Abstract
We develop a formalism for addressing many common questions about network structure. The formalism is based on Shannon-Moore network reliability and on the Birnbaum definition of importance in terms of reliability. The computational methods we suggest based on this formalism are designed to answer specific questions about how network structure affects particular aspects of the dynamics, and can be applied to a wide variety of dynamical systems on interaction networks. The formalism and methods bring well-understood analytical techniques from statistical physics and computer science to bear on current issues in network science. We introduce the concepts that underpin the formalism, explore methods of applying these concepts, and demonstrate applications to problems such as edge ranking and graph reduction.
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References
Aiello, L.M., Cherifi, C., Cherifi, H., Lambiotte, R., Lio, P., Rocha, L.M. (eds.): Accepted to appear in Complex Networks & Their Applications VII. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, COMPLEX NETWORKS 2018, Springer (2018)
Birnbaum, Z.W.: On the importance of different components in a multicomponent system. In: Krishnaiah, P.R. (ed.) Multivariate Analysis II, Proceedings of the 2nd International Symposium on Multivariate Analysis, pp. 581–592. Academic Press, New York (1969)
Colbourn, C.J.: The Combinatorics of Network Reliability. Oxford University Press, New York (1987)
Condon, A., Karp, R.M.: Algorithms for graph partitioning on the planted partition model. Random Struct. Algorithms 18(2), 116–140 (2001)
Gertsbakh, I.B., Shpungin, Y.: Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo. CRC Press (2016)
Karrer, B., Newman, M.E.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83(1), 016107 (2011)
Moore, E.F., Shannon, C.E.: Reliable circuits using less reliable relays. J. Franklin Inst. 262(3), 191–208 (1956). https://doi.org/10.1016/0016-0032(56)90559-2, http://www.sciencedirect.com/science/article/pii/0016003256905592
Nath, M., Ren, Y., Eubank, S.G.: Determining whether a particular contact network is consistent with a network model. J. Theor. Biol. 400C, 121–132 (2017)
Ren, Y., Eubank, S., Nath, M.: From network reliability to the Ising model: A parallel scheme for estimating the joint density of states. Phys. Rev. E 94(4), 042125 (2016). https://doi.org/10.1103/PhysRevE.94.042125
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Nath, M., Ren, Y., Eubank, S. (2019). An Approach to Structural Analysis Using Moore-Shannon Network Reliability. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 812. Springer, Cham. https://doi.org/10.1007/978-3-030-05411-3_44
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DOI: https://doi.org/10.1007/978-3-030-05411-3_44
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