Definition
Given a simple graph G with n vertices, its Laplacian matrix is defined as:
That is, it is the difference of the degree matrix D and the adjacency matrix A of the graph. In the case of directed graphs, either the indegree or outdegree might be used, depending on the application.
From the definition follows that:
where deg(vi) is degree of the vertex i.
The normalized Laplacian matrix is defined as:
Read more about this topic: Laplacian Matrix
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