The unreasonable effectiveness of tree-based theory for networks with clustering.
We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ℓ is sufficiently sma...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826287784403402752 |
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| author | Melnik, S Hackett, A Porter, M Mucha, P Gleeson, J |
| author_facet | Melnik, S Hackett, A Porter, M Mucha, P Gleeson, J |
| author_sort | Melnik, S |
| collection | OXFORD |
| description | We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ℓ is sufficiently small--that is, as long as it is close to the value of ℓ in a random network with negligible clustering and the same degree-degree correlations. We support this hypothesis numerically using both real-world networks from various domains and several classes of synthetic clustered networks. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks, provided that the networks are "sufficiently small" worlds. |
| first_indexed | 2024-03-07T02:03:50Z |
| format | Journal article |
| id | oxford-uuid:9e4a1111-d234-4234-86ae-a6c54be754a6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:03:50Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:9e4a1111-d234-4234-86ae-a6c54be754a62022-03-27T00:49:05ZThe unreasonable effectiveness of tree-based theory for networks with clustering.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9e4a1111-d234-4234-86ae-a6c54be754a6EnglishSymplectic Elements at Oxford2011Melnik, SHackett, APorter, MMucha, PGleeson, JWe demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ℓ is sufficiently small--that is, as long as it is close to the value of ℓ in a random network with negligible clustering and the same degree-degree correlations. We support this hypothesis numerically using both real-world networks from various domains and several classes of synthetic clustered networks. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks, provided that the networks are "sufficiently small" worlds. |
| spellingShingle | Melnik, S Hackett, A Porter, M Mucha, P Gleeson, J The unreasonable effectiveness of tree-based theory for networks with clustering. |
| title | The unreasonable effectiveness of tree-based theory for networks with clustering. |
| title_full | The unreasonable effectiveness of tree-based theory for networks with clustering. |
| title_fullStr | The unreasonable effectiveness of tree-based theory for networks with clustering. |
| title_full_unstemmed | The unreasonable effectiveness of tree-based theory for networks with clustering. |
| title_short | The unreasonable effectiveness of tree-based theory for networks with clustering. |
| title_sort | unreasonable effectiveness of tree based theory for networks with clustering |
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