Implement generators of complex networks for, at least, two of the following models of complex...

Question

Implement generators of complex networks for, at least, two of the following models of complex networks (sorted by increasing difficulty), which must include at least one of the two last ones (BA or CM):

Erdös-Rényi (ER) networks, either G(N,K) or G(N,p)
Watts-Strogatz (WS) small-world model
Barabási & Albert (BA) preferential attachment model
Configuration Model (CM)

The correction, the number, and the difficulty of the implemented models will be taken into account.

It is not allowed to use already implemented network generators such as the ones in NetworkX or Pajek. You may use libraries implementing “network” or “graph” data types, to avoid unnecessary work, but not the algorithms for the generation of networks for these models.

The delivery must include:

Source code
Networks generated for the selected models, with different sizes N (e.g. N=50, 100, 1000) and for different values of the parameters of the models:

ER: different values of "K" for G(N,K), or of "p" for G(N,p), such that e.g. =3, 6, 10
WS: different values of "p", including p=0, e.g. p=0.0, 0.1, 0.2, 0.5, 0.9, 1.0
BA: different values of "m" (number of edges that each new nodes forms with the existing nodes), e.g. m=1, 2, 5
CM: different degree distributions: Poisson (ER), e.g. =2, 4; power-law (SF) with different exponents, e.g. gamma=2.2, 2.7, 3.5

It is not necessary to generate networks for all the combinations of the parameters, e.g. for the BA you could fix N=1000 and just modify m.
It is mandatory, for each model, to generate one network of size N=1000 and another of N=10000.

Document (in PDF) with all the results:

Short explanations on how have you done the required work (software, decisions, etc.)
Plots of some of the small size generated networks, e.g. N=50 (ER, WS), N=100 (BA, CM)
Plots of the degree distributions, including the theoretical values (corresponding to the selected parameters) and the experimental ones (for the generated network), for the networks of size N>=1000.
Estimation of the exponent for the empirical degree distributions of BA and CM(SF), for the networks of size N>=1000.

Do not include in the delivery (zip, rar or tgz file) the largest networks with N > 1000 nodes, their plots of degree distribution and estimation of parameters is enough.

Files

A2-Details-BA.pdf
A2-Details-CM.pdf
A2-Details-Exponent.pdf
A2-Clauset-Power-law_distributions_in_empirical_data.pdf

activity2-requirements-r0ylld4l.zip

Sandeep Kumar · Accepted Answer

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx
",
    "import numpy as np
",
    "import random, math
",
    "import matplotlib.pyplot as plt
",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ER_network(N, p):
",
    "    G = nx.Graph()
",
    "    G.add_nodes_from(range(N))
",
    "    for i in range(0, N):
",
    "        for j in range(i+1, N):
",
    "            if random.random() i: G.add_edge(i,j)
",
    "
",
    "    for h in range(m0,N):    # add new nodes
",
    "        G.add_node(h)
",
    "        k = nx.degree(G)
",
    "        ks = []
",
    "        for i in k: ks.append(k[i])
",
    "        ks.remove(ks[-1])
",
    "        ks = [sum(ks[:i+1]) for i in range(len(ks))]
",
    "        M = 1
",
    "        th = -1
",
    "        while M  i:
",
    "                    if th == idx:
",
    "                        break
",
    "                    else:
",
    "                        G.add_edge(h, idx)
",

Implement generators of complex networks for, at least, two of the following models of complex networks (sorted by increasing difficulty), which must include at least one of the two last ones (BA or...

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