The Group Inverse of the Laplacian Matrix of a Graph
What follows is a short, selective tour of some of the connections between weighted graphs and the group inverses of their associated Laplacian matrices. The presentation below draws heavily from Kirkland–Neumann [11, Ch. 7], and the interested reader can find further results on the topic in that book. We note that Molitierno  also covers some of the material presented in this chapter, and so serves as another source for readers interested in pursuing this subject further.
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