On the Vertex-Connectivity of an Uncertain Random Graph
In many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which some edges exist with degrees in probability m...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9078756/ |
| _version_ | 1818624267332354048 |
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| author | Hao Li Xin Gao |
| author_facet | Hao Li Xin Gao |
| author_sort | Hao Li |
| collection | DOAJ |
| description | In many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which some edges exist with degrees in probability measure, and some other edges exist with degrees in uncertain measure. In this paper, we focus on the connectivity of uncertain random graphs with respect to vertices. We propose the concepts of <i>k</i>-vertex-connectivity index and the connectivity of an uncertain random graph. The former is the chance measure that an uncertain random graph is k-vertex-connected, and the latter is an uncertain random variable, which characterizes the connectivity of the uncertain random graph with respect to vertices. We discuss some properties of these concepts. Methods and formulas are also presented for calculating the <i>k</i>-vertex-connectivity index, and the distribution and expected value of the connectivity of an uncertain random graph. |
| first_indexed | 2024-12-16T18:54:14Z |
| format | Article |
| id | doaj.art-539c6dd83eca4f60946f34e663919863 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T18:54:14Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-539c6dd83eca4f60946f34e6639198632022-12-21T22:20:35ZengIEEEIEEE Access2169-35362020-01-018855048551410.1109/ACCESS.2020.29905749078756On the Vertex-Connectivity of an Uncertain Random GraphHao Li0https://orcid.org/0000-0001-9743-6983Xin Gao1https://orcid.org/0000-0002-0462-9813School of Mathematics, Renmin University of China, Beijing, ChinaSchool of Mathematical Sciences and Physics, North China Electric Power University, Beijing, ChinaIn many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which some edges exist with degrees in probability measure, and some other edges exist with degrees in uncertain measure. In this paper, we focus on the connectivity of uncertain random graphs with respect to vertices. We propose the concepts of <i>k</i>-vertex-connectivity index and the connectivity of an uncertain random graph. The former is the chance measure that an uncertain random graph is k-vertex-connected, and the latter is an uncertain random variable, which characterizes the connectivity of the uncertain random graph with respect to vertices. We discuss some properties of these concepts. Methods and formulas are also presented for calculating the <i>k</i>-vertex-connectivity index, and the distribution and expected value of the connectivity of an uncertain random graph.https://ieeexplore.ieee.org/document/9078756/Chance theorygraph theoryuncertain random graphuncertainty theoryvertex-connectivity |
| spellingShingle | Hao Li Xin Gao On the Vertex-Connectivity of an Uncertain Random Graph IEEE Access Chance theory graph theory uncertain random graph uncertainty theory vertex-connectivity |
| title | On the Vertex-Connectivity of an Uncertain Random Graph |
| title_full | On the Vertex-Connectivity of an Uncertain Random Graph |
| title_fullStr | On the Vertex-Connectivity of an Uncertain Random Graph |
| title_full_unstemmed | On the Vertex-Connectivity of an Uncertain Random Graph |
| title_short | On the Vertex-Connectivity of an Uncertain Random Graph |
| title_sort | on the vertex connectivity of an uncertain random graph |
| topic | Chance theory graph theory uncertain random graph uncertainty theory vertex-connectivity |
| url | https://ieeexplore.ieee.org/document/9078756/ |
| work_keys_str_mv | AT haoli onthevertexconnectivityofanuncertainrandomgraph AT xingao onthevertexconnectivityofanuncertainrandomgraph |