Equivalent resistance

Since the reference is taken at points $A$ and $B$ , no current flow through the top-right resistor and bottom-right resistor. The two resistors need not to be considered in the calculations. The remaining circuit is ( $R=10\Omega$ ):

$R_{eq}=R+(R+R)//(R+R)+R$

$\quad \quad = 10+20//20+10=10+10+10=\boxed{30\space \Omega}$

No current would pass through either the upper right or lower left resistor; we can eliminate those from the network. The the total resistance is given by the series contributions of the upper left, the lower right and the combined resistance of those arranged in the square.