In [74]:

    

using PyPlot
include("utils.jl")
using DiffusionTutorialUtilities
utils = DiffusionTutorialUtilities
A,xy = utils.load_graph_and_coords("newman-netsci")
utils.cgraphplot(A,xy,filled=false)


    

    




WARNING: replacing module DiffusionTutorialUtilities






    
Out[74]:

In [75]:

    

include("diffusions.jl")
using DiffusionAlgorithms


    

    




WARNING: replacing module DiffusionAlgorithms

In [76]:

    

lam1 = real(eigs(A)[1][1])


    

    
Out[76]:





10.375458631159697

In [77]:

    

function single_seed_katz(A,alpha,lam1,seed)
    n = size(A,1)
    @assert 1 <= seed <= n
    v = zeros(size(A,1))
    v[seed] = (1.-alpha)
    x = (eye(n) - alpha*(1/lam1)*A) \ v
end
x = single_seed_katz(A,0.85,lam1,1)
utils.graphplot(A,xy)
scatter(xy[:,1],xy[:,2],400*x+5,400*x,edgecolor="None",cmap="inferno")


    

    













    
Out[77]:





PyObject <matplotlib.collections.PathCollection object at 0x31edb0310>

In [78]:

    

using Interact


    

In [79]:

    

n = size(A,1)
f = figure()
@manipulate for alpha=0:0.01:0.99, seed=1:n; withfig(f) do
        x = single_seed_katz(A,alpha,lam1,seed)
        utils.graphplot(A,xy)
        scatter(xy[:,1],xy[:,2],25*max(log(n*x),0.25),max(log(n*x),0),edgecolor="None",cmap="inferno")
        axis("off")
        colorbar()
        #clim([0,sqrt(n)])
    end   
end


    

    












    












    
Out[79]:

In [11]:

    

close("all")


    

In [81]:

    

include("diffusions.jl")
include("utils.jl")
using DiffusionAlgorithms
using DiffusionTutorialUtilities

A,xy = utils.load_graph_and_coords("newman-netsci");
n = size(A,1)
# chebyshev point set of alphas
N=15; alphas = [0.999,0.995,0.99,0.95,0.9,0.85,0.8,0.75,0.66,0.5,0.25,0.1]
@manipulate for alpha=alphas, seed=1:n
    @time x = DiffusionAlgorithms.single_seed_katz_power(A,alpha,lam1,seed)
    @show extrema(x), 1/n
    @show "here"
    utils.cgraphplot(A,xy,0.05*log(1/minimum(x)*x),log(1/minimum(x)*x),utils._inferno_data)
end


    

    












    












    




WARNING: replacing module DiffusionAlgorithms
WARNING: replacing module DiffusionTutorialUtilities






    




  





    
Out[81]:

In [83]:

    

include("diffusions.jl")
include("utils.jl")
using DiffusionAlgorithms
using DiffusionTutorialUtilities

A,xy = utils.load_graph_and_coords("U3A");
lam1 = real(eigs(A)[1][1])
n = size(A,1)
# chebyshev point set of alphas
alphas = ([0.999,0.995,0.99,0.95,0.9,0.85,0.8,0.75,0.66,0.5,0.25,0.1,0.01,0.001])
@manipulate for alpha=alphas, seed=1:n
    @time x = DiffusionAlgorithms.single_seed_katz_power(A,alpha,lam1,seed)
    @show extrema(x)
    @show "done alpha=$(alpha), seed=$(seed)"
    utils.cgraphplot(A,xy,0.1*log(1/(max(minimum(x),1.e-12))*x),log(x+1.e-12),
        utils._inferno_data)
end


    

    












    












    




WARNING: replacing module DiffusionAlgorithms
WARNING: replacing module DiffusionTutorialUtilities






    




  





    
Out[83]:













    




0.080722 seconds (34.81 k allocations: 1.741 MB)
extrema(x) = (6.025341743901221e-24,0.0010872633021897504)
"done alpha=$(alpha), seed=$(seed)" = "done alpha=0.999, seed=1500"