Degree Matrix of Fully connected graph

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https://www.kaggle.com/vipulgandhi/spectral-clustering-detailed-explanation

In this blog post about spectral clustering it states that we can just use the Gaussian Kernel directly.

"Generally we use the Gaussian Kernel K directly, or we form the Graph Laplacian A"

I am confused about how to calculate the degree matrix from a fully connected weighted graph. And I want to implement this in python.

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The degree of a vertex in a fully connected graph is sometimes defined as the sum of the weights of all edges coming from that vertex.

So in other words, the degree $d_i$ of vertex $v_i$ is:

$$ d_i = \sum_j w_{ij} $$

where $w_{ij}$ is the weight of the edge between vertices $v_i$ and $v_j$.

I have found this pdf to be somewhat helpful in understanding both the algorithm and the mathematical intuition behind why it works:

https://people.csail.mit.edu/dsontag/courses/ml14/notes/Luxburg07_tutorial_spectral_clustering.pdf