A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection
In this paper we formally define the <i>hierarchical clustering network problem</i> (HCNP) as the problem to find a <i>good</i> hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final <i>picture<...
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| Autores principales: | , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/fd0e65f934ed4ea6b21152a459e216aa |
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| Sumario: | In this paper we formally define the <i>hierarchical clustering network problem</i> (HCNP) as the problem to find a <i>good</i> hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final <i>picture</i> of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as <i>the linear modularity game.</i> This new measure, (<i>the node-game shortest path betweenness measure</i>), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of <i>the node-game shortest path betweenness measure</i>, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results. |
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