On sparsity, power-law and clustering properties of graphex processes
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse, almost dense regime, (iii) a sparse regi...
| Main Authors: | , , |
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| Format: | Journal article |
| Jezik: | English |
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Cambridge University Press
2023
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| _version_ | 1826312149179301888 |
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| author | Caron, F Panero, F Rousseau, J |
| author_facet | Caron, F Panero, F Rousseau, J |
| author_sort | Caron, F |
| collection | OXFORD |
| description | This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse, almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that, under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for subgraph counts and for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph. |
| first_indexed | 2024-03-07T08:23:16Z |
| format | Journal article |
| id | oxford-uuid:78b563dd-6cdf-4baf-8588-13892b3b946f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:23:16Z |
| publishDate | 2023 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:78b563dd-6cdf-4baf-8588-13892b3b946f2024-02-05T12:58:31ZOn sparsity, power-law and clustering properties of graphex processesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:78b563dd-6cdf-4baf-8588-13892b3b946fEnglishSymplectic ElementsCambridge University Press2023Caron, FPanero, FRousseau, JThis paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse, almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that, under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for subgraph counts and for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph. |
| spellingShingle | Caron, F Panero, F Rousseau, J On sparsity, power-law and clustering properties of graphex processes |
| title | On sparsity, power-law and clustering properties of graphex processes |
| title_full | On sparsity, power-law and clustering properties of graphex processes |
| title_fullStr | On sparsity, power-law and clustering properties of graphex processes |
| title_full_unstemmed | On sparsity, power-law and clustering properties of graphex processes |
| title_short | On sparsity, power-law and clustering properties of graphex processes |
| title_sort | on sparsity power law and clustering properties of graphex processes |
| work_keys_str_mv | AT caronf onsparsitypowerlawandclusteringpropertiesofgraphexprocesses AT panerof onsparsitypowerlawandclusteringpropertiesofgraphexprocesses AT rousseauj onsparsitypowerlawandclusteringpropertiesofgraphexprocesses |