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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:

<source lang="python"> 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 </source> 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, <source lang="python"> 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: <source lang="python"> 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, <source lang="python"> 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

  1. e.g.

add_node(G, 4) add_children(G, 4, {1,2}) </source> This version of add_children makes a directed graph, since child to parent edges were not added.

Amongst other things, networkx can visualize graphs:

<source lang="python"> 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) </source>