Laplacian Matrix for a Directed Graph

This function returns the directed Laplacian matrix of any graph (DAG).

This function returns the directed Laplacian matrix of any graph (DAG).
This is a direct implementation of the paper referred below.
The Graph Laplacian is calculated using the following formula
L = I - (Phi^{1/2} * P * Phi^{-1/2} + Phi^{-1/2} * P^T * Phi^{1/2} ) / 2
where,
I : Identity matrix,
Phi : Matrix with the Perron vector of P in the diagonal and zeros elsewhere, and
P : Transition matrix of the graph. This value depends on the walk
type of the graph exploration.
!! Current implementation includes only a "PageRank" walk type.
!! Future Implementation Plan: "Random Walk"
Referred paper:
Chung, F. (2005). Laplacians and the Cheeger inequality for directed graphs. Annals of Combinatorics, 9(1), 1-19.