Abstract
In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G. Each layer network is the result of probabilistically removing links and nodes from G. The resulting network includes any link that appears in at least K layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the M-layer network is in a given configuration for some particular graph structures (explicit results are provided for a line and an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow Poisson distributions. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.
- Nahid Azimi-Tafreshi, Sergey N Dorogovtsev, and José FF Mendes. 2014 a. Giant components in directed multiplex networks. Physical Review E, Vol. 90, 5 (2014), 052809.Google Scholar
Cross Ref
- Nahid Azimi-Tafreshi, Jesus Gómez-Gardenes, and Sergey N Dorogovtsev. 2014 b. k-core percolation on multiplex networks. Physical Review E, Vol. 90, 3 (2014), 032816.Google Scholar
Cross Ref
- Amitabha Bagchi, Sainyam Galhotra, Tarun Mangla, and Cristina M Pinotti. 2015. Optimal radius for connectivity in duty-cycled wireless sensor networks. ACM Transactions on Sensor Networks (TOSN) Vol. 11, 2 (2015), 36. Google Scholar
Digital Library
- Prithwish Basu, Ravi Sundaram, and Matthew Dippel. 2015. Multiplex networks: A generative model and algorithmic complexity Proceedings of the 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2015. ACM, 456--463. Google Scholar
Digital Library
- Federico Battiston, Jacopo Iacovacci, Vincenzo Nicosia, Ginestra Bianconi, and Vito Latora. 2016. Emergence of multiplex communities in collaboration networks. PloS one, Vol. 11, 1 (2016), e0147451.Google Scholar
Cross Ref
- Gareth J Baxter, Sergey N Dorogovtsev, José FF Mendes, and Davide Cellai. 2014. Weak percolation on multiplex networks. Physical Review E, Vol. 89, 4 (2014), 042801.Google Scholar
Cross Ref
- Stefano Boccaletti, Ginestra Bianconi, Regino Criado, Charo I Del Genio, Jesús Gómez-Gardenes, Miguel Romance, Irene Sendina-Nadal, Zhen Wang, and Massimiliano Zanin. 2014. The structure and dynamics of multilayer networks. Physics Reports, Vol. 544, 1 (2014), 1--122.Google Scholar
Cross Ref
- Charles D Brummitt, Kyu-Min Lee, and K-I Goh. 2012. Multiplexity-facilitated cascades in networks. Physical Review E, Vol. 85, 4 (2012), 045102.Google Scholar
Cross Ref
- Francesco Buccafurri, Vincenzo Daniele Foti, Gianluca Lax, Antonino Nocera, and Domenico Ursino. 2013. Bridge analysis in a social internetworking scenario. Information Sciences Vol. 224 (2013), 1--18. Google Scholar
Digital Library
- Ed Bullmore and Olaf Sporns. 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience Vol. 10, 3 (2009), 186--198.Google Scholar
Cross Ref
- Davide Cellai, Eduardo López, Jie Zhou, James P Gleeson, and Ginestra Bianconi. 2013. Percolation in multiplex networks with overlap. Physical Review E, Vol. 88, 5 (2013), 052811.Google Scholar
Cross Ref
- Manlio De Domenico, Albert Solé-Ribalta, Sergio Gómez, and Alex Arenas. 2014. Navigability of interconnected networks under random failures. Proceedings of the National Academy of Sciences, Vol. 111, 23 (2014), 8351--8356.Google Scholar
Cross Ref
- Wen-Bo Du, Xing-Lian Zhou, Oriol Lordan, Zhen Wang, Chen Zhao, and Yan-Bo Zhu. 2016. Analysis of the Chinese Airline Network as multi-layer networks. Transportation Research Part E: Logistics and Transportation Review Vol. 89 (2016), 108--116.Google Scholar
Cross Ref
- Riccardo Gallotti and Marc Barthelemy. 2015. The multilayer temporal network of public transport in Great Britain. Scientific data Vol. 2 (2015).Google Scholar
- Sergio Gomez, Albert Diaz-Guilera, Jesus Gomez-Gardenes, Conrad J Perez-Vicente, Yamir Moreno, and Alex Arenas. 2013. Diffusion dynamics on multiplex networks. Physical review letters Vol. 110, 2 (2013), 028701.Google Scholar
- Saikat Guha, Donald Towsley, Philippe Nain, cCaugatay cCapar, Ananthram Swami, and Prithwish Basu. 2016. Spanning connectivity in a multilayer network and its relationship to site-bond percolation. Physical Review E, Vol. 93, 6 (2016), 062310.Google Scholar
Cross Ref
- Adam Hackett, Davide Cellai, Sergio Gómez, Alexandre Arenas, and James P Gleeson. 2016. Bond percolation on multiplex networks. Physical Review X, Vol. 6, 2 (2016), 021002.Google Scholar
Cross Ref
- JM Hammersley. 1980. A generalization of McDiarmid's theorem for mixed Bernoulli percolation Mathematical Proceedings of the Cambridge Philosophical Society, Vol. Vol. 88. Cambridge University Press, 167--170.Google Scholar
