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oai:docta.ucm.es:20.500.14352/1001162024-11-06T15:36:17Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Espínola Vílchez, María Rosario author Gómez González, Daniel author Castro Cantalejo, Javier author Gutiérrez García-Pardo, Inmaculada author 2021-10-21 In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture 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 the linear modularity game. This new measure, (the node-game shortest path betweenness measure), 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 the node-game shortest path betweenness measure, 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. Gómez, D.; Castro, J.; Gutiérrez, I.; Espínola, R. A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection. Mathematics 2021, 9, 2666. https://doi.org/10.3390/math9212666 10.3390/math9212666 https://hdl.handle.net/20.500.14352/100116 2227-7390 https//doi.org/10.3390/math9212666 https://www.mdpi.com/2227-7390/9/21/2666 A new edge betweenness measure using a game theoretical approach: an application to hierarchical community cetection