How to find the Laplacian Matrix with Network, please

Hi Dear

If we difine L_{ij} of the graph Laplacian are defined by L_{ij} = A_{ij}- k_i delta_{ij}, where A is the adjacency matrix, k_{i} is the degree of node i, delta_{ij} is the Kronecker delta, and where we do not sum over repeated indices.

N=200;L=100; coverage_range=20;

% random coordination

distinct_BOUND = 5;

P = zeros(N,2);

% rand(1,2)<0.05;

Q = rand(1,2)*L;

P(1,:) = Q;

for j = 2:N

u = true;

m = false;

while u || m

Q = rand(1,2)*L ;

% u is true if new added node is too far to all node

u = true;

for i = 1:j-1

if pdist([Q;P(i,:)],'euclidean') < coverage_range

%D = pdist(X) returns the Euclidean distance between pairs of observations in X.

u = false;

end

end

% m is true if new added node is too near to one node

m = false;

for i = 1:j-1

if pdist([Q;P(i,:)],'euclidean') < distinct_BOUND

m = true;

end

end

end

P(j,:) = Q;

end

figure;

OP=gscatter(P(:,1),P(:,2));

r = sprintf('N-%d,L-%d, cr-%d nodes', N, L, coverage_range);

could you help me to find Laplacian, I use Laplacian() but it didn't work, please

Answer 1

[Nipun]

Hi Ama,

I understand that you intend to find the Laplacian matrix of a given network matrix in MATLAB.

MATLAB has an in-built Laplacian function that works on simple, connected graphs. I recommend cleaning your graph to remove any self-loops and multi-edges. I assume that your graph has these structures that hinder the Laplacian function to calculate the expected matrix.

For more information on syntax, parameters and return type of Laplacian function, refer to the following MathWorks documentation:

https://in.mathworks.com/help/matlab/ref/graph.laplacian.html

Hope this helps.

Regards,

Nipun