. Barabási and D. J. Watts, The structure and dynamics of networks, Princeton University Press, Princeton, NJ., 167-256, 2006.

[10]

S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. doi: 10.1038/35065725.

[11]

D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. doi: 10.1038/30918.

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