2026-04-19T17:36:03Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1051992026-02-07T07:35:51Zcom_2072_1033col_2072_452950

Resistance distances on networks Carmona Mejías, Ángeles Encinas Bachiller, Andrés Marcos Mitjana Riera, Margarida Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta Graph theory Eff ective resistances resistance distances Schrodinger operator symmetric M-matrices. Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory This paper aims to study a family of distances in networks associated witheffective resistances. Speci cally, we consider the e ective resistance distance with respect to a positive parameter and a weight on the vertex set; that is, the effective resistance distance associated with an irreducible and symmetric M-matrix whose lowest eigenvalue is the parameter and the weight function is the associated eigenfunction. The main idea is to consider the network embedded in a host network with additional edges whose conductances are given in terms of the mentioned parameter. The novelty of these distances is that they take into account not only the influence of shortest and longest weighted paths but also the importance of the vertices. Finally, we prove that the adjusted forest metric introduced by P. Chebotarev and E. Shamis is nothing else but a distance associated with a Schr odinger operator with constant weight Peer Reviewed Postprint (author's final draft) 2017 Article Carmona, A., Encinas, A., Mitjana, M. Resistance distances on networks. "Applicable analysis and discrete mathematics", 2017, vol. 11, núm. 1, p. 136-147. 1452-8630 https://hdl.handle.net/2117/105199 10.2298/AADM1701136C eng http://www.doiserbia.nb.rs/Article.aspx?ID=1452-86301701136C&AspxAutoDetectCookieSupport=1 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain 12 p. application/pdf