# graph.laplacian

From igraph v0.5.3
by Gabor Csardi

##### 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.

##### concept

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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