Network connectivity dynamic modelling

• Autorzy: Eid Mohamed

Identyfikatory

DOI

10.26408/srsp-2021-07

• Konferencja: 15th Summer Safety & Reliability Seminars - SSARS 2021, 5-12 September 2021, Ciechocinek, Poland
• Języki publikacji: EN

Abstrakty

EN

The chapter presents an approach based on basic notions issued from the graph theory and from the system reliability theory. The approach seeks to describe the transitions in the connectivity state of non-directional graphs induced by systemic losses of nodes and edges. Each component loss (node or edge) represents a transition and results in a connectivity degradation. Some of the transitions are classified as non-critical while others are critical. Degradations are measured using the notion of topological graph diameter issued from the graph theory. The critical transition notion is issued from the system reliability theory. The approach determines the degraded graph diameter corresponding to each possible transition and subsequently the criticality of the transition. The criticality threshold is determined by the highest acceptable connectivity order which is a function of the degraded graph diameter. A network with 9 nodes and 15 edges is used as an academic study case to illustrate the applicability of the approach. Nodes are supposed to be identical, as well as the edges. All network components (nodes and edges) are mutually independent. These precedent hypotheses are intended to evacuate all sources of numerical useless complexity. As our main objective is to highlight the original characteristic of the proposed approach.

Słowa kluczowe

EN

network; graph; topological; algebraic; connectivity; dynamic; modelling

• Wydawca: Gdynia Maritime University ; Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Safety and Reliability of Systems and Processes
• Rocznik: 2021
• Tom: Summer Safety and Reliability Seminar 2021
• Strony: 117--127
• Opis fizyczny: Bibliogr. 26 poz., rys., tab.

Twórcy

autor

Eid Mohamed

• Eid AssociateConsultants- RiskLyse, France

• https://orcid.org/0000-0002-8274-3005

Bibliografia

• Albert, R. & Barabasi, A.-L. 2002. Statistical mechanics of complex networks. Reviews of Modern Physics 74, 2002.
• Barabasi, A.-L. & Albert, R. 1999, Emergence of scaling in random networks. Science 286, 509-512.
• Bondy, J.A. & Murty U.S.R. 2008. Graph Theory. Graduate Texts in Mathematics Series.Springer-Verlag, London.
• Cvetković, D.M. 2000. Applications of Graph Spectra: an Introduction to the Literature.
• Cvetković, D. & Simić, S.K. 2010. Towards a spectral theory of graphs based on the signless Laplacian, II. Linear Algebra and its Applications 432, 2257-2272.
• Cvetković, D.M. & Simić, S.K. 2011. Graph spectra in computer science. Linear Algebra and its Applications 434, 1545–1562.
• Cvetković, D.M., Doob, M. & Sachs, H. 1979. Spectra of Graphs - Theory and Applications. VEB Deutscher Verlag der Wissenschaften, Berlin, Academic Press, New York.
• Eid, M. 2017. Network’s connectivity dynamic modelling using a topological binary model: critical transitions concept. Proceedings of the 52nd ESReDA Seminar on Critical Infrastructures: Enhancing Preparedness and Resilience for the Security of Citizens and Services Supply Continuity, Lithuanian Energy Institute and Vytautas Magnus University, Kaunas.
• Eid, M., Souza de Cursi, E. & El Hami, A. 2012. Towards the development of a topological model to assess networks performance: connectivity, robustness and reliability. Journal of Polish Safety and Reliability Association, Summer Safety and Reliability Seminars 3(1), 23-37.
• Ellens, W., Spieksmaa, F.M., Van Mieghemc, P., Jamakovic, A. & Kooij, R.E. 2011. Effective graph resistance. Linear Algebra and its Applications 435, 2491-2506.
• Fiedler, M. 1973. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal 23(2), 298-305. http://dml.cz/bitstream/handle/10338.dmlcz/101168/CzechMathJ_23-1973-2_11.pdf, http://elib.mi.sanu.ac.rs/files/journals/zr/21/n021p007.pdf (accessed 13 May 2021).
• Huang, P., Shiu, W.C. & Sun P.K. 2016. Maximizing the spectral radius of k-connected graphs with given diameter. Linear Algebra Application 488, 350-362.
• Hückel, E. 1931. Quantentheoretische Beiträge zum Benzolproblem. Zeitschrift für Physik 70, 204-286.
• Klein, D.J. & Randic, M. 1993. Resistance distance. Journal of Mathematical Chemistry 12, 81-95.
• König, D. 1936. Theorie der Endlichen und Unendlichen Graphen. Akademische Verlagsgesellschaft M.R.H., Leipzig.
• Li, D., Wang, G.& Meng, J. 2017. Some results on the distance and distance signless Laplacian spectral radius of graphs and digraphs. Applied Mathematics and Computation 293, 218-225.
• Lin, H., Hong, Y., Wang, J. &Shu J. 2013. On the distance spectrum of graphs. Linear Algebra and its Applications 439, 1662-1669.
• Lisnianski, A., Frenkel, I. & Ding, Y. 2010. Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers. Springer.
• Modarres, M., Kaminskiy, M. & Krivtsov, V. 2009. Reliability Engineering and Risk Analysis: a Practical Guide. CRC Press, Boca Raton.
• Mohar, B. 1991. The Laplacian spectrum of graphs. Journal of Graph Theory, Combinatorics, and Applications 2, 871-898.
• Natvig, B. 2011. Multistate Systems Reliability Theory with Applications. John Wiley & Sons, Ltd. Book Series: Wiley Series in Probability and Statistics.
• Rose, K. Eldridge, S. & Chapin, L. 2015. The Internet of Things: an Overview Understanding the Issues and Challenges of a More Connected World. The Internet Society (ISOC).
• Van Mieghem, P. 2011. Graph Spectra for Complex Networks. Cambridge University Press, Cambridge.
• Wang Y., Chakrabarti, D.,Wang C. & Faloutsos, C. 2003. Epidemic spreading in real networks: an eigenvalue viewpoint. 22ndSymposium on Reliable Distributed Computing, Florence, 6-8.
• Wate Mizuno, M. 2011. The Works of KŐNIG Dénes (1884-1944) in the Domain of Mathematical Recreations and his Treatment of Recreational Problems in his Works of Graph Theory. Thesis submitted on 9 May 2011, HAL Id: tel-00591307.
• Wilson, J.R. 1998. Introduction to Graph Theory. Longman Group Ltd, 4th edition.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).