def sbm(U, q, n, p, weighted=None, edges_constructor=add_edges_exact_sparse, pOut=None):
U = set(U)
g = networkx.Graph()
# Pick our communities from the universe.
communities = makeCommunities(U, q, n)
# Add all nodes from the (new) universe, then add all of their edges.
g.add_nodes_from(U)
for nodes in communities:
#add_edges(g, nodes, p, weighted=weighted)
#add_edges_cm(g, nodes, p, weighted=weighted)
#add_edges_exact(g, nodes, p, weighted=weighted)
edges_constructor(g, nodes, p, weighted=weighted)
if weighted:
for a, b in g.edges_iter():
newweight = 1. - product(1.-x for x in g.edge[a][b]['weights'])
g.edge[a][b]['weight'] = newweight
# Set the planted communities:
nxutil.cmtyInit(g)
for c, nodes in enumerate(communities):
nxutil.cmtyAddFromList(g, c, nodes)
# external edges?
if pOut:
#add_edges_out(g=g, p=pOut, g_layers=(g,), weighted=weighted,
# edges_constructor=edges_constructor)
add_edges_out_sparse(g=g, p=pOut, g_layers=(g,), weighted=weighted,
edges_constructor=edges_constructor)
return g
def overlap_communities(g, n_min=1):
"""Return graph with communities set to all pairwise overlap of
given graph communities.
n_min = minimum size of overlap to be returned."""
g_new = g.copy()
nxutil.cmtyInit(g_new)
cmtys = nxutil.communities(g)
cmtys_list = list(cmtys)
overlap_cmtys = { }
overlap_cmty_i = 0
print cmtys_list
for i, c1 in enumerate(cmtys_list):
c1nodes = cmtys[c1]
for j, c2 in enumerate(cmtys_list[i+1:]):
c2nodes = cmtys[c2]
newCmtyNodes = c1nodes & c2nodes
print c1, c2, len(c1nodes), len(c2nodes), len(newCmtyNodes)
if len(newCmtyNodes) > n_min:
overlap_cmtys[overlap_cmty_i] = newCmtyNodes
overlap_cmty_i += 1
nxutil.cmtyAddFromList(g_new, overlap_cmty_i, newCmtyNodes)
return g_new
def overlap_communities(g, n_min=1):
"""Return graph with communities set to all pairwise overlap of
given graph communities.
n_min = minimum size of overlap to be returned."""
g_new = g.copy()
nxutil.cmtyInit(g_new)
cmtys = nxutil.communities(g)
cmtys_list = list(cmtys)
overlap_cmtys = {}
overlap_cmty_i = 0
print cmtys_list
for i, c1 in enumerate(cmtys_list):
c1nodes = cmtys[c1]
for j, c2 in enumerate(cmtys_list[i + 1:]):
c2nodes = cmtys[c2]
newCmtyNodes = c1nodes & c2nodes
print c1, c2, len(c1nodes), len(c2nodes), len(newCmtyNodes)
if len(newCmtyNodes) > n_min:
overlap_cmtys[overlap_cmty_i] = newCmtyNodes
overlap_cmty_i += 1
nxutil.cmtyAddFromList(g_new, overlap_cmty_i, newCmtyNodes)
return g_new
def make_overlap_test(N_U, q1, n1, p1, q2, n2, p2, pU):
"""
N_U: number of nodes in the universe.
q1, q2: sizes of level1 and level2 communities.
n1, n2: number of nodes in level1 and level2 communities.
p1, p2: edge densities
pU: background connection probability.
"""
U = set(range(N_U))
g = networkx.Graph()
#n1 = 25
#q1 = 40
#p1 = .95
level1 = [ random.sample(U, n1) for _ in range(q1) ]
U = set().union(*level1)
print sum(len(x) for x in level1), [ len(x) for x in level1 ]
print len(U)
g.add_nodes_from(U)
for points in level1:
add_edges(g, points, p1)
#level2 = None
#n2 = 100
#q2 = 10
#p2 = .65
#level2 = [ random.sample(U, size2) for _ in range(q2) ]
level2 = partition_nodes(U, q2, n2)
for points in level2:
add_edges(g, points, p2)
add_edges(g, list(g.nodes()), pU)
g1 = g.copy()
nxutil.cmtyInit(g1)
for c, nodes in enumerate(level1):
nxutil.cmtyAddFromList(g1, c, nodes)
g2 = g.copy()
nxutil.cmtyInit(g2)
for c, nodes in enumerate(level2):
nxutil.cmtyAddFromList(g2, c, nodes)
return g, g1, g2
def make_overlap_test(N_U, q1, n1, p1, q2, n2, p2, pU):
"""
N_U: number of nodes in the universe.
q1, q2: sizes of level1 and level2 communities.
n1, n2: number of nodes in level1 and level2 communities.
p1, p2: edge densities
pU: background connection probability.
