Equivalent Resistance between A and B
simulate this circuit &ndash; Schematic created using CircuitLab

From this rearrangement, you can see that there are 4 nodes. One way to solve this is nodal analysis. You put a unit current source between a and b, and set B to 0, giving you three node equations:

$$A:\frac{(V_A-V_3)}{2}+\frac{(V_A-V_4)}{1}+\frac{(V_A-0)}{5}-1=0$$

$$3: \frac{(V_3-V_A)}{2}+\frac{(V_3-V_4)}{2}+\frac{(V_3-0)}{3}=0$$

$$4: \frac{(V_4-V_A)}{1}+\frac{(V_4-V_3)}{2}+\frac{(V_4-0)}{4}=0$$

You then solve for A to get the voltage. Since you know the current going into the system (1 Amp), you can use:

$$\frac{V}{I}=R$$

Since I=1, the resistance will actually just be the voltage at A.