How do I calculate the equivalent resistance between the points A and B?

Eq Resistance=1 Ohm

This arrangement is similar to wheatstone bridge

as that will be in formP/Q=R/S no current will flow through bridge , now u can easily find eq resistance

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In this figure the resistances are short circuted the 1’st resistance(2’nd line) comes in series with the resistance on the 1’st line and becomes 2ohm,so does the 3’rd resistance(2’nd line) comes in series with the resistance on the third line and becomes 2ohm.

Thus a 1ohm,and two 2ohm resistances come parallel which makes the  equialent restance=1/2ohm