Equivalent resistance using wye-delta
If you're happy to trade accuracy for speed, I'd note that the circuit is a 10 ohm in parallel with everything else. Everything else is going to work out to be at least 10 ohm, so Req is approximately 6 ohm. Good to within an order of magnitude.

For accuracy and generality it has to be nodal analysis (with a dummy source). Apply at every node and stick into a big matrix to be solved by a linear algebra package.