Homomorphism density calculator for step graphons

#Define variables if you want to use them

x = var('x')

#Define the length of each step (should sum up to one...)

I=[0.3,0.3,0.4]

#Define the values of the graphon W on each step in a len(I)xlen(I) matrix

W=[[0.3,0.3,0],[1,0.1,0.4],[0.5,0,1]]

​

#Define the number of vertices of the graph H

n=4

#Define the edge set of H, write edges: [i,j] with i<j using the vertex set 0,...,n-1

H=[[0,1],[1,2],[2,3],[0,3]]

​

#########Below is the code (ignore)###########

​

#Function generating all possible distributions of the vertices of H among the steps

def distr(l):

    if l == 0:

        yield []

    else:

        for vector in distr(l-1):

            for l in range(len(I)):

                yield vector + [l]

​

#Function to calculate the density

def density(H,W,I):

    #Generate list of distributions of vertices

    Distributions=[ w for w in distr(n) ]

    result=0

​

    #Loop over all distributions

    for D in Distributions:

​

        #Calculate the probability that this vertex distribution occurs

        p=1

        for i in range(n):

            p=p*I[D[i]]

        #Calculate the H-density for this vertex distribution

        d=1

        for i in range(n):

            for j in range(i,n):

                if [i,j] in H:

                    d=d*W[D[i]][D[j]]

​

        #sum up the weighted partial H-densities

        result=result+p*d

    return simplify(result)

density(H,W,I)