KirchhoffMatrix

KirchhoffMatrix[g] gives the Kirchhoff matrix (Laplacian matrix) of the graph g.

KirchhoffMatrix[{v -> w, ...}] uses rules v -> w to specify the graph g.

Examples

Kirchhoff matrix of a path graph:

KirchhoffMatrix[PathGraph[{1, 2, 3}]] // MatrixForm

From edge rules:

KirchhoffMatrix[{1 -> 2, 2 -> 3, 3 -> 1}]

Please visit the official Wolfram Language Reference for more details.