RT Journal Article
T1 A new edge betweenness measure using a game theoretical approach: an application to hierarchical community cetection
A1 Espínola Vílchez, María Rosario
A1 Gómez González, Daniel
A1 Castro Cantalejo, Javier
A1 Gutiérrez García-Pardo, Inmaculada
A2 Jiménez Losada, Andrés
A2 Goubko, Mikhail
AB 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.
PB MDPI
YR 2021
FD 2021-10-21
LK https://hdl.handle.net/20.500.14352/100116
UL https://hdl.handle.net/20.500.14352/100116
LA eng
NO 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
NO Ministerio de Ciencia, Innovación y Universidades (España)
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 20 abr 2025