- Olav Kallenberg. 2006. Foundations of modern probability. Springer Science & Business Media.Google Scholar
- Mikko Kivel"a, Alex Arenas, Marc Barthelemy, James P Gleeson, Yamir Moreno, and Mason A Porter. 2014. Multilayer networks. Journal of complex networks Vol. 2, 3 (2014), 203--271.Google Scholar
Cross Ref
- Kyu-Min Lee, Jung Yeol Kim, Won-kuk Cho, Kwang-Il Goh, and IM Kim. 2012. Correlated multiplexity and connectivity of multiplex random networks. New Journal of Physics Vol. 14, 3 (2012), 033027.Google Scholar
Cross Ref
- Vincent Marceau, Pierre-André Noël, Laurent Hébert-Dufresne, Antoine Allard, and Louis J Dubé. 2011. Modeling the dynamical interaction between epidemics on overlay networks. Physical Review E, Vol. 84, 2 (2011), 026105.Google Scholar
Cross Ref
- Giulia Menichetti, Daniel Remondini, Pietro Panzarasa, Raúl J Mondragón, and Ginestra Bianconi. 2014. Weighted multiplex networks. PloS one, Vol. 9, 6 (2014), e97857.Google Scholar
Cross Ref
- Byungjoon Min, Su Do Yi, Kyu-Min Lee, and K-I Goh. 2014. Network robustness of multiplex networks with interlayer degree correlations. Physical Review E, Vol. 89, 4 (2014), 042811.Google Scholar
Cross Ref
- Raul J Mondragon, Jacopo Iacovacci, and Ginestra Bianconi. 2017. Multilink Communities of Multiplex Networks. arXiv preprint arXiv:1706.09011 (2017).Google Scholar
- Yohsuke Murase, János Török, Hang-Hyun Jo, Kimmo Kaski, and János Kertész. 2014. Multilayer weighted social network model. Physical Review E, Vol. 90, 5 (2014), 052810.Google Scholar
Cross Ref
- Vincenzo Nicosia, Ginestra Bianconi, Vito Latora, and Marc Barthelemy. 2013. Growing multiplex networks. Physical review letters Vol. 111, 5 (2013), 058701.Google Scholar
- Vincenzo Nicosia and Vito Latora. 2015. Measuring and modeling correlations in multiplex networks. Physical Review E, Vol. 92, 3 (2015), 032805.Google Scholar
Cross Ref
- James Orlin. 1977. Contentment in graph theory: covering graphs with cliques Indagationes Mathematicae (Proceedings), Vol. Vol. 80. Elsevier, 406--424.Google Scholar
- Alessandro Pelizzola. 1995. Critical temperature of two coupled Ising planes. Physical Review B, Vol. 51, 17 (1995), 12005.Google Scholar
Cross Ref
- Filippo Radicchi and Ginestra Bianconi. 2017. Redundant interdependencies boost the robustness of multiplex networks. Physical Review X, Vol. 7, 1 (2017), 011013.Google Scholar
Cross Ref
- Jason Redi and Ram Ramanathan. 2011. The DARPA WNaN network architecture. In Military Communications Conference, 2011-milcom 2011. IEEE, 2258--2263.Google Scholar
Cross Ref
- Saulo DS Reis, Yanqing Hu, Andrés Babino, José S Andrade Jr, Santiago Canals, Mariano Sigman, and Hernán A Makse. 2014. Avoiding catastrophic failure in correlated networks of networks. Nature Physics, Vol. 10, 10 (2014), 762--767.Google Scholar
Cross Ref
- Dan Roth. 1996. On the hardness of approximate reasoning. Artificial Intelligence Vol. 82, 1--2 (1996), 273--302. Google Scholar
Digital Library
- Albert Sole-Ribalta, Manlio De Domenico, Nikos E Kouvaris, Albert Dáz-Guilera, Sergio Gómez, and Alex Arenas. 2013. Spectral properties of the Laplacian of multiplex networks. Physical Review E, Vol. 88, 3 (2013), 032807.Google Scholar
Cross Ref
- Michael Szell, Renaud Lambiotte, and Stefan Thurner. 2010. Multirelational organization of large-scale social networks in an online world. Proceedings of the National Academy of Sciences, Vol. 107, 31 (2010), 13636--13641.Google Scholar
Cross Ref
- Salil P Vadhan. 2001. The complexity of counting in sparse, regular, and planar graphs. SIAM J. Comput. Vol. 31, 2 (2001), 398--427. Google Scholar
Digital Library
- Moti Yanuka and R Englman. 1990. Bond-site percolation: empirical representation of critical probabilities. Journal of Physics A: Mathematical and General, Vol. 23, 7 (1990), L339.Google Scholar
Cross Ref
- Kun Zhao and Ginestra Bianconi. 2013. Percolation on interdependent networks with a fraction of antagonistic interactions. Journal of Statistical Physics Vol. 152, 6 (2013), 1069--1083.Google Scholar
Cross Ref
- Di Zhou, Jianxi Gao, H Eugene Stanley, and Shlomo Havlin. 2013. Percolation of partially interdependent scale-free networks. Physical Review E, Vol. 87, 5 (2013), 052812.Google Scholar
Cross Ref
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On a Class of Stochastic Multilayer Networks
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