A *series-parallel network* is any network which can be constructed using just, well, series and parallel connections.
For the formal definitions lovers out there,

A network is *series-parallel* iff:
- It is simple (i.e. a single impedance: one R, one L, or one C); - OR -
- It is two series-parallel networks connected in series; - OR -
- It is two series-parallel networks connected in parallel.

It is very easy to calculate the effective resistance (or effective impedance, if you're into such twisted matters) of series-parallel networks. This makes people underestimate Thevenin's theorem, because they immediately say...

# Huh? Aren't they all series-parallel?

NO!

The classic counterexample is Wheatstone's bridge:

+--'\/\/\/\/`-+-`\/\/\/\/`--+
| 1 | 2 |
| \ |
------+ / 3 +----
| \ |
| 4 / 5 |
+--'\/\/\/\/`-+-`\/\/\/\/`--+

# OK, so how *do* I calculate the effective resistance of a bridge?

Linear algebra. Write a whole bunch of linear equations for voltage and current, and solve them.

# Ummm, but how do I know these equations have a unique solution?

Didn't we just mention Thevenin's theorem?

# So how do I *really* prove Thevenin's theorem, not the weak-kneed version for series-parallel networks?

Didn't we just mention linear algebra?