Laplacian Matrix

up:: Adjacency Matrix

Given a Simple Graph with adjacency matrix and a diagonal matrix of Node Degrees , the Laplacian matrix is defined as

Properties

Note that, per definition,

Thus, it is equivalent to the adjacency matrix description of the graph , since one can infer its adjacency matrix from the off-diagonal elements, and since the diagonal elements (i.e. node degrees) are equal to the row-wise sum of . In other words, it has no more information than the adjacency matrix . Nevertheless, it is useful in some applications.

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References

• Laplacian matrix - Wikipedia