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Graph-Theoretic Approach to Network Analysis



Author(s)

Nabil Hassan

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DOI:10.17265/1934-7332/2013.12.001

Professor and Chairman Electrical Engineering Department, WVS Tubman College, Harper, Maryland County, Liberia

Networks are a class of general systems represented by their UC-structure. Suppressing the nature of elements the network becomes a weighted graph visualizing the constraints imposed by interconnections rather than the elements themselves. These constraints follow generalized Kirchhoff’s laws derived from physical constraints. Once we have a graph; then the working environment becomes the graph-theory. An algorithm derived from graph theory is developed within the paper in order to analyze general networks. The algorithm is based on computing all the spanning trees in the graph G with an associated weight. This weight is the product of admittance’s of the edges forming the spanning tree. In the first phase this algorithm computes a depth first spanning tree together with its cotree. Both are used as parents for controlled generation of off-springs. The control is represented in selecting the off-springs that were not generated previously. While the generation of off-springs, is based on replacement of one or more tree edges by cycle edges corresponding to cotree edges. The algorithm can generate a frequency domain analysis of the network.

UC-structure, network, spanning tree, depth-first search, spanning trees generation algorithm.