Gromov centrality: a multiscale measure of network centrality using triangle inequality excess
Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the cent...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2022
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| _version_ | 1797111333225758720 |
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| author | Babul, S Devriendt, K Lambiotte, R |
| author_facet | Babul, S Devriendt, K Lambiotte, R |
| author_sort | Babul, S |
| collection | OXFORD |
| description | Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and it recovers as limits well-known concepts such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks. |
| first_indexed | 2024-03-07T08:07:18Z |
| format | Journal article |
| id | oxford-uuid:e50ad10c-b528-486f-a3c3-e775d74c2313 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:07:18Z |
| publishDate | 2022 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:e50ad10c-b528-486f-a3c3-e775d74c23132023-11-08T10:31:43ZGromov centrality: a multiscale measure of network centrality using triangle inequality excessJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e50ad10c-b528-486f-a3c3-e775d74c2313EnglishSymplectic ElementsAmerican Physical Society2022Babul, SDevriendt, KLambiotte, RCentrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and it recovers as limits well-known concepts such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks. |
| spellingShingle | Babul, S Devriendt, K Lambiotte, R Gromov centrality: a multiscale measure of network centrality using triangle inequality excess |
| title | Gromov centrality: a multiscale measure of network centrality using triangle inequality excess |
| title_full | Gromov centrality: a multiscale measure of network centrality using triangle inequality excess |
| title_fullStr | Gromov centrality: a multiscale measure of network centrality using triangle inequality excess |
| title_full_unstemmed | Gromov centrality: a multiscale measure of network centrality using triangle inequality excess |
| title_short | Gromov centrality: a multiscale measure of network centrality using triangle inequality excess |
| title_sort | gromov centrality a multiscale measure of network centrality using triangle inequality excess |
| work_keys_str_mv | AT babuls gromovcentralityamultiscalemeasureofnetworkcentralityusingtriangleinequalityexcess AT devriendtk gromovcentralityamultiscalemeasureofnetworkcentralityusingtriangleinequalityexcess AT lambiotter gromovcentralityamultiscalemeasureofnetworkcentralityusingtriangleinequalityexcess |