L2 boundedness of normalized graphon

Let $W: [0, 1]^2 \to [0, 1]$ be a graphon, i.e. a symmetric measurable function. Let $d(x) := \int_{[0, 1]} W(x, y) \, \mathrm{d}y$ be its degree function. Set$$W'(x, y) \: := \: \frac{W(x, y)}{d(x)^{1/2} d(y)^{1/2}} \cdot \mathbf{1} \{d(x) d(y) > 0\}$$the corresponding degree-normalized graphon. Is its L2 norm $\|W'\|_2 = \left( \int_{[0, 1]^2} W'(x, y)^2 \, \mathrm{d}x \mathrm{d}y \right)^{1/2}$ necessarily finite?