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modified on 19 September 2014 at 16:45 ••• 4,894 views

Code:networkx

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The networkx library is a great tool for quick graph operations in python put together by the wonderful folks at Los Alamos National Labs. It uses a representation based on dictionaries of dictionaries.

A dictionary of sets is simpler, so I'll show that too. For both representations, each node is a dictionary key, and the value stores the names of its child nodes. So, a graph with nodes 1,2,3 connected in a triangle would look like:

G = {1: {2,3}, 2: {1,3}, 3: {1,2} } # dict-of-sets
G = {1: {2:1,3:1}, 2: {1:1,3:1}, 3: {1:1,2:1} } # dict-of-dicts

The {1, 2, 3} notation means create a set, while {1:1, 2:2, 3:3} means create a dictionary.

To test whether a node, u is parent to a node v, we can just write,

def is_child(G, u, v):
    return v in G[u] # both formats

To add a node to a tree, I would need to create a new key in the dictionary -- like so:

def add_node(G, u):
    assert u not in G
    G[u] = set() # dict-of-sets
 
def add_node(G, u):
    assert u not in G
    G[u] = {} # dict-of-dicts

To put in parent-child edges, I have to add members to the right set,

def add_children(G, u, kids):
    G[u] += kids # dict-of-set
 
def add_children(G, u, kids):
    k,v in kids.iteritems(): # dict-of-dict
	G[u][k] = v
 
# e.g.
add_node(G, 4)
add_children(G, 4, {1,2})

This version of add_children makes a directed graph, since child to parent edges were not added.

Amongst other things, networkx can visualize graphs:

import matplotlib.pyplot as plt
import networkx as nx
 
nG=nx.from_dict_of_lists(G) # maybe works for dict-of-set
nG=nx.from_dict_of_dicts(G) # for dict-of-dict
nx.draw(nG)
plt.show()