Monograph - 2021raph
Safety and Reliability of Systems and Processes
Summer Safety and Reliability Seminar 2021
Kołowrocki Krzysztof, Poland
Bogalecka Magdalena, Poland
Dąbrowska Ewa, Poland
Torbicki Mateusz, Poland
Gdynia Maritime University, 2021
ISBN 978-83-7421-354-7 (printed)
e-ISBN 978-83-7421-355-4 (eBook)
Network connectivity dynamic modelling
Eid Associate Consultants - RiskLyse, France, mohamed.eid(at)risklyse.eu
ABSTRACT: 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.
KEYWORDS: network, graph, topological, algebraic, connectivity, dynamic, modelling
To cite this chapter:
Eid M. 2021. Network connectivity dynamic modelling. In K. Kołowrocki et al. (Eds.), Safety and Reliability of Systems and Processes, Summer Safety and Reliability Seminar 2021. Gdynia Maritime University, Gdynia, 117-127, doi:10.26408/srsp-2021-07.