It may look like there are series and parallel combinations, but there are NOT! None of the resistors are in parallel or series. This is known as an irreducible network. You can still find an equivalent resistance however. Connect a 1 amp test source to the circuit and compute the voltage over the test source using node-voltage or mesh-current analysis. Then you can find Req by Ohm's law:
Req = Vtest / Itest
Since you selected Itest to be 1, the division is simple.