How to represent a strange graph in some data structure

Question

A simple way to represent a graph is with a data structure of the form:

{1:[2,3],
 2:[1,3],
 3:[1,2]}

Where the keys in this dictionary are nod

Answer 1

Represent your graph as a mapping of strings to mapping of strings to sets.

To be more clear, in python you would have:

graph = {
    'A': {
        'B': set(['C', 'D', ...]),
        'E': set(['F']),
    },
    ...
}

An edge exists between A and B if the key B is contained by the entry A in the graph mapping.

This edge can be walked if the node from which we come from is contained in the set mapped to by graph['A']['B'].

The following python class implements this specification (you can find a commented version on this gist):

class Graph(object):
    def __init__(self):
        self.nodes = {}

    def addEdge(self, (node1, comingFrom1), (node2, comingFrom2)):
        self.nodes.setdefault(node1, {})[node2] = comingFrom1
        self.nodes.setdefault(node2, {})[node1] = comingFrom2

    def isEdge(self, comingFrom, passingBy, goingTo):
        try:
            return comingFrom in self.nodes[passingBy][goingTo]
        except KeyError:
            return False

    def destinations(self, comingFrom, passingBy):
        dests = set()
        try:
            for node, directions in self.nodes[passingBy].iteritems():
                if comingFrom in directions:
                    dests.add(node)
        except KeyError:
            pass

        return dests

    def sources(self, passingBy, goingTo):
        return self.destinations(goingTo, passingBy)

This class can be used like this:

    >>> graph = Graph()
>>> graph.addEdge(('0', set([        ])), ('1', set(['3', '2'])))
>>> graph.addEdge(('1', set(['0'     ])), ('3', set(['4'     ])))
>>> graph.addEdge(('1', set(['0'     ])), ('2', set(['5'     ])))
>>> graph.addEdge(('3', set(['1', '2'])), ('4', set([        ])))
>>> graph.addEdge(('3', set(['4'     ])), ('2', set(['5'     ])))
>>> graph.addEdge(('2', set(['1', '3'])), ('5', set([        ])))

>>> print graph.isEdge('0', '1', '3')
True
>>> print graph.isEdge('1', '3', '2')
False
>>> print graph.isEdge('1', '2', '5')
True
>>> print graph.isEdge('5', '2', '3')
True
>>> print graph.isEdge('3', '2', '5')
True

>>> print graph.destinations('0', '1')
set(['3', '2'])
>>> print graph.destinations('1', '3')
set(['4'])
>>> print graph.destinations('3', '4')
set([])

>>> print graph.sources('0', '1')
set([])
>>> print graph.sources('1', '3')
set(['0'])
>>> print graph.sources('3', '4')

The chosen data structures and their usage already allows to build a directed graph, only the addEdge method would need to be adapted.