A continuous-time network evolution model describing $ N $-interactions
We have introduced a new continuous-time network evolution model. We have described cooperation, so we have considered the cliques of nodes. The evolution of the network was based on cliques of nodes of the network and was governed by a branching process. The basic properties of the evolution proces...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241695 |
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| author | István Fazekas Attila Barta László Fórián Bettina Porvázsnyik |
| author_facet | István Fazekas Attila Barta László Fórián Bettina Porvázsnyik |
| author_sort | István Fazekas |
| collection | DOAJ |
| description | We have introduced a new continuous-time network evolution model. We have described cooperation, so we have considered the cliques of nodes. The evolution of the network was based on cliques of nodes of the network and was governed by a branching process. The basic properties of the evolution process were described. Asymptotic theorems were proved for the number of cliques having a fixed size and the degree of a fixed node. The generating function was calculated, and then the probability of extinction was obtained. For the proof, advanced results of multi-type branching processes were used. Besides precise mathematical proofs, simulation examples also supported our results. |
| format | Article |
| id | doaj-art-b24b605034b94c14a27fce86ea2e28e3 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-b24b605034b94c14a27fce86ea2e28e32025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912357213574210.3934/math.20241695A continuous-time network evolution model describing $ N $-interactionsIstván Fazekas0Attila Barta1László Fórián2Bettina Porvázsnyik3Faculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen, HungaryFaculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen, HungaryFaculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen, HungaryFaculty of Informatics, University of Debrecen, P.O. Box 400, 4002 Debrecen, HungaryWe have introduced a new continuous-time network evolution model. We have described cooperation, so we have considered the cliques of nodes. The evolution of the network was based on cliques of nodes of the network and was governed by a branching process. The basic properties of the evolution process were described. Asymptotic theorems were proved for the number of cliques having a fixed size and the degree of a fixed node. The generating function was calculated, and then the probability of extinction was obtained. For the proof, advanced results of multi-type branching processes were used. Besides precise mathematical proofs, simulation examples also supported our results.https://www.aimspress.com/article/doi/10.3934/math.20241695network evolutionrandom graphcliquedegree processmulti-type branching process |
| spellingShingle | István Fazekas Attila Barta László Fórián Bettina Porvázsnyik A continuous-time network evolution model describing $ N $-interactions AIMS Mathematics network evolution random graph clique degree process multi-type branching process |
| title | A continuous-time network evolution model describing $ N $-interactions |
| title_full | A continuous-time network evolution model describing $ N $-interactions |
| title_fullStr | A continuous-time network evolution model describing $ N $-interactions |
| title_full_unstemmed | A continuous-time network evolution model describing $ N $-interactions |
| title_short | A continuous-time network evolution model describing $ N $-interactions |
| title_sort | continuous time network evolution model describing n interactions |
| topic | network evolution random graph clique degree process multi-type branching process |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241695 |
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