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2016-04-03 21:56:38 +0200 | asked a question | Graph theory for symbolic electrical circuit analysis? Looking for how to go from graph theory directly to solve circuit/nodal analysis. This link has been helpful: (have to google graphsandckts.pdf because I can't post the link) but I seem to be getting lost in the graph theory part. Circuit analysis software like SPICE must do something like this numerically. I can build a directed graph in Sagemath by adding vertices/edges. Sagemath will return the incidence matrix. Or you can enter the incidence matrix directly but for something like a circuit netlist it can be a lot easier to enter nodes, ie. vertices of the graph. Resistances/impedances go into a diagonal matrix R, known voltages/currents go into a vector. I'm not clear on finding the spanning tree/re-arranging the incidence matrix. Seems like this should be some standard graph theory or linear algebra functions. You eliminate one row/column and should have a matrix A =[ At I ] where At = edges in the graph spanning tree and I = n x n identity matrix. The rest should be basic linear algebra: transpose, inverse, multiplying it out |

2016-03-26 15:01:36 +0200 | commented question | Nodal analysis in network This link might help. Usually the linear equations for Kirchoff's laws are setup by inspection and solved numerically or a program like Spice (open source: Qucs) does it. I think the question is how to use the incidence matrix and cycle matrix of the network graph and voltages/current to solve for current/voltage. http://www2.math.uu.se/~takis/L/Circuits/2000/handouts/graphsandckts/graphsandckts.pdf (link text) |

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