Kirchhoff's current law, which states that the sum of the currents entering and exiting a node is zero, is essential in the analysis.The first step is to recognize that at a node where equal resistances exist, current entering the node will be distributed equally between the number of output branches - in this case three.

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Currentiwill be split into 3 branch currents. Since the resistance is same (i.e. r ohm), Current in each branch will bei/3. Thisi/3current will in turn split into 2 branch currents each of valuei/6.

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The next step is to sum the voltage from input node "a" to output node "b." Any path you take travels along three edges, The current between 2 diagonally opposite side will be composed oftwo i/3 currents and one i/6 current.

So that total voltage drop will be same along any path, let the volage drop be V

(i/3)r + (i/3)r + (i/6)r = V

V = (5i/6)r

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Finally, apply Ohms law, which says that the resistance is equal to the voltage divided by the current.

Let the equivalent resistance be R

R = V / i

R = (5i/6)r/i

R = 5r/6 ohm

=> R = 5(6)/6 = 5ohm