common graphon functions

[dufourc1]

function graphon_product(x,y)
    return x * y
end

function graphon_exp_07(x,y)
    return exp(-(x^0.7 + y^0.7))
end

function graphon_polynomial(x,y)
    return 0.25 * (x^2 + y^2 + sqrt(x) + sqrt(y))
end

function graphon_mean(x,y)
    return 0.5 * (x + y)
end

function graphon_logit_sum(x,y)
    return 1 / (1 + exp(-10 * (x^2 + y^2)))
end

function graphon_latent_distance(x,y)
    return abs(x - y)
end

function graphon_logit_max_power(x,y)
    return 1 / (1 + exp(-(max(x, y) ^ 2 + min(x, y) ^ 4)))
end

function graphon_exp_max_power(x,y)
    return exp(-max(x, y) ^ (3 / 4))
end

function graphon_exp_polynomial(x,y)
    return exp(-0.5 * (min(x, y) + sqrt(x) + sqrt(y)))
end

function graphon_log(x,y)
    return log1p(0.5 * max(x, y))
end