Non-random connectivity comes in pairs
Documentation for research article DOI:10.1162/netn_a_00004

• About
• TWO-POINT DISTRIB.
• Fig 1A
• Fig 1B
• statistic
• GAMMA DISTRIB.
• K(a,b)
• Figure 2A
• Figure 2B
• Figure 2C
• statistic
• SYMMETRY IN PAIRS
• Figure 3A
• Figure 3B
• TROUBLESHOOTING
• Problems

Here's how the factor \(K(\alpha,\beta)\) and the probability density function \(f^T_{\alpha, \beta}(x)\) of the truncated gamma distribution are computed

from scipy.special import gamma
import scipy.integrate as integrate
import numpy as np


def K(a,b):

    int_f_0_1 = integrate.quad(
        lambda x: 1/(b**a*gamma(a))*x**(a-1)*np.exp(-x/b),0,1)
    K_ab = 1./(int_f_0_1[0])

    return K_ab


def fT(x,a,b):
    '''
    computes the probability density function $f^T_{\alpha, \beta}$ 
    of the truncated gamma distribution $\Gamma^{T}(\alpha,\beta)$
    '''

    if x < 0:
        fT_ab = 0
    elif x>1:
        fT_ab = 0
    else:
        K_ab = K(a,b)

        fT_ab = K_ab * 1/(b**a*gamma(a))*x**(a-1)*np.exp(-x/b)

    return fT_ab

This script is used as gamma_functions.py in the subsequent calculations and plots for the network with gamma distributed connection probabilities.