On the notion of effective impedance

Anna Muranova

Research output: Contribution to journalArticlepeer-review


It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two mathematical models of such networks: complex-weighted graphs and graphs with weights from the ordered field of rational functions. The notion of effective impedance in both approaches is defined.

Original languageEnglish
Pages (from-to)723-741
Number of pages19
JournalOperators and Matrices
Issue number3
Publication statusPublished - 2020


  • weighted graphs
  • electrical networks
  • Laplace operator
  • ordered field of rational functions
  • Ordered field of rational functions
  • Weighted graphs
  • Electrical network

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

Cite this