Handling Graphs with NetworkX¶
Python offers the library NetworkX for manipulating graphs. You can learn more here:
https://networkx.github.io/documentation/stable/tutorial.html
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import networkx as nx
%matplotlib inline
Creating a graph¶
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G = nx.Graph()
Add nodes to the graph
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G.add_node(1)
G.add_nodes_from([2,3])
G.add_node('Alice')
G.add_node('Bob')
print(G.nodes())
Draw the graph
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nx.draw_networkx(G)
Add edges to the graph
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G.add_edge(1,2)
G.add_edges_from([(1,3),('Alice','Bob')])
e = (1,'Alice')
G.add_edge(*e)
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nx.draw_networkx(G)
Adding an edge with a new node will create the node Charlie in the graph
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G.add_edge('Alice','Charlie')
print(G.edges())
print(G.nodes())
nx.draw_networkx(G)
A graph is a dictionary with nodes as the keys
Each node is a dictionary with the neighbors as the keys, and the edge properties as values
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G[1]
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print(G.nodes)
print(G.edges)
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print(G.nodes[1])
Creating a graph from edges
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G2 = nx.Graph()
G2.add_edges_from([(1,2),(1,3),('Alice','Bob'),(1,'Alice')])
print(G2.nodes())
print(G2.edges())
nx.draw(G2)
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G2.remove_edge(1,3)
G2.remove_node(3)
G2.remove_node(1)
print(G2.nodes())
print(G2.edges())
nx.draw_networkx(G2)
Reading a graph from a file with list of edges
http://networkx.readthedocs.io/en/networkx-1.11/reference/readwrite.html
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#Read a graph from a list of edges
G3 = nx.read_edgelist('graph_edges.txt')
print(G3.nodes())
print(G3.edges())
nx.draw_networkx(G3)
Graph attributes¶
You can assign attributes and values to the nodes and edges of the graph
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G3.nodes['Alice']['gender'] = 'female'
G3.nodes['Bob']['gender'] = 'male'
G3.nodes['Charlie']['gender'] = 'male'
G3.nodes['1']['value'] = 1
G3.nodes['2']['value'] = -1
G3.nodes['3']['value'] = 0
for n in G3.nodes():
print(G3.nodes[n])
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for n in G3.nodes():
print(G3[n])
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G3.nodes['Alice']['value'] = 1
G3.nodes['Bob']['value'] = -1
G3.nodes['Charlie']['value'] = 1
for n in G3.nodes():
print(n+ ":" + str(G3.nodes[n]['value']))
for n in G3.nodes():
print(n,G3.nodes[n])
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G3['Alice']['Bob']['label'] = 'strong'
print(G3['Bob']['Alice'])
print(G3['Alice'])
print(G3['Bob'])
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nx.draw_networkx(G3, with_labels=True)
Weighted graphs¶
A special attribute of a an edge is the "weight". When adding weighted edges, you enter triples consisting of the two edge endpoints and the weight of the edge. This weight is stored in an attribute "weight" by default.
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G4 = nx.Graph()
G4.add_weighted_edges_from([(1,2,0.5),(2,3,0.1),(3,4,0.7)])
for (a,b) in G4.edges():
print (G4[a][b])
for (a,b,w) in G4.edges(data =True): #data=True returns weight as well
print (str(a)+" "+ str(b) + " " + str(w['weight']))
for n in G4:
print(G4[n])
Directed Graphs¶
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DG=nx.DiGraph()
DG.add_weighted_edges_from([(1,2,0.5), (3,1,0.75), (1,4,0.1)])
print(DG.edges())
for n in DG:
print(DG[n])
nx.draw_networkx(DG)
Graph Operations¶
Some common graph operations and algorithms are implemented in networkx library.
http://networkx.readthedocs.io/en/networkx-1.11/reference/algorithms.html
Neighbors, degrees and adjancency matrix
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print(G.neighbors(1)) # returns the neighbors of a node
print(G.degree(1)) # returns the degree of a node
print(G4.degree(3, weight='weight'))
print(G4.degree(3))
A = nx.adjacency_matrix(G)
print(A)
#the adjacency matrix is stored as a sparse matrix
print(type(A))
Neighbors and degrees for directed or weighted graphs
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nx.draw_networkx(DG)
print(list(DG.successors(1)))
print(list(DG.neighbors(1)))
print(list(DG.predecessors(1)))
print(DG.out_degree(1,weight='weight'))
print(DG.out_degree(1))
print(DG.in_degree(1))
Connected components¶
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G3.add_edge('1','Alice')
G3.remove_edge('1','Alice') #you can also remove_node, or a list of nodes or edges (remove_nodes_from, remove_edges_from)
G3.add_edge('Alice','Charlie')
G3.add_edge('1','4')
nx.draw_networkx(G3)
print(nx.number_connected_components(G3))
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C = nx.connected_components(G3)
print(type(C))
for c in C:
print(c)
Get the connected component subgraphs
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connected_subgraphs = [nx.subgraph(G3,c) for c in nx.connected_components(G3)]
for GC in connected_subgraphs:
print(GC.nodes())
print(GC.edges())
print(len(GC))
Get the largest connected component
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# Get the nodes
largest_cc = max(nx.connected_components(G3), key=len)
print(largest_cc)
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#Get the subgraph
largest_cc = max(nx.connected_components(G3), key=len)
print(largest_cc)
CC_max = nx.subgraph(G3,largest_cc)
nx.draw_networkx(CC_max)
Shortest paths¶
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G3.add_edge('1','Alice')
nx.draw_networkx(G3)
sp = nx.shortest_path(G3,'3','Bob')
print(sp)
print(len(sp)-1)
print(nx.shortest_path_length(G3,'3','Bob'))
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SP1 = nx.single_source_shortest_path(G3,'1')
print(SP1)
#print(nx.single_source_shortest_path_length(G3,'1'))
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SP = dict(nx.all_pairs_shortest_path(G3))
print(SP)
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print(SP['1']['Bob'])
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DG2 = nx.DiGraph()
DG2.add_edges_from([(1,2),(1,3),(3,2),(2,5),(4,1),(4,2),(4,3),(5,1),(5,4)])
nx.draw_networkx(DG2)
Pagerank¶
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pr = nx.pagerank(DG2)
print(pr)
pr = nx.pagerank(G3)
print(pr)
HITS¶
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[h,a] = nx.hits(DG2)
print(h)
print(a)
print(a[2])
Class Example¶
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G4 = nx.read_edgelist('graph-example.txt')
nx.draw_networkx(G4)
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print(nx.pagerank(G4))
print(nx.pagerank(G4, alpha = 0.5))
print(nx.pagerank(G4, alpha = 0.5, personalization = {'1':1}))
print(nx.pagerank(G4, alpha = 0.5, personalization = {'6':1}))
Betweeness¶
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BC = nx.edge_betweenness_centrality(G3)
print(BC)
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nx.draw_networkx(G3)
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nx.draw_circular(G3)
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nx.draw_spectral(G3)
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nx.draw_spring(G3)
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nx.draw_spring(DG2)
An example¶
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karate=nx.read_gml("karate.gml",label='id')
nx.draw_networkx(karate)
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pr = nx.pagerank(karate)
nx.draw_networkx(karate,node_size=[10000*v for v in pr.values()])
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