Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL)
Arguably, the most fundamental problem in Network Science is finding structure within a complex network. Often, this is achieved by partitioning the network’s nodes into communities in a way that maximizes an objective function. However, finding the maximizing partition is generally a computationall...
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MDPI AG
2025-06-01
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| author | Tania Ghosh Royce K. P. Zia Kevin E. Bassler |
| author_facet | Tania Ghosh Royce K. P. Zia Kevin E. Bassler |
| author_sort | Tania Ghosh |
| collection | DOAJ |
| description | Arguably, the most fundamental problem in Network Science is finding structure within a complex network. Often, this is achieved by partitioning the network’s nodes into communities in a way that maximizes an objective function. However, finding the maximizing partition is generally a computationally difficult NP-complete problem. Recently, a machine learning algorithmic scheme was introduced that uses information within a set of partitions to find a new partition that better maximizes an objective function. The scheme, known as RenEEL, uses Extremal Ensemble Learning. Starting with an ensemble of <i>K</i> partitions, it updates the ensemble by considering replacing its worst member with the best of <i>L</i> partitions found by analyzing a reduced network formed by collapsing nodes, which all the ensemble partitions agree should be grouped together, into super-nodes. The updating continues until consensus is achieved within the ensemble about what the best partition is. The original <i>K</i> ensemble partitions and each of the <i>L</i> partitions used for an update are found using a simple “base” partitioning algorithm. We perform an empirical study of how the effectiveness of RenEEL depends on the values of <i>K</i> and <i>L</i> and relate the results to the extreme value statistics of record-breaking. We find that increasing <i>K</i> is generally more effective than increasing <i>L</i> for finding the best partition. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-f067752cf2ff44e3bc06d65e7df3351a2025-08-20T03:27:17ZengMDPI AGEntropy1099-43002025-06-0127662810.3390/e27060628Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL)Tania Ghosh0Royce K. P. Zia1Kevin E. Bassler2Department of Physics, University of Houston, Houston, TX 77204, USADepartment of Physics, University of Houston, Houston, TX 77204, USADepartment of Physics, University of Houston, Houston, TX 77204, USAArguably, the most fundamental problem in Network Science is finding structure within a complex network. Often, this is achieved by partitioning the network’s nodes into communities in a way that maximizes an objective function. However, finding the maximizing partition is generally a computationally difficult NP-complete problem. Recently, a machine learning algorithmic scheme was introduced that uses information within a set of partitions to find a new partition that better maximizes an objective function. The scheme, known as RenEEL, uses Extremal Ensemble Learning. Starting with an ensemble of <i>K</i> partitions, it updates the ensemble by considering replacing its worst member with the best of <i>L</i> partitions found by analyzing a reduced network formed by collapsing nodes, which all the ensemble partitions agree should be grouped together, into super-nodes. The updating continues until consensus is achieved within the ensemble about what the best partition is. The original <i>K</i> ensemble partitions and each of the <i>L</i> partitions used for an update are found using a simple “base” partitioning algorithm. We perform an empirical study of how the effectiveness of RenEEL depends on the values of <i>K</i> and <i>L</i> and relate the results to the extreme value statistics of record-breaking. We find that increasing <i>K</i> is generally more effective than increasing <i>L</i> for finding the best partition.https://www.mdpi.com/1099-4300/27/6/628community detectioncomplex networksmodularityextreme value statistics |
| spellingShingle | Tania Ghosh Royce K. P. Zia Kevin E. Bassler Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL) Entropy community detection complex networks modularity extreme value statistics |
| title | Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL) |
| title_full | Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL) |
| title_fullStr | Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL) |
| title_full_unstemmed | Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL) |
| title_short | Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL) |
| title_sort | extreme value statistics of community detection in complex networks with reduced network extremal ensemble learning reneel |
| topic | community detection complex networks modularity extreme value statistics |
| url | https://www.mdpi.com/1099-4300/27/6/628 |
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