A Simple Taxonomy of Multilayer Networks
Andrey A. Shchurov, Radek Ma?ík "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.
References
[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.
Keywords
complex systems, computer networks,
multilayer networks, taxonomy.