Manríquez, RonaldGuerrero-Nancuante, CamiloMartínez, FelipeTaramasco, Carla2022-11-302022-11-302021Manríquez, R.;Guerrero-Nancuante, C.; Martínez, F.;Taramasco, C. A Generalization of the Importance of Vertices for an Undirected Weighted Graph. Symmetry 2021, 13, 902. https://doi.org/10.3390/sym13050902http://repositoriobibliotecas.uv.cl/handle/uvscl/7556Establishing a node importance ranking is a problem that has attracted the attention of many researchers in recent decades. For unweighted networks where the edges do not have any attached weight, many proposals have been presented, considering local or global information of the networks. On the contrary, it occurs in undirected edge-weighted networks, where the proposals to address this problem have been more scarce. In this paper, a ranking method of node importance for undirected and edge-weighted is provided, generalizing the measure of line importance (DIL) based on the centrality degree proposed by Opsahl. The experimentation was done on five real networks and the results illustrate the benefits of our proposal.© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).EDGE-WEIGHTED GRAPHVERTEX IMPORTANCECOMPLEX NETWORKSArticulohttps://doi.org/10.3390/sym13050902