Random graphs and real networks with weak geometric coupling
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space. However, it has been shown that finite-size effects can also induce...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013337 |
| _version_ | 1797210220295880704 |
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| author | Jasper van der Kolk M. Ángeles Serrano Marián Boguñá |
| author_facet | Jasper van der Kolk M. Ángeles Serrano Marián Boguñá |
| author_sort | Jasper van der Kolk |
| collection | DOAJ |
| description | Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space. However, it has been shown that finite-size effects can also induce substantial clustering, even when the coupling to this space is weak or nonexistent. In this paper, we study the weakly geometric regime, where clustering is absent in the thermodynamic limit but present in finite systems. Extending Mercator, a network embedding tool based on the popularity×similarity S^{1}/H^{2} static geometric network model, we show that, even when the coupling to the geometric space is weak, geometric information can be recovered from the connectivity alone for networks of any size. The fact that several real networks are best described in this quasigeometric regime suggests that the transition between nongeometric and geometric networks is not a sharp one. |
| first_indexed | 2024-04-24T10:07:08Z |
| format | Article |
| id | doaj.art-41c252155d01473a9262667ba0e8b36c |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:08Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-41c252155d01473a9262667ba0e8b36c2024-04-12T17:40:57ZengAmerican Physical SocietyPhysical Review Research2643-15642024-03-016101333710.1103/PhysRevResearch.6.013337Random graphs and real networks with weak geometric couplingJasper van der KolkM. Ángeles SerranoMarián BoguñáGeometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space. However, it has been shown that finite-size effects can also induce substantial clustering, even when the coupling to this space is weak or nonexistent. In this paper, we study the weakly geometric regime, where clustering is absent in the thermodynamic limit but present in finite systems. Extending Mercator, a network embedding tool based on the popularity×similarity S^{1}/H^{2} static geometric network model, we show that, even when the coupling to the geometric space is weak, geometric information can be recovered from the connectivity alone for networks of any size. The fact that several real networks are best described in this quasigeometric regime suggests that the transition between nongeometric and geometric networks is not a sharp one.http://doi.org/10.1103/PhysRevResearch.6.013337 |
| spellingShingle | Jasper van der Kolk M. Ángeles Serrano Marián Boguñá Random graphs and real networks with weak geometric coupling Physical Review Research |
| title | Random graphs and real networks with weak geometric coupling |
| title_full | Random graphs and real networks with weak geometric coupling |
| title_fullStr | Random graphs and real networks with weak geometric coupling |
| title_full_unstemmed | Random graphs and real networks with weak geometric coupling |
| title_short | Random graphs and real networks with weak geometric coupling |
| title_sort | random graphs and real networks with weak geometric coupling |
| url | http://doi.org/10.1103/PhysRevResearch.6.013337 |
| work_keys_str_mv | AT jaspervanderkolk randomgraphsandrealnetworkswithweakgeometriccoupling AT mangelesserrano randomgraphsandrealnetworkswithweakgeometriccoupling AT marianboguna randomgraphsandrealnetworkswithweakgeometriccoupling |