notebook.community

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In [1]:

    
%config InlineBackend.figure_format ='retina'
%matplotlib inline

import networkx as nx
import pandas as pd

import matplotlib.pyplot as plt
import seaborn as sns

# Set options
sns.set_style('darkgrid')
pd.set_option("display.max_rows", 10)



In [2]:

    
users = [
    { "id": 0, "name": "Hero" },
    { "id": 1, "name": "Dunn" },
    { "id": 2, "name": "Sue" },
    { "id": 3, "name": "Chi" },
    { "id": 4, "name": "Thor" },
    { "id": 5, "name": "Clive" },
    { "id": 6, "name": "Hicks" },
    { "id": 7, "name": "Devin" },
    { "id": 8, "name": "Kate" },
    { "id": 9, "name": "Klein" }
]

friendships = [(0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (3, 4),
               (4, 5), (5, 6), (5, 7), (6, 8), (7, 8), (8, 9)]

for user in users:
    user["friends"] = []
    
for i, j in friendships:
    users[i]["friends"].append(users[j])
    users[j]["friends"].append(users[i])



In [3]:

    
g = nx.Graph()

g.add_nodes_from([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
g.add_edges_from(friendships)



In [4]:

    
g.number_of_nodes()









    Out[4]:





10



In [5]:

    
g.number_of_edges()









    Out[5]:





12



In [6]:

    
nx.draw_networkx(g)
plt.axis('off')

A node's degree is the number of connections it has.



In [7]:

    
nx.degree(g, 3)









    Out[7]:





3



In [8]:

    
nx.degree(g, 4)









    Out[8]:





2

The local clustering coefficient is the fraction of a node's connections that are also connected.



In [9]:

    
nx.clustering(g, 0)









    Out[9]:





1.0



In [10]:

    
nx.clustering(g, 4)









    Out[10]:





0



In [11]:

    
nx.clustering(g, 1)









    Out[11]:





0.6666666666666666

Betweenness centrality estimates which nodes are important in connecting networks



In [12]:

    
df = pd.DataFrame()

df["node"] = g.nodes()
df["centrality"] = pd.Series(nx.degree_centrality(g))
df["eigenvector"] = pd.Series(nx.eigenvector_centrality(g))
df["betweenness"] = pd.Series(nx.betweenness_centrality(g, normalized = True, endpoints = True))

df









    Out[12]:







  
    
      
      node
      centrality
      eigenvector
      betweenness
    
  
  
    
      0
      0
      0.222222
      0.385777
      0.200000
    
    
      1
      1
      0.333333
      0.514787
      0.277778
    
    
      2
      2
      0.333333
      0.514787
      0.277778
    
    
      3
      3
      0.333333
      0.473312
      0.600000
    
    
      4
      4
      0.222222
      0.233613
      0.644444
    
    
      5
      5
      0.333333
      0.150158
      0.655556
    
    
      6
      6
      0.222222
      0.083563
      0.333333
    
    
      7
      7
      0.222222
      0.083563
      0.333333
    
    
      8
      8
      0.333333
      0.072853
      0.388889
    
    
      9
      9
      0.111111
      0.027299
      0.200000



In [13]:

    
nx.betweenness_centrality(g, normalized = True, endpoints = True)









    Out[13]:





{0: 0.2,
 1: 0.2777777777777778,
 2: 0.2777777777777778,
 3: 0.6,
 4: 0.6444444444444445,
 5: 0.6555555555555556,
 6: 0.33333333333333337,
 7: 0.33333333333333337,
 8: 0.3888888888888889,
 9: 0.2}



In [14]:

    
nx.betweenness_centrality(g, normalized = True, endpoints = False)









    Out[14]:





{0: 0.0,
 1: 0.09722222222222221,
 2: 0.09722222222222221,
 3: 0.5,
 4: 0.5555555555555556,
 5: 0.5694444444444444,
 6: 0.16666666666666666,
 7: 0.16666666666666666,
 8: 0.2361111111111111,
 9: 0.0}



In [ ]:

	node	centrality	eigenvector	betweenness
0	0	0.222222	0.385777	0.200000
1	1	0.333333	0.514787	0.277778
2	2	0.333333	0.514787	0.277778
3	3	0.333333	0.473312	0.600000
4	4	0.222222	0.233613	0.644444
5	5	0.333333	0.150158	0.655556
6	6	0.222222	0.083563	0.333333
7	7	0.222222	0.083563	0.333333
8	8	0.333333	0.072853	0.388889
9	9	0.111111	0.027299	0.200000