# graph.laplacian

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##### Graph Laplacian

The Laplacian of a graph.

Keywords
graphs
##### Usage
graph.laplacian(graph, normalized=FALSE)
##### Arguments
graph
The input graph.
normalized
Whether to calculate the normalized Laplacian. See definitions below.
##### Details

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.

##### Value

• A square matrix with as many rows as the number of vertices in the input graph.

Graph Laplacian

##### Aliases
• graph.laplacian
##### Examples
g <- graph.ring(10)
graph.laplacian(g)
graph.laplacian(g, norm=TRUE)
Documentation reproduced from package igraph, version 0.5.3, License: GPL (>= 2)

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