The effective resistance between $$A$$ and $$B$$, if resistance of each resistor is $$R$$, will be

step 1: observe symmetry

The network is symmetric about the vertical axis (through the center).
So the left and right junctions of the diamond are at the same potential.

⇒ no current flows through the horizontal central resistor
⇒ remove that resistor

step 2: reduce the diamond

Now between the left and right junctions, we have three independent parallel paths:

• top path: two resistors → R + R = 2R
• bottom path: two resistors → R + R = 2R
• central vertical path: two resistors → R + R = 2R

So:

$$R_{\text{diamond}}=2R\parallel2R\parallel2R$$

$$=\frac{2R}{3}$$

step 3: include outer resistors

From A to diamond: R
From diamond to B: R

So total:

$$R_{eq}=R+\frac{2R}{3}+R=2R+\frac{2R}{3}=\frac{8R}{3}$$