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)]
Adding edges randomly in a graph
Degree Distribution Graph of the implementation of Erdos-Renyi model on the above program:
