How does random graph generator work in networkx?

I used the source code of Networkx to generate a random graph with Poisson degree distribution.

I change some parts of codes that I need as follows:

import random
import networkx
import math
from networkx.generators.classic import empty_graph

def gnp_random_graph(n, p, seed=None):
    """Return a random graph G_{n,p}.

    Parameters
    ----------
    n : int
        The number of nodes.
    p : float
        Probability for edge creation.
        possible edges: n[n-1]/2
    seed : int, optional
        Seed for random number generator (default=None). 

    """
    #My sample  
    z = 4 #mean degree
    n = 10 #Number of nodes
    p = math.exp**(-z)*z**(k)/(math.factorial(k)) ##I add this myself #k is missing   

    #This part is from the source 
    G=empty_graph(n)

    if not seed is None:
        random.seed(seed)

    for u in xrange(n):
        for v in xrange(u+1,n):
            if random.random() < p:
                G.add_edge(u,v)
return G

In the last part for generating edges, I don't understand how it count degree a开发者_StackOverflow社区nd compare with p(Probability distribution of degree(k))? For me it looks like it generate a random number btw (0,1). But how one should use domain for p and compare the random number with p(k)?

Unless the number of nodes/edges are large, this gives a bernoulli distribution. You can get networkx to give you a poisson degree distribution easily.

import numpy as np
from scipy.stats import poisson

def poissongraph(n,mu):
    z= np.zeros(n) #n is number of nodes
    for i in range(n):
        z[i]=poisson.rvs(mu) #mu is the expected value
    G=expected_degree_graph(z)
    return G

This works, because generating a graph this way (using Brenoulli-sampling), will result in a graph with a Poisson degree-distribution (explained in detail here (pdf)).