Prerequisite– Python Basics, NetworkX Basics
We are going to divide the nodes of the graph into two or more communities using the Girvan Newman algorithm. The Girvan Newman Algorithm removes the edges with the highest betweenness until there are no edges remain. Betweenness is the number of the shortest paths between pairs of nodes that run through it.
We will use a Girvan Newman Algorithm for this task.
Algorithm:
- Create a graph of N nodes and its edges or take an inbuilt graph like a barbell graph.
- Calculate the betweenness of all existed edges in the graph.
- Now remove all the edge(s) with the highest betweenness.
- Now recalculate the betweenness of all the edges that got affected by the removal of edges.
- Now repeat steps 3 and 4 until no edges remain.
Python Code:
Python3
import networkx as nx def edge_to_remove(g): d1 = nx.edge_betweenness_centrality(g) list_of_tuples = list(d1.items()) sorted(list_of_tuples, key = lambda x:x[1], reverse = True) # Will return in the form (a,b) return list_of_tuples[0][0] def girvan(g): a = nx.connected_components(g) lena = len(list(a)) print (' The number of connected components are ', lena) while (lena == 1): # We need (a,b) instead of ((a,b)) u, v = edge_to_remove(g) g.remove_edge(u, v) a = nx.connected_components(g) lena=len(list(a)) print (' The number of connected components are ', lena) return a # Driver Code g = nx.barbell_graph(5,0) a = girvan(g) print ('Barbell Graph') for i in a: print (i.nodes()) print ('.............') g1 = nx.karate_club_graph() a1 = girvan(g1) print ('Karate Club Graph') for i in a1: print (i.nodes()) print ('.............') |
Output:
Barbell Graph
The number of connected components are 1
The number of connected components are 2
[0, 1, 2, 3, 4]
………….
[8, 9, 5, 6, 7]
………….
Karate Club Graph
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 1
The number of connected components are 2
[32, 33, 2, 8, 9, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]
………….
[0, 1, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 19, 21]
………….
