2026, Vol. 7, Issue 1, Part A
Graph-theoretic approach to analyze simple electrical network topology
Author(s): Carlos Eduardo Ramírez and María Fernanda González
Abstract: The mathematical analysis of electrical networks has evolved substantially since Gustav Kirchhoff first established the foundational laws of circuit theory in 1845. This research presents a graph-theoretic methodology for analyzing simple electrical network topologies, transforming circuit analysis problems into equivalent graph representations that leverage established algorithms from discrete mathematics [1]. The approach maps electrical network elements to graph edges while circuit nodes become graph vertices, enabling application of incidence matrices, adjacency relationships, and Laplacian formulations to derive circuit equations systematically [2]. A software implementation was developed in Python utilizing NetworkX and NumPy libraries to validate the theoretical framework against conventional nodal and mesh analysis techniques. Test circuits ranging from 5 to 100 nodes were analyzed to evaluate computational efficiency and numerical accuracy across varying network complexities. Results demonstrated that graph-theoretic methods reduced computation time by 32.4% compared to traditional nodal analysis for networks exceeding 50 nodes, with the advantage increasing to 41.7% for 100-node configurations [3]. Memory consumption showed even greater improvements, with graph-based storage requiring 56.2% less memory than full matrix representations for sparse networks typical of practical circuits. Numerical accuracy remained comparable across all methods, with relative errors below 0.15% for ideal conditions and below 2.5% even under 5% parameter uncertainty [4]. The research establishes graph theory as a viable alternative framework for network analysis, particularly beneficial for large-scale or sparse topologies where computational resources constrain traditional approaches. The methodology extends naturally to more complex network types including nonlinear elements and time-varying parameters through appropriate graph edge weighting schemes [5].
DOI: 10.22271/27084531.2026.v7.i1a.112
Pages: 33-38 | Views: 27 | Downloads: 11
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How to cite this article:
Carlos Eduardo Ramírez, María Fernanda González. Graph-theoretic approach to analyze simple electrical network topology. Int J Res Circuits Devices Syst 2026;7(1):33-38. DOI: 10.22271/27084531.2026.v7.i1a.112
