hiperwalk.WeightedGraph.laplacian_matrix#
- WeightedGraph.laplacian_matrix()[source]#
Return the graph’s Laplacian matrix.
See also
Notes
The Laplacian matrix is given by
\[L = W - A,\]where \(A\) is the graph’s adjacency matrix and \(W\) is a diagonal matrix whose entries are the sum of the weights of the edges incident to a given vertex.
\[\begin{split}W_{i, j} = \begin{cases} \sum_{k = 0}^{|V| - 1}A_{ik}, & \text{if } i = j\\ 0, & \text{otherwise}. \end{cases}\end{split}\]