Editing Network analysis (electrical circuits) (section)

===General form of network node elimination===
{{main|Star-mesh transform}}

The star-to-delta and series-resistor transformations are special cases of the general resistor network node elimination algorithm.  Any node connected by {{mvar|N}} resistors {{math|(''R''{{sub|1}} … ''R{{sub|N}}'')}} to nodes {{math|'''1''' … '''''N'''''}} can be replaced by <math>\tbinom{N}{2}</math> resistors interconnecting the remaining {{mvar|N}} nodes.  The resistance between any two nodes {{mvar|x, y}} is given by:
:<math>R_\mathrm{xy} = R_x R_y\sum_{i=1}^N \frac{1}{R_i}</math>
For a star-to-delta ({{math|1=''N'' = 3}}) this reduces to:
:<math>\begin{align}
R_\mathrm{ab} &= R_a R_b \left(\frac 1 R_a+\frac 1 R_b+\frac 1 R_c\right) = \frac{R_a R_b(R_a R_b + R_a R_c + R_b R_c)}{R_a R_b R_c} \\
&= \frac{R_a R_b + R_b R_c + R_c R_a}{R_c}
\end{align}</math>
For a series reduction ({{math|1=''N'' = 2}}) this reduces to:
:<math>R_\mathrm{ab} = R_a R_b \left(\frac 1 R_a+\frac 1 R_b\right) = \frac{R_a R_b(R_a + R_b)}{R_a R_b} = R_a + R_b</math>
For a dangling resistor ({{math|1=''N'' = 1}}) it results in the elimination of the resistor because <math>\tbinom{1}{2} = 0</math>.