In spectral clustering, the weighted adjacency matrix $W$ represents the similarity graph of the data points. Each entry $w_{i,j}$ denotes the non-negative similarity between points $i$ and $j$, calculated by a specific function. For example, using the Gaussian similarity function:

$w_{i,j} = \exp(- \frac{||x_i - x_j||^2}{2\sigma^2})$

Here, $||\cdot||$ denotes the L2 norm, and $\sigma$ is a scaling parameter. The matrix $W$ is symmetric, and all weights satisfy $w_{i,j} \geq 0$.