def test_strong_product_size():
K5 = nx.complete_graph(5)
P5 = nx.path_graph(5)
K3 = nx.complete_graph(3)
G = nx.strong_product(P5, K3)
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = nx.strong_product(K3, K5)
assert_equal(nx.number_of_nodes(G), 3 * 5)
def test_strong_product_size():
K5=nx.complete_graph(5)
P5=nx.path_graph(5)
K3 = nx.complete_graph(3)
G=strong_product(P5,K3)
assert_equal(nx.number_of_nodes(G),5*3)
G=strong_product(K3,K5)
assert_equal(nx.number_of_nodes(G),3*5)
def test_strong_product_combinations():
P5 = nx.path_graph(5)
K3 = nx.complete_graph(3)
G = nx.strong_product(P5, K3)
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = nx.strong_product(nx.MultiGraph(P5), K3)
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = nx.strong_product(P5, nx.MultiGraph(K3))
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = nx.strong_product(nx.MultiGraph(P5), nx.MultiGraph(K3))
assert_equal(nx.number_of_nodes(G), 5 * 3)
def test_strong_product_combinations():
P5 = nx.path_graph(5)
K3 = nx.complete_graph(3)
G = strong_product(P5, K3)
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = strong_product(nx.MultiGraph(P5), K3)
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = strong_product(P5, nx.MultiGraph(K3))
assert_equal(nx.number_of_nodes(G), 5 * 3)
G = strong_product(nx.MultiGraph(P5), nx.MultiGraph(K3))
assert_equal(nx.number_of_nodes(G), 5 * 3)
def graphStrongProdPower(graph, k):
binaryOfK = bin(k)[2:]
resultingGraph = "empty"
currentProdGraph = graph
#print(binaryOfK)
for i in range(len(binaryOfK) - 1, -1, -1):
if (binaryOfK[i] == '1'):
if (resultingGraph == "empty"):
resultingGraph = currentProdGraph
else:
resultingGraph = nx.strong_product(graph, currentProdGraph)
if (i > 0):
currentProdGraph = nx.strong_product(currentProdGraph,
currentProdGraph)
return resultingGraph
def graphStrongProdPower(graph, k):
#we get the binary representation of k
binaryOfK = bin(k)[2:]
resultingGraph = "empty"
currentProdGraph = graph
#we go through and figure out which powers of 2 of the graph we need to get to figure out the strong graph product power
for i in range(len(binaryOfK) - 1, -1, -1):
if (binaryOfK[i] == '1'):
if (resultingGraph == "empty"):
resultingGraph = currentProdGraph
else:
resultingGraph = nx.strong_product(resultingGraph,
currentProdGraph)
if (i > 0):
currentProdGraph = nx.strong_product(currentProdGraph,
currentProdGraph)
return resultingGraph
def test_strong_product_random():
G = nx.erdos_renyi_graph(10, 2 / 10.)
H = nx.erdos_renyi_graph(10, 2 / 10.)
GH = nx.strong_product(G, H)
for (u_G, u_H) in GH.nodes():
for (v_G, v_H) in GH.nodes():
if (u_G == v_G and H.has_edge(u_H, v_H)) or \
(u_H == v_H and G.has_edge(u_G, v_G)) or \
(G.has_edge(u_G, v_G) and H.has_edge(u_H, v_H)):
assert_true(GH.has_edge((u_G, u_H), (v_G, v_H)))
else:
assert_true(not GH.has_edge((u_G, u_H), (v_G, v_H)))
def test_strong_product_random():
G = nx.erdos_renyi_graph(10,2/10.)
H = nx.erdos_renyi_graph(10,2/10.)
