1. Centrality – Python - NetworkX

2. Degree Centrality Degree Centrality – Find the “Celebrities”
Figure 1.1 Network
>>> degree_centrality = net.degree_centrality(g)
>>> degree_centrality
{1: 0.375, 2: 0.25, 3: 0.375, 4: 0.5, 5: 0.5, 6: 0.5, 7: 0.5, 8: 0.375, 9: 0.125}
Define sort_map funtion
Sort the degree centrality
>>> import sort_map
>>> sorted_degree_centrality = sort_map.sort_map(degree_centrality)
>>> sorted_degree_centrality
[(4, 0.5), (5, 0.5), (6, 0.5), (7, 0.5), (1, 0.375), (3, 0.375), (8, 0.375), (2, 0.25), (9, 0.125)]
sort_map.py
import operator
def sort_map(map):
sortedList = map.items()
sortedList.sort(key=operator.itemgetter(1), reverse=True)
return sortedList

3. Closeness Centrality Closeness Centrality - Find the Gossipmongers
Figure 1.1 Network
>>> closeness_centrality = net.closeness_centrality(g)
>>> closeness_centrality
{1: , 2: , 3: , 4: , 5: , 6: , 7: 0.5, 8: , 9: }
>>> import sort_map
>>> sorted_closeness_centrality = sort_map.sort_map(closeness_centrality)
>>> sorted_closeness_centrality
[(4, ), (5, ), (6, ), (7, 0.5), (1, ), (3, ), (8, ), (2, ), (9, )]

4. Betweenness Centrality
Betweenness Centrality - Find the Communication Bottlenecks and/or Community Bridges
Figure 1.1 Network
>>> bet_centrality = net.betweenness_centrality(g)
>>> bet_centrality
{1: , 2: 0.0, 3: , 4: , 5: , 6: , 7: 0.25, 8: 0.0, 9: 0.0}
>>> import sort_map
>>> sorted_bet_centrality = sort_map.sort_map(bet_centrality)
>>> sorted_bet_centrality
[(4, ), (7, 0.25), (5, ), (6, ), (1, ), (3, ), (2, 0.0), (8, 0.0), (9, 0.0)]

5. Eigenvector Centrality
Figure 1.1 Network
>>> eigenvector_centrality = net. eigenvector_centrality(g)
>>> eigenvector_centrality
{1: , 2: , 3: , 4: , 5: , 6: , 7: , 8: , 9: }
>>> import sort_map
>>> sorted_eigenvector_centrality = sort_map.sort_map(eigenvector_centrality)
>>> sorted_eigenvector_centrality
[(5, ), (6, ), (7, ), (8, ), (4, ), (1, ), (3, ), (9, ), (2, )]

6. Putting It Together Adjust the values
Values Rounded
>>> rounded_degree_centrality = {k: round(v, 3) for k, v in degree_centrality.items()}
>>> rounded_closeness_centrality = {k: round(v, 3) for k, v in closeness_centrality.items()}
>>> rounded_bet_centrality = {k: round(v, 3) for k, v in bet_centrality.items()}
>>> rounded_eigenvector_centrality = {k: round(v, 3) for k, v in eigenvector_centrality.items()}
Build a table with four centralities
Making some conclusions about the figure 1.1
>>> table = [[node, rounded_degree_centrality[node], rounded_closeness_centrality[node], rounded_bet_centrality[node], rounded_eigenvector_centrality[node]] for node in g.nodes()]

7. Putting It Together Build a table with four centralities
node
degree
closeness
betweenness
eigenvector 1
0.375
0.471
0.107
0.196 2
0.250
0.348
0.000
0.112 3 4
0.500
0.615
0.536
0.379 5
0.214
0.468 6 7
0.410 8
0.384 9
0.125
0.117