On M-polynomials of Dunbar graphs in social networks
Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We de...
| Главные авторы: | , , |
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| Формат: | Journal article |
| Язык: | English |
| Опубликовано: |
MDPI
2020
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| _version_ | 1826266472811331584 |
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| author | Acharjee, S Bora, B Dunbar, RIM |
| author_facet | Acharjee, S Bora, B Dunbar, RIM |
| author_sort | Acharjee, S |
| collection | OXFORD |
| description | Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We develop a novel application of M-polynomials, the (m,n,r) -agent recruitment graph where n>1 , to study the relationship between the Dunbar graphs of social networks and the small-world phenomenon. We show that the small-world effects are only possible if everyone uses the full range of their network when selecting steps in the small-world chain. Topological indices may provide valuable insights into the structure and dynamics of social network graphs because they incorporate an important element of the dynamical transitivity of such graphs. |
| first_indexed | 2024-03-06T20:39:28Z |
| format | Journal article |
| id | oxford-uuid:33c7f394-a7c5-491c-a2a9-f2f70f64f577 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:39:28Z |
| publishDate | 2020 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oxford-uuid:33c7f394-a7c5-491c-a2a9-f2f70f64f5772022-03-26T13:22:14ZOn M-polynomials of Dunbar graphs in social networksJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:33c7f394-a7c5-491c-a2a9-f2f70f64f577EnglishSymplectic ElementsMDPI2020Acharjee, SBora, BDunbar, RIMTopological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We develop a novel application of M-polynomials, the (m,n,r) -agent recruitment graph where n>1 , to study the relationship between the Dunbar graphs of social networks and the small-world phenomenon. We show that the small-world effects are only possible if everyone uses the full range of their network when selecting steps in the small-world chain. Topological indices may provide valuable insights into the structure and dynamics of social network graphs because they incorporate an important element of the dynamical transitivity of such graphs. |
| spellingShingle | Acharjee, S Bora, B Dunbar, RIM On M-polynomials of Dunbar graphs in social networks |
| title | On M-polynomials of Dunbar graphs in social networks |
| title_full | On M-polynomials of Dunbar graphs in social networks |
| title_fullStr | On M-polynomials of Dunbar graphs in social networks |
| title_full_unstemmed | On M-polynomials of Dunbar graphs in social networks |
| title_short | On M-polynomials of Dunbar graphs in social networks |
| title_sort | on m polynomials of dunbar graphs in social networks |
| work_keys_str_mv | AT acharjees onmpolynomialsofdunbargraphsinsocialnetworks AT borab onmpolynomialsofdunbargraphsinsocialnetworks AT dunbarrim onmpolynomialsofdunbargraphsinsocialnetworks |