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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Develop an algorithm based on an incidence matrix to calculate the reliability of complex systems

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pp. 2055–2062Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2676 Crossmark XML
Received:
01 Nov 2025
Published Online:
22 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2676
Pages:
2055–2062

Abstract

Evaluating the reliability of complex network systems is crucial to the efficiency of their operations and the continuity of applications in sectors of strategic importance (e.g., aviation, telecommunications, and energy), where failures may result in significant financial losses and endanger the affected systems’ valuable assets and infrastructure. Traditional approaches commonly rely on simplified suppositions which cannot adequately reflect the dynamic relationships between the components. Therefore, advanced analytical models, such as the incidence matrix, have been used as powerful tools in comprehensive reliability assessment. The paper emphasizes the importance of the incidence matrix for improving reliability assessment accuracy and computational speed. The study proposed an integrated model that accounts for multiple failure cases, thereby enabling more robust reliability estimation methods. It is vital to evaluate the reliability of complex network systems. Furthermore, the paper considers the potential fusion of modern methods, including artificial intelligence, with the incidence matrix to enhance predictive power. It has been shown that incidence matrix-based approaches successfully address the complexity of electrical networks and real-time systems such as railways or maritime networks. These results highlight the effectiveness of the methodology for hyperspace mapping of critical subsystems, thereby improving reliability management. It also outlines directions for future research that will focus on integrating novel computational methods to enhance the methodology for analyzing the reliability of complex network systems. 

Keywords

Incidence matrixReliability evaluationComplex systemsNetwork analysisMATLAB algorithms

Subject Classifications

Primary 90B25Secondary 68M15

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