Abstract
Algebraic connectivity (second smallest eigenvalue of the supra-Laplacian matrix of the underlying multilayer network) and inter-layer coupling strength play an important role in the diffusion processes on the multiplex networks. In this work, we study the effect of inter-layer coupling strength, topological structure on algebraic connectivity in weighted multiplex networks. The results show a remarkable transition in the value of algebraic connectivity from classical cases where the inter-layer coupling strength is homogeneous. We investigate various topological structures in multiplex networks using configuration model, the Barabasi-Albert model (BA) and empirical data-set of multiplex networks. The threshold value \(d_c^{'}\) is found smaller in heterogeneous networks for all the multiplex networks as compared to the homogeneous case. Experimental results reveal that the topological structure (average clustering coefficient) and inter-layer coupling strength has considerable effect on threshold values for the algebraic connectivity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aguirre, J., Sevilla-Escoboza, R., Gutiérrez, R., Papo, D., Buldú, J.: Synchronization of interconnected networks: the role of connector nodes. Phys. Rev. Lett. 112(24), 248701 (2014)
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47 (2002)
Allen-Perkins, A., de Assis, T.A., Pastor, J.M., Andrade, R.F.: Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators. Phys. Rev. E 96(4), 042312 (2017)
Boccaletti, S., et al.: The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1–122 (2014)
Royal Society (Great Britain): Proceedings of the Royal Society of London, no. v. 58. Taylor & Francis (1895). https://books.google.co.in/books?id=60aL0zlT-90C
Cozzo, E., Banos, R.A., Meloni, S., Moreno, Y.: Contact-based social contagion in multiplex networks. Phys. Rev. E 88(5), 050801 (2013)
De Abreu, N.M.M.: Old and new results on algebraic connectivity of graphs. Linear Algebra Appl. 423(1), 53–73 (2007)
De Domenico, M., Granell, C., Porter, M.A., Arenas, A.: The physics of spreading processes in multilayer networks. Nat. Phys. 12(10), 901 (2016)
Gomez, S., Diaz-Guilera, A., Gomez-Gardenes, J., Perez-Vicente, C.J., Moreno, Y., Arenas, A.: Diffusion dynamics on multiplex networks. Phys. Rev. Lett. 110(2), 028701 (2013)
Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014)
Magnani, M., Micenkova, B., Rossi, L.: Combinatorial analysis of multiple networks. arXiv preprint arXiv:1303.4986 (2013)
Martínez, J.H., Boccaletti, S., Makarov, V.V., Buldú, J.M.: Multiplex networks of musical artists: the effect of heterogeneous inter-layer links. arXiv preprint arXiv:1805.08711 (2018)
Mohar, B., Alavi, Y., Chartrand, G., Oellermann, O.: The Laplacian spectrum of graphs. In: Graph Theory, Combinatorics, and Applications, vol. 2(871–898), p. 12 (1991)
Newman, M.E.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577–8582 (2006)
Radicchi, F., Arenas, A.: Abrupt transition in the structural formation of interconnected networks. Nat. Phys. 9(11), 717 (2013)
Saumell-Mendiola, A., Serrano, M.Á., Boguná, M.: Epidemic spreading on interconnected networks. Phys. Rev. E 86(2), 026106 (2012)
Sole-Ribalta, A., De Domenico, M., Kouvaris, N.E., Diaz-Guilera, A., Gomez, S., Arenas, A.: Spectral properties of the Laplacian of multiplex networks. Phys. Rev. E 88(3), 032807 (2013)
Wang, Y., Xiao, G.: Effects of interconnections on epidemics in network of networks. In: 2011 7th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM), pp. 1–4. IEEE (2011)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Kumar, R., Singh, A., Cherifi, H. (2018). Effect of Topological Structure and Coupling Strength in Weighted Multiplex Networks. In: Chen, X., Sen, A., Li, W., Thai, M. (eds) Computational Data and Social Networks. CSoNet 2018. Lecture Notes in Computer Science(), vol 11280. Springer, Cham. https://doi.org/10.1007/978-3-030-04648-4_33
Download citation
DOI: https://doi.org/10.1007/978-3-030-04648-4_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04647-7
Online ISBN: 978-3-030-04648-4
eBook Packages: Computer ScienceComputer Science (R0)