Implementation of Erdos-Renyi Model on Social Networks

Last Updated : 01 Oct, 2020

Prerequisite: Introduction to Social Networks, Erdos-Renyi Model

Erdos Renyi model is used to create random networks or graphs on social networking. In the Erdos Reny model, each edge has a fixed probability of being present and being absent independent of the edges in a network.

Implementing a Social Network using the Erdos-Renyi model:

Step 1) Import necessary modules like networkx, matplotlib.pyplot, and random module.

Python3

# Import Required modules 
import networkx as nx 
import matplotlib.pyplot as plt 
import random

Step 2) Create a distribution graph for the model.

Python3

# Distribution graph for Erdos_Renyi model 
def distribution_graph(g): 
    print(nx.degree(g)) 
    all_node_degree = list(dict((nx.degree(g))).values()) 
  
    unique_degree = list(set(all_node_degree)) 
    unique_degree.sort() 
    nodes_with_degree = [] 
    for i in unique_degree: 
        nodes_with_degree.append(all_node_degree.count(i)) 
  
    plt.plot(unique_degree, nodes_with_degree) 
    plt.xlabel("Degrees") 
    plt.ylabel("No. of nodes") 
    plt.title("Degree distribution") 
    plt.show()

Step 3) Take N i.e number of nodes from the user.

Python3

# Take N number of nodes as input 
print("Enter number of nodes") 
N = int(input())

Step 4) Now take P i.e the probability from the user for edges.

Python3

# Take P probability value for edges 
print("Enter value of probability of every node") 
P = float(input())

Step 5) Create a graph with N nodes without any edges.

Python3

# Create an empty graph object 
g = nx.Graph() 
  
# Adding nodes 
g.add_nodes_from(range(1, N + 1))

Step 6) Add the edges to the graph randomly, take a pair of nodes, and get a random number R. If R<P (probability), add an edge. Repeat steps 5 and 6 for all possible pairs of nodes and then display the whole social network (graph) formed.

Python3

# Add edges to the graph randomly. 
for i in g.nodes(): 
    for j in g.nodes(): 
        if (i < j): 
              
            # Take random number R. 
            R = random.random() 
              
            # Check if R<P add the edge  
            # to the graph else ignore. 
            if (R < P): 
                g.add_edge(i, j) 
    pos = nx.circular_layout(g) 
      
    # Display the social network  
    nx.draw(g, pos, with_labels=1) 
    plt.show()

Step 7) Display the connecting nodes.

Python3

# Display connection between nodes     
distribution_graph(g)

Below is the complete program of the above step-wise approach:

Python3

# Implementation of Erdos-Renyi Model on a Social Network 
  
  
# Import Required modules 
import networkx as nx 
import matplotlib.pyplot as plt 
import random 
  
  
# Distribution graph for Erdos_Renyi model 
def distribution_graph(g): 
    print(nx.degree(g)) 
    all_node_degree = list(dict((nx.degree(g))).values()) 
  
    unique_degree = list(set(all_node_degree)) 
    unique_degree.sort() 
    nodes_with_degree = [] 
    for i in unique_degree: 
        nodes_with_degree.append(all_node_degree.count(i)) 
  
    plt.plot(unique_degree, nodes_with_degree) 
    plt.xlabel("Degrees") 
    plt.ylabel("No. of nodes") 
    plt.title("Degree distribution") 
    plt.show() 
  
          
# Take N number of nodes from user 
print("Enter number of nodes") 
N = int(input()) 
  
  
# Take P probability value for edges 
print("Enter value of probability of every node") 
P = float(input()) 
  
  
# Create an empty graph object 
g = nx.Graph() 
  
  
# Adding nodes 
g.add_nodes_from(range(1, N + 1)) 
  
  
# Add edges to the graph randomly. 
for i in g.nodes(): 
    for j in g.nodes(): 
        if (i < j): 
              
            # Take random number R. 
            R = random.random() 
              
            # Check if R<P add the edge to the graph else ignore. 
            if (R < P): 
                g.add_edge(i, j) 
    pos = nx.circular_layout(g) 
      
    # Display the social network  
    nx.draw(g, pos, with_labels=1) 
    plt.show() 
  
# Display connection between nodes     
distribution_graph(g) 

Output:

Enter number of nodes
10
Enter value of probability of every node
0.4
[(1, 5), (2, 3), (3, 4), (4, 2), (5, 3), (6, 5), (7, 4), (8, 2), (9, 2), (10, 2)]