Find the equivalent resistance of the given electrical network across terminals A and B:

The resistor between A and B has resistance $$R_1 = 1 \, \Omega$$.

For the other path, A → C → B, the resistors AC and CB are in series. Therefore,

$$R_2 = 1 + 1 = 2 \, \Omega$$

Now, these two paths are connected in parallel between A and B. Hence,

$$R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2}$$

$$R_{\text{eq}} = \frac{1 \times 2}{1 + 2} = \frac{2}{3} \, \Omega$$

Therefore, the equivalent resistance between A and B is $$\frac{2}{3} \, \Omega$$.

Hence, the correct option is C.