Handling Graphs with NetworkX¶
Python offers the library NetworkX for manipulating graphs. You can learn more here:
http://networkx.readthedocs.io/en/networkx-1.11/
http://networkx.readthedocs.io/en/networkx-1.11/tutorial/index.html
In [1]:
import networkx as nx
%matplotlib inline
In [2]:
#Creating a graph
G = nx.Graph()
#Add nodes to the graph
G.add_node(1)
G.add_nodes_from([2,3])
G.add_node('Alice')
G.add_node('Bob')
print(G.nodes())
In [4]:
#add edges to the graph
G.add_edge(1,2)
G.add_edges_from([(1,3),('Alice','Bob')])
e = (1,'Alice')
G.add_edge(*e)
# adding an edge with a new node will create the node Charlie in the graph
G.add_edge('Alice','Charlie')
print(G.edges())
print(G.nodes())
In [7]:
#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
G[1]
#G.node[1]
Out[7]:
In [28]:
#Creating a graph from edges
G2 = nx.Graph()
G2.add_edges_from([(1,2),(1,3),('Alice','Bob'),(1,'Alice')])
print(G2.nodes())
print(G2.edges())
In [29]:
G2.remove_edge(1,3)
G2.remove_node(3)
G2.nodes()
Out[29]:
Reading a graph from a file
http://networkx.readthedocs.io/en/networkx-1.11/reference/readwrite.html
In [11]:
#Read a graph from a list of edges
G3 = nx.read_edgelist('graph_edges.txt')
print(G3.nodes())
print(G3.edges())
You can also assign properties and values to the nodes and edges of the graph
In [12]:
G3.node['Alice']['gender'] = 'female'
G3.node['Bob']['gender'] = 'male'
G3.node['Charlie']['gender'] = 'male'
G3.node['1']['value'] = 1
G3.node['2']['value'] = -1
G3.node['3']['value'] = 0
for n in G3.nodes():
print(G3.node[n])
G3.node['Alice']['value'] = 1
G3.node['Bob']['value'] = -1
G3.node['Charlie']['value'] = 1
for n in G3.nodes():
print(n+ ":" + str(G3.node[n]['value']))
for n in G3.nodes():
print(n,G3.node[n])
In [13]:
G3.edge['Alice']['Bob']['label'] = 10
print(G3.edge['Bob']['Alice'])
print(G3['Alice'])
print(G3['Bob'])
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.
In [7]:
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.edge[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¶
In [5]:
DG=nx.DiGraph()
DG.add_weighted_edges_from([(1,2,0.5), (3,1,0.75), (1,4,0.1)])
print(DG.edges())
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
In [8]:
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
In [39]:
print(DG.successors(1))
print(DG.neighbors(1))
print(DG.predecessors(1))
print(DG.out_degree(1,weight='weight'))
print(DG.out_degree(1))
print(DG.in_degree(1))
Connected components
In [20]:
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')
print(nx.number_connected_components(G3))
C = nx.connected_components(G3)
for GC in nx.connected_component_subgraphs(G3):
print(GC.nodes())
print(GC.edges())
for c in C:
print(c)
#CL = nx.max_clique(G3)
Shortest paths
In [21]:
G3.add_edge('1','Alice')
sp = nx.shortest_path(G3,'3','Bob')
print(sp)
print(len(sp)-1)
print(nx.shortest_path_length(G3,'3','Bob'))
SP1 = nx.single_source_shortest_path(G3,'1')
#print(SP1)
#print(nx.single_source_shortest_path_length(G3,'1'))
SP = nx.all_pairs_shortest_path(G3)
print(SP)
print(SP['1']['Bob'])
Link Analysis
In [47]:
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)])
pr = nx.pagerank(DG2)
print(pr)
[h,a] = nx.hits(DG2)
print(h)
print(a)
print(a[2])
pr = nx.pagerank(G3)
print(pr)
Betweeness
In [22]:
BC = nx.edge_betweenness_centrality(G3)
print(BC)
In [14]:
nx.draw_networkx(G3)
In [49]:
nx.draw_circular(G3)
In [50]:
nx.draw_spectral(G3)
In [51]:
nx.draw_spring(G3)
In [52]:
nx.draw_spring(DG2)
An example¶
In [55]:
karate=nx.read_gml("karate.gml")
nx.draw_networkx(karate)
In [54]:
pr = nx.pagerank(karate)
nx.draw_networkx(karate,node_size=[10000*v for v in pr.values()])
