Obtaining laplacian of a graph

The Neumann Laplacian of a simple graph(G) can be formed from the commands degree(G) and adjacency(G), L= D- A .

Could someone suggest how Dirichlet laplacian can be obtained?

[Christine Tobler]

Could you please provide a definition / a link to a definition of the Dirichlet laplacian for a graph?

[Deepa Maheshvare]

Please find the link here

[Christine Tobler]

Based on formula (1.10) in that paper, that would be L = 2*d*I + (2*d*I - D) - A, with I the identity and d a scalar depending on the dimensionality of the graph, wouldn't it?

[Deepa Maheshvare]

I tried the above formula for an 1 D graph with 5 nodes.

d = 1,

L = 2*d*I + (2*d*I - D) - A,

gives,

     3    -1     0     0     0
    -1     2    -1     0     0
     0    -1     2    -1     0
     0     0    -1     2    -1
     0     0     0    -1     3

whereas, the pseudo dirichlet 2*d*I-A (1.9)gives

     2    -1     0     0     0
    -1     2    -1     0     0
     0    -1     2    -1     0
     0     0    -1     2    -1
     0     0     0    -1     2

which matches with the laplacian computed using centered difference formula for the second derivative operator with dirichlet boundary condition.

Also, I am not sure how the dimensionality of any given graph can be determined.

Any suggestions?

[Christine Tobler]

A graph doesn't have an inherent dimensionality, this would have to be based on the construction of the graph. Perhaps the linked paper has more information.