"""
Hybrid
"""
__author__ = """Aric Hagberg (hagberg@lanl.gov)\nDan Schult (dschult@colgate.edu)"""
# Copyright (C) 2004-2008 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
_all__ = ['kl_connected_subgraph', 'is_kl_connected']
import copy
from networkx import shortest_path
def kl_connected_subgraph(G,k,l,low_memory=False,same_as_graph=False):
""" Returns the maximum locally (k,l) connected subgraph of G.
(k,l)-connected subgraphs are presented by Fan Chung and Li
in "The Small World Phenomenon in hybrid power law graphs"
to appear in "Complex Networks" (Ed. E. Ben-Naim) Lecture
Notes in Physics, Springer (2004)
low_memory=True then use a slightly slower, but lower memory version
same_as_graph=True then return a tuple with subgraph and
pflag for if G is kl-connected
"""
H=copy.deepcopy(G) # subgraph we construct by removing from G
graphOK=True
deleted_some=True # hack to start off the while loop
while deleted_some:
deleted_some=False
for edge in H.edges():
(u,v)=edge
### Get copy of graph needed for this search
if low_memory:
verts=set([u,v])
for i in range(k):
[verts.update(G.neighbors(w)) for w in verts.copy()]
G2=G.subgraph(list(verts))
else:
G2=copy.deepcopy(G)
###
path=[u,v]
cnt=0
accept=0
while path:
cnt += 1 # Found a path
if cnt>=l:
accept=1
break
# record edges along this graph
prev=u
for w in path:
if prev!=w:
G2.remove_edge(prev,w)
prev=w
# path=shortest_path(G2,u,v,k) # ??? should "Cutoff" be k+1?
path=shortest_path(G2,u,v) # ??? should "Cutoff" be k+1?
# No Other Paths
if accept==0:
H.remove_edge(u,v)
deleted_some=True
if graphOK: graphOK=False
# We looked through all edges and removed none of them.
# So, H is the maximal (k,l)-connected subgraph of G
if same_as_graph:
return (H,graphOK)
return H
def is_kl_connected(G,k,l,low_memory=False):
"""Returns True if G is kl connected """
graphOK=True
for edge in G.edges():
(u,v)=edge
### Get copy of graph needed for this search
if low_memory:
verts=set([u,v])
for i in range(k):
[verts.update(G.neighbors(w)) for w in verts.copy()]
G2=G.subgraph(verts)
else:
G2=copy.deepcopy(G)
###
path=[u,v]
cnt=0
accept=0
while path:
cnt += 1 # Found a path
if cnt>=l:
accept=1
break
# record edges along this graph
prev=u
for w in path:
if w!=prev:
G2.remove_edge(prev,w)
prev=w
# path=shortest_path(G2,u,v,k) # ??? should "Cutoff" be k+1?
path=shortest_path(G2,u,v) # ??? should "Cutoff" be k+1?
# No Other Paths
if accept==0:
graphOK=False
break
# return status
return graphOK
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