Question from Fil: Centrality challenge: today as I was teaching about closeness and betweenness centrality in class, a student asked for an example of a network where the node with highest closeness centrality is not also the one with highest betweenness. I could not think of a simple example. Output of file: Closeness: ['a', 1, 2, 3, 4, 33, 11…

centrality_challenge

'''
Question from Fil:
Centrality challenge: today as I was teaching about closeness 
and betweenness centrality in class, a student asked for an 
example of a network where the node with highest closeness 
centrality is not also the one with highest betweenness. I 
could not think of a simple example. Anyone?
'''

import networkx as nx

G = nx.Graph()
G.add_edge(1,2)
G.add_edge(11,22)
G.add_edge(1,3)
G.add_edge(11,33)
G.add_edge(2,4)
G.add_edge(22,44)
G.add_edge(3,4)
G.add_edge(33,44)

G.add_edge(1,11)
G.add_edge(2,22)
G.add_edge(3,33)
G.add_edge(4,44)

G.add_edge(1,'a')
G.add_edge(3,'a')
G.add_edge(2,'a')
G.add_edge(4,'a')

nx.circular_layout(G)

closenessC = nx.closeness_centrality(G, distance='weight')
print 'Closeness: ', sorted(closenessC, key=closenessC.get, reverse=True)

betweennessC = nx.betweenness_centrality(G, weight='weight')
print 'Betweenness: ',sorted(betweennessC, key=betweennessC.get, reverse=True)