The Laplacian of a graph.
- The input graph.
- Whether to calculate the normalized Laplacian. See definitions below.
The Laplacian Matrix of a graph is a symmetric matrix having the same number of rows and columns as the number of vertices in the graph and element (i,j) is d[i], the degree of vertex i if if i==j, -1 if i!=j and there is an edge between vertices i and j and 0 otherwise.
A normalized version of the Laplacian Matrix is similar: element (i,j) is 1 if i==j, -1/sqrt(d[i] d[j]) if i!=j and there is an edge between vertices i and j and 0 otherwise.
- A square matrix with as many rows as the number of vertices in the input graph.
g <- graph.ring(10) graph.laplacian(g) graph.laplacian(g, norm=TRUE)