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

# Source code for networkx.generators.random_clustered

# -*- coding: utf-8 -*-
"""Generate graphs with given degree and triangle sequence.
"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
import random
import networkx as nx
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
'Joel Miller (joel.c.miller.research@gmail.com)'])

__all__ = ['random_clustered_graph']

[docs]def random_clustered_graph(joint_degree_sequence, create_using=None, seed=None):
"""Generate a random graph with the given joint degree and triangle
degree sequence.

This uses a configuration model-like approach to generate a
random pseudograph (graph with parallel edges and self loops) by
randomly assigning edges to match the given indepdenent edge
and triangle degree sequence.

Parameters
----------
joint_degree_sequence : list of integer pairs
Each list entry corresponds to the independent edge degree and
triangle degree of a node.
create_using : graph, optional (default MultiGraph)
Return graph of this type. The instance will be cleared.
seed : hashable object, optional
The seed for the random number generator.

Returns
-------
G : MultiGraph
A graph with the specified degree sequence. Nodes are labeled
starting at 0 with an index corresponding to the position in
deg_sequence.

Raises
------
NetworkXError
If the independent edge degree sequence sum is not even
or the triangle degree sequence sum is not divisible by 3.

Notes
-----
As described by Miller _ (see also Newman _ for an equivalent
description).

A non-graphical degree sequence (not realizable by some simple
graph) is allowed since this function returns graphs with self
loops and parallel edges.  An exception is raised if the
independent degree sequence does not have an even sum or the
triangle degree sequence sum is not divisible by 3.

This configuration model-like construction process can lead to
duplicate edges and loops.  You can remove the self-loops and
parallel edges (see below) which will likely result in a graph
that doesn't have the exact degree sequence specified.  This
"finite-size effect" decreases as the size of the graph increases.

References
----------
..  J. C. Miller "Percolation and Epidemics on Random Clustered Graphs."
Physical Review E, Rapid Communication (to appear).
..  M.E.J. Newman, "Random clustered networks".
Physical Review Letters (to appear).

Examples
--------
>>> deg_tri=[[1,0],[1,0],[1,0],[2,0],[1,0],[2,1],[0,1],[0,1]]
>>> G = nx.random_clustered_graph(deg_tri)

To remove parallel edges:

>>> G=nx.Graph(G)

To remove self loops:

>>> G.remove_edges_from(G.selfloop_edges())

"""
if create_using is None:
create_using = nx.MultiGraph()
elif create_using.is_directed():
raise nx.NetworkXError("Directed Graph not supported")

if not seed is None:
random.seed(seed)

# In Python 3, zip() returns an iterator. Make this into a list.
joint_degree_sequence = list(joint_degree_sequence)

N = len(joint_degree_sequence)
G = nx.empty_graph(N,create_using)

ilist = []
tlist = []
for n in G:
degrees = joint_degree_sequence[n]
for icount in range(degrees):
ilist.append(n)
for tcount in range(degrees):
tlist.append(n)

if len(ilist)%2 != 0 or len(tlist)%3 != 0:
raise nx.NetworkXError('Invalid degree sequence')

random.shuffle(ilist)
random.shuffle(tlist)
while ilist: