Graph 기초

In [1]:

import networkx as nx

In [ ]:

Graph 는 vertex(node)와 edge로 구성되어 있다.
동그란 꼭지점을 vertex라고 하고, vertex를 잇는 선을 edge라고 한다.

Symmetric Networks¶

In [2]:

G_symmetric = nx.Graph()
G_symmetric.add_edge('Amitabh Bachchan','Abhishek Bachchan')
G_symmetric.add_edge('Amitabh Bachchan','Aamir Khan')
G_symmetric.add_edge('Amitabh Bachchan','Akshay Kumar')
G_symmetric.add_edge('Amitabh Bachchan','Dev Anand')
G_symmetric.add_edge('Abhishek Bachchan','Aamir Khan')
G_symmetric.add_edge('Abhishek Bachchan','Akshay Kumar')
G_symmetric.add_edge('Abhishek Bachchan','Dev Anand')
G_symmetric.add_edge('Dev Anand','Aamir Khan')

In [7]:

nx.draw_networkx(G_symmetric)

Asymmetric Networks¶

In [4]:

G_asymmetric = nx.DiGraph()
G_asymmetric.add_edge('A','B')
G_asymmetric.add_edge('A','D')
G_asymmetric.add_edge('C','A')
G_asymmetric.add_edge('D','E')

In [8]:

nx.spring_layout(G_asymmetric)
nx.draw_networkx(G_asymmetric)

Weighted Networks¶

In [10]:

G_weighted = nx.Graph()
G_weighted.add_edge('Amitabh Bachchan','Abhishek Bachchan', weight=25)
G_weighted.add_edge('Amitabh Bachchan','Aaamir Khan', weight=8)
G_weighted.add_edge('Amitabh Bachchan','Akshay Kumar', weight=11)
G_weighted.add_edge('Amitabh Bachchan','Dev Anand', weight=1)
G_weighted.add_edge('Abhishek Bachchan','Aaamir Khan', weight=4)
G_weighted.add_edge('Abhishek Bachchan','Akshay Kumar',weight=7)
G_weighted.add_edge('Abhishek Bachchan','Dev Anand', weight=1)
G_weighted.add_edge('Dev Anand','Aaamir Khan',weight=1)

In [11]:

nx.draw_networkx(G_weighted)

Multigraph¶

In [18]:

G = nx.MultiGraph()   # or MultiDiGraph
nx.add_path(G, [0, 1, 2])
key = G.add_edge(2, 3, weight=5)
[e for e in G.edges()]

Out[18]:

[(0, 1), (1, 2), (2, 3)]

In [19]:

G.edges.data() # default data is {} (empty dict)

Out[19]:

MultiEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])

In [20]:

G.edges.data('weight', default=1)

Out[20]:

MultiEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])

In [21]:

G.edges(keys=True) # default keys are integers

Out[21]:

MultiEdgeView([(0, 1, 0), (1, 2, 0), (2, 3, 0)])

In [22]:

G.edges.data(keys=True)

Out[22]:

MultiEdgeDataView([(0, 1, 0, {}), (1, 2, 0, {}), (2, 3, 0, {'weight': 5})])

In [23]:

G.edges.data('weight', default=1, keys=True)

Out[23]:

MultiEdgeDataView([(0, 1, 0, 1), (1, 2, 0, 1), (2, 3, 0, 5)])

In [24]:

G.edges([0, 3])

Out[24]:

MultiEdgeDataView([(0, 1), (3, 2)])

In [25]:

G.edges(0)

Out[25]:

MultiEdgeDataView([(0, 1)])

In [ ]:

Degree

In [27]:

nx.degree(G_symmetric, 'Dev Anand') #This will return a value of 3, as Dev Anand has worked with only three actors in the network.

Out[27]:

3

In [28]:

nx.average_clustering(G_symmetric)

Out[28]:

0.8666666666666666

In [ ]:

Distance

In [29]:

nx.shortest_path(G_symmetric, 'Dev Anand', 'Akshay Kumar')

Out[29]:

['Dev Anand', 'Abhishek Bachchan', 'Akshay Kumar']

In [30]:

T = nx.bfs_tree(G_symmetric, 'Dev Anand')

In [31]:

T

Out[31]:

<networkx.classes.digraph.DiGraph at 0x7fbbc6ee2160>

In [34]:

G_fb = nx.read_edgelist("facebook_combined.txt", create_using = nx.Graph(), nodetype=int)

In [35]:

print(nx.info(G_fb))

Name: 
Type: Graph
Number of nodes: 4039
Number of edges: 88234
Average degree:  43.6910

In [37]:

nx.draw_networkx(G_fb)

In [38]:

import matplotlib.pyplot as plt

In [39]:

pos = nx.spring_layout(G_fb)
betCent = nx.betweenness_centrality(G_fb, normalized=True, endpoints=True)
node_color = [20000.0 * G_fb.degree(v) for v in G_fb]
node_size =  [v * 10000 for v in betCent.values()]
plt.figure(figsize=(20,20))
nx.draw_networkx(G_fb, pos=pos, with_labels=False,
                 node_color=node_color,
                 node_size=node_size )
plt.axis('off')

Out[39]:

(-0.9308566050006861,
 0.8176587007397182,
 -1.0643712768569509,
 1.099375713826708)

In [40]:

sorted(betCent, key=betCent.get, reverse=True)[:5]

Out[40]:

[107, 1684, 3437, 1912, 1085]