A Simple Taxonomy of Multilayer Networks

International Journal of Computer Trends and Technology (IJCTT)          
© 2016 by IJCTT Journal
Volume-31 Number-1
Year of Publication : 2016
Authors : Andrey A. Shchurov, Radek Mařík


Andrey A. Shchurov, Radek Mařík "A Simple Taxonomy of Multilayer Networks". International Journal of Computer Trends and Technology (IJCTT) V31(1):20-24, January 2016. ISSN:2231-2803. www.ijcttjournal.org. Published by Seventh Sense Research Group.

Abstract -
one of the major goals of multilayer networks is providing proper and suitable representations of complex systems with many interdependent components, which, in turn, might interact through many different channels. However, the terminology referring to systems with multiple different relations has not yet reached a consensus. This work introduces a simple taxonomy of multilayer networks. Four different dimensions characterize the basic metrics of structural properties. Based on the taxonomy, an appropriate formal definition is presented.

[1] M. v. Steen, Graph Theory and Complex Networks: An Introduction, 1st ed., Maarten van Steen, 2010.
[2] S. Boccaletti, G. Bianconi, R. Criado, C. del Genio, J. Gomez-Gardenes, M. Romance, I. Sendina-Nadal, Z. Wang and M. Zanin, "The structure and dynamics of multilayer networks," Physics Reports, vol. 544, no. 1, pp. 1-122, 2014.
[3] S. Strogatz, "Exploring complex networks," Nature, vol. 410, pp. 268-276, 2001.
[4] R. Albert and A.-L. Barabasi, "Statistical mechanics of complex networks," Rev. Mod. Phys., vol. 74, no. 1, pp. 47- 97, January 2002.
[5] M. Newman, "The Structure and Function of Complex Networks," SIAM Review, vol. 45, no. 2, pp. 167-256, 2003.
[6] G. Xie, J. Zhan, D. Maltz, H. Zhang, A. Greenberg, G. Hjalmtysson and J. Rexford, "On static reachability analysis of IP networks," in in Proc. IEEE INFOCOM, 2005.
[7] P. Matousek, J. Rab, O. Rysavy and M. Sveda, "A Formal Model for Network-Wide Security Analysis," in Engineering of Computer Based Systems, 2008. ECBS 2008. 15th Annual IEEE International Conference and Workshop on the, 2008.
[8] M. De Domenico, A. Sole-Ribalta, E. Cozzo, M. Kivela, Y. Moreno, M. Porter, S. Gomez and A. Arenas, "Mathematical Formulation of Multilayer Networks," Phys. Rev. X, vol. 3, no. 4, p. 041022, December 2013.
[9] M. Kivela, A. Arenas, M. Barthelemy, J. Gleeson, Y. Moreno and M. Porter, "Multilayer networks," Journal of Complex Networks, vol. 2, no. 3, pp. 203-271, 2014.
[10] J. D. McCabe, Network Analysis, Architecture, and Design, 3rd ed., Morgan Kaufmann Publishers, 2007.
[11] A. Shchurov, "A Multilayer Model of Computer Networks," International Journal of Computer Trends and Technology (IJCTT), vol. 26, no. 1, pp. 12-16, 2015.
[12] D. Cai, Z. Shao, X. He, X. Yan and J. Han, "Community mining from multi-relational networks," in In Proceedings of the 9th European Conference on Principles and Practice of Knowledge Discovery in Databases, 2005.
[13] D. Zhou, S. Orshanskiy, H. Zha and L. Giles, "Co-ranking Authors and Documents in a Heterogeneous Network," in Proceedings of the 2007 Seventh IEEE International Conference on Data Mining, 2007.
[14] M. Dickison, S. Havlin and H. Stanley, "Epidemics on interconnected networks," Phys. Rev. E, vol. 85, no. 6, p. 066109, 2012.
[15] A. Saumell-Mendiola, A. Serrano and M. Boguna, "Epidemic spreading on interconnected networks," Phys. Rev. E, vol. 86, no. 2, p. 026106, 2012.
