Methods for simplifying complex electric circuits efficiently and find the equivalent resistance between two points? I find it hard to simplify complex electrical circuits both 2 and 3 dimensional (cube, prism,etc.). Is there any efficient method to simplify a circuit for the purpose of calculating the equivalent resistance between two points?
I have discovered many techniques by solving variety of questions. They are:


*

*Redraw the circuit by taking the nodes at convenient positions or by morphing the circuit.

*Find equi-potent points by symmetry, balanced Wheatstone bridges and blank wires.

*$\Delta-Y$ conversion and vice versa.


Are there other efficient techniques like these which help simplify a circuit?
Please do not talk of using Kirchhoff's law and solving matrix equation as they lengthy and cumbersome. 
 A: There are a number of techniques that can be employed to analyse in an efficient way complex passive networks by means of paper-and-pencil calculations. Of course, for a computer, matrix methods are the way to go.
Here are a few:


*

*For certain type of networks (e.g., series-parallel networks, ladder networks), one can apply the regula falsi (false position): you start from a convenient resistor (e.g., the last one in a ladder network) and you assume that the current in that resistor is an arbitrary value, e.g., 1A; from this, you can walk the network up to the input terminals to find a voltage and a current whose ratio yields the equivalent resistance. This method is also useful to calculate the current in the last resistor knowing the voltage or the current at the input: you just have to take a proportion.

*Middlebrook's extra element theorem (EET) [1,2] and its extension, the $n$EET [3,4]. These are lesser known theorems of network theory which allow to find solutions in so-called "low-entropy" form, that is, a readable form evidencing the most significant terms. I gave an example of outcome from this theorem in this answer. They are not specific to the calculation of equivalent resistances -- they are much more general, in fact -- but they can be also efficiently applied in this case. In the references given below there are examples of applications.

*Bartlett's bisection theorem. This theorem, also, is not specific to the calculation of equivalent resistances, but sometimes it can be applied to this aim when the network has certain symmetries.

*Exploit the symmetry of the network, especially when you have networks with equal resistances. This is probably what you mean in your points 1 and 2. There exists also a number of works which give a systematic treatment of symmetrical networks, I'll add the references as soon as I find them in my messy folders.


[1] R. D. Middlebrook, "Null Double Injection and the  Extra Element Theorem", IEEE Trans. Edu., 32, 167-180, 1989 online copy 
[2] V. Vorperian, Fast Analytical Techniques for Electrical and Electronic Circuits, Cambridge University Press, 2011.
[3] R. D. Middlebrook, V. Vorperian, J. Lindal, "The N Extra Element Theorem", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45, 919-935, 1998.
[4] R. W. Erickson, "The $n$ Extra Element Theorem", online.
