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I've been learning about electrical circuits, and I can see how Graph Theory naturally lends itself well to problems with circuits.

I was wondering what some examples of applications of Graph Theory in electric circuit analysis; if there are any that are particularly conducive to use graphs and thus more interesting.

Also, are directed graphs or undirected graphs used more often when applying Graph Theory to electrical circuits?

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    $\begingroup$ One application is the following: circuit solvers/simulators used for circuit analysis use some form of what is called Modified Nodal Analysis (MNA). The idea is to view the circuit as an undirected graph with the impedances in the graph weights. The solution involves computing the Laplacian of the graph. However, there are many other applications. In fact, electrical circuits one of the canonical applications of graph theory. See also: math.stackexchange.com/a/313466/423711 . $\endgroup$
    – FeedbackLooper
    Commented Jul 19, 2021 at 15:44
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    $\begingroup$ @FeedbackLooper Oh wow, I had no clue about it being a canonical application! That application sounds interesting too, I'll read up on it. Thanks $\endgroup$
    – dfish
    Commented Jul 19, 2021 at 15:57
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    $\begingroup$ Application of graphs to passive electrical circuits goes back at least to the 1970s and I'd bet farther back than then. Simplest codes dealt with the standard components (supplies, resistors, capacitors, inductors) in the frequency domain and involved undirected graphs. More sophisticated analyses in the time domain required directed graphs. $\endgroup$
    – A rural reader
    Commented Jul 19, 2021 at 18:32

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