"""
U = set(range(N_U))
g = networkx.Graph()
#n1 = 25
#q1 = 40
#p1 = .95
level1 = [random.sample(U, n1) for _ in range(q1)]
U = set().union(*level1)
print sum(len(x) for x in level1), [len(x) for x in level1]
print len(U)
g.add_nodes_from(U)
for points in level1:
add_edges(g, points, p1)
#level2 = None
#n2 = 100
#q2 = 10
#p2 = .65
#level2 = [ random.sample(U, size2) for _ in range(q2) ]
level2 = partition_nodes(U, q2, n2)
for points in level2:
add_edges(g, points, p2)
add_edges(g, list(g.nodes()), pU)
g1 = g.copy()
nxutil.cmtyInit(g1)
for c, nodes in enumerate(level1):
nxutil.cmtyAddFromList(g1, c, nodes)
g2 = g.copy()
nxutil.cmtyInit(g2)
for c, nodes in enumerate(level2):
nxutil.cmtyAddFromList(g2, c, nodes)
return g, g1, g2
def sbm(U,
q,
n,
p,
weighted=None,
edges_constructor=add_edges_exact_sparse,
pOut=None):
U = set(U)
g = networkx.Graph()
# Pick our communities from the universe.
communities = makeCommunities(U, q, n)
# Add all nodes from the (new) universe, then add all of their edges.
g.add_nodes_from(U)
for nodes in communities:
#add_edges(g, nodes, p, weighted=weighted)
#add_edges_cm(g, nodes, p, weighted=weighted)
#add_edges_exact(g, nodes, p, weighted=weighted)
edges_constructor(g, nodes, p, weighted=weighted)
if weighted:
for a, b in g.edges_iter():
newweight = 1. - product(1. - x for x in g.edge[a][b]['weights'])
g.edge[a][b]['weight'] = newweight
# Set the planted communities:
nxutil.cmtyInit(g)
for c, nodes in enumerate(communities):
nxutil.cmtyAddFromList(g, c, nodes)
# external edges?
if pOut:
#add_edges_out(g=g, p=pOut, g_layers=(g,), weighted=weighted,
# edges_constructor=edges_constructor)
add_edges_out_sparse(g=g,
p=pOut,
g_layers=(g, ),
weighted=weighted,
edges_constructor=edges_constructor)
return g
def sbm_incomplete(U, q, n, p, weighted=None,
edges_constructor=None):
"""Create a SBM graph from a universe of nodes, possibly
excluding some of the nodes."""
U = set(U)
g = networkx.Graph()
# Pick our communities from the universe. Note that the size of
# the universe decreases.
# is n constant, or does it change for all communities?
if isinstance(n, (int, float)):
communities = [ random.sample(U, n) for _ in range(q) ]
else:
communities = [ random.sample(U, int(round(_))) for _ in n ]
U = set().union(*communities)
#print sum(len(x) for x in communities), [ len(x) for x in communities ]
#print len(U)
# Add all nodes from the (new) universe, then add all of their edges.
g.add_nodes_from(U)
# is p constant for all communities, or per-community?
if isinstance(p, (int, float)):
for nodes in communities:
edges_constructor(g, nodes, p, weighted=weighted)
else:
for nodes, p in zip(communities, p):
edges_constructor(g, nodes, p, weighted=weighted)
if weighted:
for a, b in g.edges_iter():
newweight = 1. - product(1.-x for x in g.edge[a][b]['weights'])
g.edge[a][b]['weight'] = newweight
# Set the planted communities:
nxutil.cmtyInit(g)
for c, nodes in enumerate(communities):
nxutil.cmtyAddFromList(g, c, nodes)
return g
def sbm_incomplete(U, q, n, p, weighted=None, edges_constructor=None):
"""Create a SBM graph from a universe of nodes, possibly
excluding some of the nodes."""
U = set(U)
g = networkx.Graph()
# Pick our communities from the universe. Note that the size of
# the universe decreases.
# is n constant, or does it change for all communities?
if isinstance(n, (int, float)):
communities = [random.sample(U, n) for _ in range(q)]
else:
communities = [random.sample(U, int(round(_))) for _ in n]
U = set().union(*communities)
#print sum(len(x) for x in communities), [ len(x) for x in communities ]
#print len(U)
# Add all nodes from the (new) universe, then add all of their edges.
g.add_nodes_from(U)
# is p constant for all communities, or per-community?
if isinstance(p, (int, float)):
for nodes in communities:
edges_constructor(g, nodes, p, weighted=weighted)
else:
for nodes, p in zip(communities, p):
edges_constructor(g, nodes, p, weighted=weighted)
if weighted:
for a, b in g.edges_iter():
newweight = 1. - product(1. - x for x in g.edge[a][b]['weights'])
g.edge[a][b]['weight'] = newweight
# Set the planted communities:
nxutil.cmtyInit(g)
for c, nodes in enumerate(communities):
nxutil.cmtyAddFromList(g, c, nodes)
return g