Authors: R. Mahendran, S. Kavitha
Abstract: Electrical circuit analysis has traditionally relied on algebraic and differential equation based techniques such as Kirchhoff’s laws, nodal analysis, and mesh analysis. With the increasing complexity of modern electrical networks, including large-scale power systems, integrated circuits, and communication networks, these classical approaches often become computationally intensive and conceptually opaque. Graph theory offers an elegant mathematical framework that represents electrical circuits as graphs composed of nodes and edges, enabling systematic, compact, and scalable analysis. This paper presents a comprehensive study of graph theory applications in electrical circuit analysis. Fundamental graph concepts such as trees, loops, cut-sets, incidence matrices, and tie-set matrices are discussed in the context of circuit modeling. The paper further explores how graph-theoretic methods simplify network topology description, aid in automated circuit analysis, and support advanced applications such as fault detection and network optimization. Illustrative examples, tables, and two-dimensional figures are included to demonstrate practical implementation. The study highlights the relevance of graph theory as a bridge between abstract mathematics and real-world electrical engineering problems.
Keywords: Graph theory, electrical circuits, network topology, incidence matrix, tie set, cut-set, circuit analysis
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