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 = sets.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.delete_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.delete_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.delete_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
