RESISTANCE DISTANCES ON NETWORKS

Applicable Analysis and Discrete Mathematics

article

A. Carmona¹  A.M. Encinas¹  M. Mitjana² 

[1] Universitat Politcnica de Catalunya;Universitat Politcnica de Catalunya Av. dEduard Maristany

关键词: Symmetric M-matrices;    Resistance distances;    Effective resistances;    Schrödinger operators;   

DOI  :  10.2298/AADM1701136C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

This paper aims to study a family of distances in networks associated witheffective resistances. Specifically, we consider the effective resistance distancewith respect to a positive parameter and a weight on the vertex set; that is,the effective resistance distance associated with an irreducible and symmetricM–matrix whose lowest eigenvalue is the parameter and the weight functionis the associated eigenfunction. The main idea is to consider the networkembedded in a host network with additional edges whose conductances aregiven in terms of the mentioned parameter. The novelty of these distancesis that they take into account not only the influence of shortest and longestweighted paths but also the importance of the vertices. Finally, we provethat the adjusted forest metric introduced by P. Chebotarev and E. Shamisis nothing else but a distance associated with a Schr¨odinger operator withconstant weight.

【 授权许可】

Unknown