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"""
========================
Cycle finding algorithms
========================
"""
# Copyright (C) 2010 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
import networkx as nx
__all__ = ['cycle_basis']
def cycle_basis(G,root=None):
""" Returns a list of cycles which form a basis for cycles of G.
A basis for cycles of a network is a minimal collection of
cycles such that any cycle in the network can be written
as a sum of cycles in the basis. Here summation of cycles
is defined as "exclusive or" of the edges. Cycle bases are
useful, e.g. when deriving equations for electric circuits
using Kirchhoff's Laws.
Parameters
----------
G : NetworkX Graph
root : node of G, optional (default=arbitrary choice from G)
Returns
-------
A list of cycle lists. Each cycle list is a list of nodes
which forms a cycle (loop) in G.
Examples
--------
>>> G=nx.Graph()
>>> G.add_cycle([0,1,2,3])
>>> G.add_cycle([0,3,4,5])
>>> print nx.cycle_basis(G,0)
[[3, 4, 5, 0], [1, 2, 3, 0]]
Notes
-----
This algorithm is adapted from algorithm CACM 491 published:
Paton, K. An algorithm for finding a fundamental set of
cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518.
"""
if G.is_multigraph() or G.is_directed():
raise Exception("cycle_basis() not implemented for directed or multiedge graphs.")
gnodes=set(G.nodes())
cycles=[]
while gnodes: # loop over connected components
if root is None:
root=gnodes.pop()
stack=[root]
pred={root:root}
used={root:set()}
while stack: # walk the spanning tree finding cycles
z=stack.pop() # use last-in so cycles easier to find
zused=used[z]
for nbr in G[z]:
if nbr not in used: # new node
pred[nbr]=z
stack.append(nbr)
used[nbr]=set([z])
elif nbr is z: # self loops
cycles.append([z])
elif nbr not in zused:# found a cycle
pn=used[nbr]
cycle=[nbr,z]
p=pred[z]
while p not in pn:
cycle.append(p)
p=pred[p]
cycle.append(p)
cycles.append(cycle)
used[nbr].add(z)
gnodes-=set(pred)
root=None
return cycles
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