The previous Laplacian matrix assumed al the edges were the same weight, hence the edge matrix placed a 1 (or -1) at every edge. To accomodate the edge weights, we change the definition of the matrix as follows:
where di is the degree of vertex i and wij is the weight of the edge adjacent to i and j.
Considering the graph we've been using throughout this blog, the Laplacian matrix using the new definition is:
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