The Reliability of a Class of Two-Layer Networks with Unreliable Edges
It is well known that networks are dynamic graphs, and the topology of a network can be described by a graph. Thus, the reliability of a network under edge failure is defined as the probability that its corresponding topological graph remains connected under the condition that the edges fail with in...
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MDPI AG
2024-11-01
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| author | Sun Xie Haixing Zhao Jun Yin |
| author_facet | Sun Xie Haixing Zhao Jun Yin |
| author_sort | Sun Xie |
| collection | DOAJ |
| description | It is well known that networks are dynamic graphs, and the topology of a network can be described by a graph. Thus, the reliability of a network under edge failure is defined as the probability that its corresponding topological graph remains connected under the condition that the edges fail with independent probabilities. In this paper, the reliability of a class of two-layer networks is considered, where each layer is a complete graph and the edges joining different layers are one-to-one correspondingly connected. The edge failure probability is uniform in the same layer and distinct in different layers and between layers. The recursive formula for the reliability (reliability polynomial) of the two-layer network is obtained, and the corresponding algorithm is also given. Furthermore, the reliability of several networks is computed by Python, which verifies the correctness of the algorithm. |
| format | Article |
| id | doaj-art-927b9e6d0b9040a7a4eb37928a370ac9 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-927b9e6d0b9040a7a4eb37928a370ac92025-08-20T02:08:12ZengMDPI AGAxioms2075-16802024-11-01131176110.3390/axioms13110761The Reliability of a Class of Two-Layer Networks with Unreliable EdgesSun Xie0Haixing Zhao1Jun Yin2School of Mathematics and Physics, Qinghai University, Xining 810016, ChinaThe State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining 810008, ChinaThe College of Computer, Qinghai Normal University, Xining 810016, ChinaIt is well known that networks are dynamic graphs, and the topology of a network can be described by a graph. Thus, the reliability of a network under edge failure is defined as the probability that its corresponding topological graph remains connected under the condition that the edges fail with independent probabilities. In this paper, the reliability of a class of two-layer networks is considered, where each layer is a complete graph and the edges joining different layers are one-to-one correspondingly connected. The edge failure probability is uniform in the same layer and distinct in different layers and between layers. The recursive formula for the reliability (reliability polynomial) of the two-layer network is obtained, and the corresponding algorithm is also given. Furthermore, the reliability of several networks is computed by Python, which verifies the correctness of the algorithm.https://www.mdpi.com/2075-1680/13/11/761two-layer networkreliabilitycomplete graphedge failure probabilityalgorithm |
| spellingShingle | Sun Xie Haixing Zhao Jun Yin The Reliability of a Class of Two-Layer Networks with Unreliable Edges Axioms two-layer network reliability complete graph edge failure probability algorithm |
| title | The Reliability of a Class of Two-Layer Networks with Unreliable Edges |
| title_full | The Reliability of a Class of Two-Layer Networks with Unreliable Edges |
| title_fullStr | The Reliability of a Class of Two-Layer Networks with Unreliable Edges |
| title_full_unstemmed | The Reliability of a Class of Two-Layer Networks with Unreliable Edges |
| title_short | The Reliability of a Class of Two-Layer Networks with Unreliable Edges |
| title_sort | reliability of a class of two layer networks with unreliable edges |
| topic | two-layer network reliability complete graph edge failure probability algorithm |
| url | https://www.mdpi.com/2075-1680/13/11/761 |
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