[16] J. Donges, H. Schultz, N. Marwan, Y. Zou and J. Kurths, "Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks," Eur. Phys. J.B., vol. 84, no. 4, pp. 635-651, 2011.
[17] S. Buldyrev, R. Parshani, G. Paul, E. Stanley and S. Havlin, "Catastrophic cascade of failures in interdependent networks," Nature, vol. 464, pp. 1025-1028, 2010.
[18] R. Parshani, S. Buldyrev and S. Havlin, "Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition," Phys. Rev. Lett., vol. 105, no. 4, p. 048701, 2010.
[19] J. Gao, S. Buldyrev, S. Havlin and E. Stanley, "Robustness of a Network of Network," Phys. Rev. Lett., vol. 107, no. 19, p. 195701, 2011.
[20] M. Newman, "Mixing patterns in networks," Phys. Rev. E, vol. 67, p. 026126, 2003.
[21] A. Vazquez, "Spreading dynamics on heterogeneous populations: Multitype network approach," Phys. Rev. E, vol. 74, no. 6, p. 066114, 2006.
[22] M. Kurant and P. Thiran, "Layered Complex Networks," Phys. Rev. Lett., vol. 96, no. 13, April 2006.
[23] M. Kurant, P. Thiran and P. Hagmann, "Error and Attack Tolerance of Layered Complex Networks," Phys. Rev. E, vol. 76, no. 2, August 2007.
[24] L. Sola, M. Romance, R. Criado, J. Flores, A. García del Amo and S. Boccaletti, "Eigenvector centrality of nodes in multiplex networks," Chaos, vol. 23, no. 2, p. 033131, 2013.
[25] V. Stroele, J. Oliveira, G. Zimbrao and J. Souza, "Mining and Analyzing Multirelational Social Networks," in Computational Science and Engineering, 2009. CSE '09. International Conference on, 2009.
[26] P. Pattison and S. Wasserman, "Logit models and logistic regressions for social networks: II. Multivariate relations," British Journal of Mathematical and Statistical Psychology, vol. 52, pp. 169-193, 1999.
[27] M. Barigozzi, G. Fagiolo and D. Garlaschelli, "Multinetwork of international trade: A commodity-specific analysis," Phys. Rev. E, vol. 81, p. 046104, 2010.
[28] M. Berlingerio, M. Coscia, F. Giannotti, A. Monreale and D. Pedreschi, "Foundations of Multidimensional Network Analysis," in Advances in Social Networks Analysis and Mining (ASONAM), 2011 International Conference on, 2011.
[29] P. Mucha and M. Porter, "Communities in multislice voting networks," Chaos, vol. 20, no. 4, p. 041108, 2010.
[30] P. Mucha, T. Richardson, K. Macon, M. Porter and J.-P. Onne, "Community Structure in Time-Dependent, Multiscale and Multiplex Networks," Science, vol. 328, pp. 876-878, 2010.
[31] S. Funk and V. Jansen, "Interacting epidemics on overlay networks," Phys. Rev. E, vol. 81, no. 3, p. 036118, 2010.
[32] P. Holme and J. Saramaki, "Temporal networks," Physics Reports, vol. 519, no. 3, pp. 97-125, 2012.
[33] M. Rocklin and A. Pinar, "Latent Clustering on Graphs with Multiple Edge Types," in Proceedings of the 8th International Conference on Algorithms and Models for the Web Graph, 2011.
[34] R. Criado, M. Romance and M. Vela-Perez, "Hyperstructures, a New Approach to Complex Systems," I.J. Bifurcation and Chaos, vol. 20, no. 3, pp. 877-883, 2010.
[35] F. Sorrentino, "Synchronization of hypernetworks of coupled dynamical systems," New Journal of Physics, vol. 14, no. 3, p. 033035, 2012.
[36] C. Berge, Hypergraphs: Combinatorics of Finite Sets, North Holland, 1989.
[37] A. Wong-Jiru, Graph Theoretical Analysis of Networkcentric Operations Using Multi-layer Models, BiblioScholar, 2012.

complex systems, computer networks, multilayer networks, taxonomy.