Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Antigraph¶

""" Complement graph class for small footprint when working on dense graphs.

This class allows you to add the edges that *do not exist* in the dense
graph. However, when applying algorithms to this complement graph data
structure, it behaves as if it were the dense version. So it can be used
directly in several NetworkX algorithms.

This subclass has only been tested for k-core, connected_components,
and biconnected_components algorithms but might also work for other
algorithms.

"""
#    Copyright (C) 2015 by
#    Jordi Torrents <jtorrents@milnou.net>
#    All rights reserved.
#    BSD license.
import networkx as nx
from networkx.exception import NetworkXError

__author__ = """\n""".join(['Jordi Torrents <jtorrents@milnou.net>'])

__all__ = ['AntiGraph']

class AntiGraph(nx.Graph):
"""
Class for complement graphs.

The main goal is to be able to work with big and dense graphs with
a low memory foodprint.

In this class you add the edges that *do not exist* in the dense graph,
the report methods of the class return the neighbors, the edges and
the degree as if it was the dense graph. Thus it's possible to use
an instance of this class with some of NetworkX functions.
"""

all_edge_dict = {'weight': 1}
def single_edge_dict(self):
return self.all_edge_dict
edge_attr_dict_factory = single_edge_dict

def __getitem__(self, n):
"""Return a dict of neighbors of node n in the dense graph.

Parameters
----------
n : node
A node in the graph.

Returns
-------
adj_dict : dictionary
The adjacency dictionary for nodes connected to n.

"""
return dict((node, self.all_edge_dict) for node in
set(self.adj) - set(self.adj[n]) - set([n]))

def neighbors(self, n):
"""Return a list of the nodes connected to the node n in
the dense graph.

Parameters
----------
n : node
A node in the graph

Returns
-------
nlist : list
A list of nodes that are adjacent to n.

Raises
------
NetworkXError
If the node n is not in the graph.

"""
try:
return list(set(self.adj) - set(self.adj[n]) - set([n]))
except KeyError:
raise NetworkXError("The node %s is not in the graph."%(n,))

def neighbors_iter(self, n):
"""Return an iterator over all neighbors of node n in the
dense graph.

"""
try:
return iter(set(self.adj) - set(self.adj[n]) - set([n]))
except KeyError:
raise NetworkXError("The node %s is not in the graph."%(n,))

def degree(self, nbunch=None, weight=None):
"""Return the degree of a node or nodes in the dense graph.
"""
if nbunch in self:      # return a single node
return next(self.degree_iter(nbunch,weight))
else:           # return a dict
return dict(self.degree_iter(nbunch,weight))

def degree_iter(self, nbunch=None, weight=None):
"""Return an iterator for (node, degree) in the dense graph.

The node degree is the number of edges adjacent to the node.

Parameters
----------
nbunch : iterable container, optional (default=all nodes)
A container of nodes.  The container will be iterated
through once.

weight : string or None, optional (default=None)
The edge attribute that holds the numerical value used
as a weight.  If None, then each edge has weight 1.
The degree is the sum of the edge weights adjacent to the node.

Returns
-------
nd_iter : an iterator
The iterator returns two-tuples of (node, degree).

See Also
--------
degree

Examples
--------
>>> G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_path([0,1,2,3])
>>> list(G.degree_iter(0)) # node 0 with degree 1
[(0, 1)]
>>> list(G.degree_iter([0,1]))
[(0, 1), (1, 2)]

"""
if nbunch is None:
nodes_nbrs = ((n, {v: self.all_edge_dict for v in
set(self.adj) - set(self.adj[n]) - set([n])})
for n in self.nodes_iter())
else:
nodes_nbrs= ((n, {v: self.all_edge_dict for v in
set(self.nodes()) - set(self.adj[n]) - set([n])})
for n in self.nbunch_iter(nbunch))

if weight is None:
for n,nbrs in nodes_nbrs:
yield (n,len(nbrs)+(n in nbrs)) # return tuple (n,degree)
else:
# AntiGraph is a ThinGraph so all edges have weight 1
for n,nbrs in nodes_nbrs:
yield (n, sum((nbrs[nbr].get(weight, 1) for nbr in nbrs)) +
(n in nbrs and nbrs[n].get(weight, 1)))

def adjacency_iter(self):
"""Return an iterator of (node, adjacency set) tuples for all nodes
in the dense graph.

This is the fastest way to look at every edge.
For directed graphs, only outgoing adjacencies are included.

Returns
-------
adj_iter : iterator
An iterator of (node, adjacency set) for all nodes in
the graph.

"""
for n in self.adj:
yield (n, set(self.adj) - set(self.adj[n]) - set([n]))

if __name__ == '__main__':
# Build several pairs of graphs, a regular graph
# and the AntiGraph of it's complement, which behaves
# as if it were the original graph.
Gnp = nx.gnp_random_graph(20,0.8)
Anp = AntiGraph(nx.complement(Gnp))
Gd = nx.davis_southern_women_graph()
Ad = AntiGraph(nx.complement(Gd))
Gk = nx.karate_club_graph()
Ak = AntiGraph(nx.complement(Gk))
pairs = [(Gnp, Anp), (Gd, Ad), (Gk, Ak)]
# test connected components
for G, A in pairs:
gc = [set(c) for c in nx.connected_components(G)]
ac = [set(c) for c in nx.connected_components(A)]
for comp in ac:
assert comp in gc
# test biconnected components
for G, A in pairs:
gc = [set(c) for c in nx.biconnected_components(G)]
ac = [set(c) for c in nx.biconnected_components(A)]
for comp in ac:
assert comp in gc
# test degree
for G, A in pairs:
node = list(G.nodes())
nodes = list(G.nodes())[1:4]
assert G.degree(node) == A.degree(node)
assert sum(G.degree().values()) == sum(A.degree().values())
# AntiGraph is a ThinGraph, so all the weights are 1
assert sum(A.degree().values()) == sum(A.degree(weight='weight').values())
assert sum(G.degree(nodes).values()) == sum(A.degree(nodes).values())