added two functions from the DeLange paper about laplacian eigenvalues

kdesmooth.m

@@ -0,0 +1,7 @@
+function y = kdesmooth(lambda,x,sigma)
+
+y=zeros(1,length(x));
+for i=1:length(lambda)
+    y = y + 1/(sqrt(2*pi*sigma.^2)).*exp(-((x-lambda(i))/(sqrt(2)*sigma)).^2);
+end
+%y  = y/sum(y);

laplacian_eigenplot.m

@@ -0,0 +1,20 @@
+function laplacian_eigenplot(A)
+n=length(A);
+% 1. compute the diagonal degree matrix
+D = diag(sum(A));
+% 2. Compute the normalized Laplacian
+L = eye(n) - D^(-1/2)*A*D^(-1/2);
+
+% 3. Compute the eigenvalues lambda
+lambda = eig(L);
+
+% 4. Define the grid over which to compute the smoothing
+nx = 500;
+x = linspace(0,2,nx);
+
+% 5. Draw histogram and the distribution
+hold on;
+nbins = 200;
+histogram(eig(L),nbins,'Normalization','countdensity');
+sigma=0.005;
+plot(x, kdesmooth(eig(L),x,sigma),'r','LineWidth',2);