# American Institute of Mathematical Sciences

March  2015, 10(1): i-iii. doi: 10.3934/nhm.2015.10.1i

## Preface: "New trends, models and applications in complex and multiplex networks"

 1 Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, ETSI Agrónomos, 28040, Madrid, Spain, Spain 2 Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, 28933 Móstoles (Madrid), Spain, Spain

Published  February 2015

The real world surrounding us is full of complex systems from various types and categories. Internet, the World Wide Web, biological and biochemical networks (brain, metabolic, protein and genomic networks), transport networks (underground, train, airline networks, road networks), communication networks (computer servers, Internet, online social networks), and many others (social community networks, electric power grids and water supply networks,...) are a few examples of the many existing kinds and types of networks [1,2,3,4,6,8,9,10,11]. In the recent past years, the study of structure and dynamics of complex networks has been the subject of intense interest. Recent advances in the study of complex networked systems has put the spotlight on the existence of more than one type of links whose interplay can affect the structure and function of those systems [5,7]. In these networks, relevant information may not be captured if the single layers are analyzed separately, since these different components and units interact with others through different channels of connectivity and dependencies. The global characteristics and behavior of these systems depend on multiple dimensions of integration, relationship or cleavage of its units.

Citation: Rosa M. Benito, Regino Criado, Juan C. Losada, Miguel Romance. Preface: "New trends, models and applications in complex and multiplex networks". Networks and Heterogeneous Media, 2015, 10 (1) : i-iii. doi: 10.3934/nhm.2015.10.1i
##### References:
 [1] R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 10.1103/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, $1^{st}$ Edition, Addison-Wesley, Boston, 1997. [4] A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks, $1^{st}$ Edition, Cambridge University Press, New York, 2008. doi: 10.1017/CBO9780511791383. [5] S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang and M. Zanin, The structure and dynamics of multilayer networks, Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001. [6] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-308. doi: 10.1016/j.physrep.2005.10.009. [7] M. De Domenico, A. Solè-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M. A. Porter, S. Gómez and A. Arenas, Mathematical formulation of multi-layer networks, Phys. Rev. X, 3 (2013), 399-404. [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., 2006. [10] S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. [11] D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442.

show all references

##### References:
 [1] R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97. doi: 10.1103/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, $1^{st}$ Edition, Addison-Wesley, Boston, 1997. [4] A. Barrat, M. Barthélemy and A. Vespignani, Dynamical Processes on Complex Networks, $1^{st}$ Edition, Cambridge University Press, New York, 2008. doi: 10.1017/CBO9780511791383. [5] S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang and M. Zanin, The structure and dynamics of multilayer networks, Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001. [6] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports, 424 (2006), 175-308. doi: 10.1016/j.physrep.2005.10.009. [7] M. De Domenico, A. Solè-Ribalta, E. Cozzo, M. Kivelä, Y. Moreno, M. A. Porter, S. Gómez and A. Arenas, Mathematical formulation of multi-layer networks, Phys. Rev. X, 3 (2013), 399-404. [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., 2006. [10] S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), 268-276. [11] D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442.
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