GH = strong_product(G,H)
for (u_G,u_H) in GH.nodes_iter():
for (v_G,v_H) in GH.nodes_iter():
if (u_G==v_G and H.has_edge(u_H,v_H)) or \
(u_H==v_H and G.has_edge(u_G,v_G)) or \
(G.has_edge(u_G,v_G) and H.has_edge(u_H,v_H)):
assert_true(GH.has_edge((u_G,u_H),(v_G,v_H)))
else:
assert_true(not GH.has_edge((u_G,u_H),(v_G,v_H)))
def test_strong_product_null():
null = nx.null_graph()
empty10 = nx.empty_graph(10)
K3 = nx.complete_graph(3)
K10 = nx.complete_graph(10)
P3 = nx.path_graph(3)
P10 = nx.path_graph(10)
# null graph
G = nx.strong_product(null, null)
assert_true(nx.is_isomorphic(G, null))
# null_graph X anything = null_graph and v.v.
G = nx.strong_product(null, empty10)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(null, K3)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(null, K10)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(null, P3)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(null, P10)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(empty10, null)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(K3, null)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(K10, null)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(P3, null)
assert_true(nx.is_isomorphic(G, null))
G = nx.strong_product(P10, null)
assert_true(nx.is_isomorphic(G, null))
def test_strong_product_raises():
P = nx.strong_product(nx.DiGraph(), nx.Graph())
def test_strong_product_null():
null=nx.null_graph()
empty10=nx.empty_graph(10)
K3=nx.complete_graph(3)
K10=nx.complete_graph(10)
P3=nx.path_graph(3)
P10=nx.path_graph(10)
# null graph
G=strong_product(null,null)
assert_true(nx.is_isomorphic(G,null))
# null_graph X anything = null_graph and v.v.
G=strong_product(null,empty10)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(null,K3)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(null,K10)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(null,P3)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(null,P10)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(empty10,null)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(K3,null)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(K10,null)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(P3,null)
assert_true(nx.is_isomorphic(G,null))
G=strong_product(P10,null)
assert_true(nx.is_isomorphic(G,null))
def test_strong_product_raises():
P = strong_product(nx.DiGraph(), nx.Graph())
#89149963 3/7 colors
#89150081 3/7
#89150083 3/7
#69210692 2/3
i = 0
start = time.time()
for s in s_gen:
if i <= 69210691:
i += 1
continue
#generate the confusability graph G of X given Y, YR
gxyyr = indset.generateGXYYR(s)
gxyyr2 = nx.strong_product(gxyyr, gxyyr)
#from that generate G R given K graphs.
pairs = indset.generateGRK(gxyyr, s)
# grklist = [grk for (grk, k) in pairs]
# klist = [k for (grk, k) in pairs]
r1 = 4
g1min = nx.Graph()
k1min = []
for (g1, k1) in pairs:
c = coloring.minimalColoring(g1, 0)
if c < r1:
r1 = c
g1min = g1.copy()
def test_strong_product_raises():
with pytest.raises(nx.NetworkXError):
P = nx.strong_product(nx.DiGraph(), nx.Graph())
import networkx as nx
#basic example
G = nx.cycle_graph(5)
A1 = nx.nx_agraph.to_agraph(G)
A1.draw('testpentagon', format='png', prog='circo')
strong = nx.strong_product(G, G)
A2 = nx.nx_agraph.to_agraph(strong)
A2.draw('teststrong', format='png', prog='circo')
print nx.maximum_independent_set(strong)
import networkx as nx
import matplotlib.pyplot as plt
from random import choice
def setUtil(graph):
if graph.number_of_nodes() == 0:#G is empty
return 0
#v = any vertex in G
v = choice(graph.nodes())
neighborhood = graph.copy().neighbors(v) + [v]
#print neighborhood
withV = graph.copy()
withV.remove_nodes_from(neighborhood)
withoutV = graph.copy()
withoutV.remove_node(v)
return max(1 + setUtil(withV), setUtil(withoutV))
G = nx.cycle_graph(7)
S = nx.strong_product(G, G)
Q = nx.strong_product(G, S)
print setUtil(Q)
