Counting edges with non-duplicate nodes in Python

edges.py

#!/usr/bin/env python
"""
Computes the number of edges on the Graph
"""

from __future__ import division

import networkx as nx
from collections import defaultdict

def choose(n, k):
    """
    A fast way to calculate binomial coefficients by Andrew Dalke (contrib).
    """
    if 0 <= k <= n:
        ntok = 1
        ktok = 1
        for t in xrange(1, min(k, n - k) + 1):
            ntok *= n
            ktok *= t
            n -= 1
        return ntok // ktok
    else:
        return 0

def count_edges(G):
    """
    Counts the edges with virtual nodes
    """
    edges = 0

    for node in nx.nodes_iter(G):
        data = G.node[node]
        if data['type'] == 'virtual':
            edges += choose(nx.degree(G, node) ,2)

        else:
            # All neighbors are virtual
            nbunch = defaultdict(int)
            for vn in G.neighbors(node):
                for vnn in G.neighbors(vn):
                    nbunch[vnn] += 1

            for nb, freq in nbunch.items():
                if nb == node: continue
                freq -= 1
                if freq > 0:
                    edges -= (freq / 2)

    return edges


if __name__ == "__main__":
    G = nx.read_graphml('graph.graphml')
    print count_edges(G)

graph.graphml

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd">
  <key attr.name="label" attr.type="string" for="node" id="d1" />
  <key attr.name="type" attr.type="string" for="node" id="d0" />
  <graph edgedefault="undirected">
    <node id="A">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="C">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="B">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="E">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="D">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="G">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="F">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="I">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="H">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="K">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="J">
      <data key="d0">node</data>
      <data key="d1">A</data>
    </node>
    <node id="V1">
      <data key="d0">virtual</data>
      <data key="d1">V1</data>
    </node>
    <node id="V2">
      <data key="d0">virtual</data>
      <data key="d1">V2</data>
    </node>
    <node id="V3">
      <data key="d0">virtual</data>
      <data key="d1">V3</data>
    </node>
    <node id="V4">
      <data key="d0">virtual</data>
      <data key="d1">V4</data>
    </node>
    <edge source="A" target="V1" />
    <edge source="A" target="V2" />
    <edge source="C" target="V1" />
    <edge source="B" target="V2" />
    <edge source="E" target="V1" />
    <edge source="E" target="V3" />
    <edge source="D" target="V1" />
    <edge source="D" target="V3" />
    <edge source="G" target="V1" />
    <edge source="G" target="V3" />
    <edge source="G" target="V4" />
    <edge source="F" target="V3" />
    <edge source="F" target="V4" />
    <edge source="I" target="V1" />
    <edge source="I" target="V2" />
    <edge source="I" target="V4" />
    <edge source="H" target="V4" />
    <edge source="K" target="V3" />
    <edge source="J" target="V2" />
    <edge source="J" target="V3" />
  </graph>
</graphml>

make_graph.py

#!/usr/bin/env python
"""
Builds the whiteboard graph
"""

import networkx as nx

NODES = {
    "V1": {"type": "virtual", "label": "V1"},
    "V2": {"type": "virtual", "label": "V2"},
    "V3": {"type": "virtual", "label": "V3"},
    "V4": {"type": "virtual", "label": "V4"},
    "A":  {"type": "node", "label": "A"},
    "B":  {"type": "node", "label": "A"},
    "C":  {"type": "node", "label": "A"},
    "D":  {"type": "node", "label": "A"},
    "E":  {"type": "node", "label": "A"},
    "F":  {"type": "node", "label": "A"},
    "G":  {"type": "node", "label": "A"},
    "H":  {"type": "node", "label": "A"},
    "I":  {"type": "node", "label": "A"},
    "J":  {"type": "node", "label": "A"},
    "K":  {"type": "node", "label": "A"},
}

EDGES = [
    ('A', 'V1'),
    ('A', 'V2'),
    ('B', 'V2'),
    ('C', 'V1'),
    ('D', 'V1'),
    ('D', 'V3'),
    ('E', 'V1'),
    ('E', 'V3'),
    ('K', 'V3'),
    ('F', 'V3'),
    ('F', 'V4'),
    ('G', 'V3'),
    ('G', 'V4'),
    ('G', 'V1'),
    ('H', 'V4'),
    ('I', 'V1'),
    ('I', 'V2'), 
    ('I', 'V4'),
    ('J', 'V2'), 
    ('J', 'V3'),
]

if __name__ == "__main__":
    G = nx.Graph()
    for key, data in NODES.items():
        G.add_node(key, **data)

    for edge in EDGES:
        G.add_edge(*edge)

    nx.write_graphml(G, 'graph.graphml')