def fill_list(self):
def check_small_worlds_conditions(graph):
"""
Checks that n > k > ln(n) > 1
See the paper "Collective dynamics of 'small-world' networks",
by Duncan J. Watts & Steven H. Strogatz
"""
n = graph.number_of_nodes()
k = topology.average_degree(graph)
return n > k > math.log(n) > 1
statistics = [("Number of nodes (n)", lambda graph: graph.number_of_nodes()),
("Number of edges", lambda graph: graph.number_of_edges()),
("Average degree (k)", topology.average_degree),
("n > k > ln(n) > 1", check_small_worlds_conditions),
("Directed?", lambda graph: graph.is_directed()),
("Clustering coefficient", NX.average_clustering),
("Clustering coefficient (random)", lambda graph: \
topology.average_clustering_random_graph(graph.number_of_nodes(), graph.number_of_edges())),
("Average shortest path", topology.average_shortest_path),
("Average shortest path (random)", lambda graph: \
topology.average_shortest_path_random_graph(graph.number_of_nodes(), graph.number_of_edges()))
]
for label, func in statistics:
self.list.Append([label, "%s" % func(self.graph)])
self.list.SetColumnWidth(0, 230)
self.list.SetColumnWidth(1, 120)
def greed(self, g): #greed method, factor=log(2,n)/2+1/2
graph = g.graph
n = graph.number_of_nodes()
result = [0]
for i in range(n - 1):
k = g.nearest(result[-1], exclude=result)
result.append(k[1])
g.route = result
return result
def check_small_worlds_conditions(graph):
"""
Checks that n > k > ln(n) > 1
See the paper "Collective dynamics of 'small-world' networks",
by Duncan J. Watts & Steven H. Strogatz
"""
n = graph.number_of_nodes()
k = topology.average_degree(graph)
return n > k > math.log(n) > 1
def cheapest(self, g): #cheapest method, factor=2
graph = g.graph
nlist = [0]
nlist.append(g.nearest(nlist[0], exclude=nlist)[1])
nodes = graph.number_of_nodes()
while len(nlist) < nodes:
cost_min = float("inf")
nelem = len(nlist)
for n2 in range(nodes):
if n2 in nlist:
continue
for i in range(nelem):
cost = g.savings(nlist[i], nlist[(i + 1) % nelem], n2)
if cost < cost_min:
cost_min = cost
indices = [i, n2]
nlist.insert((indices[0] + 1) % nelem, indices[1])
g.route = nlist
return nlist
def farthest(self, g): #farthest method, factor=log(2,n)+0.16
graph = g.graph
nlist = [0]
nlist.append(g.farthest(nlist[0], exclude=nlist)[1])
nodes = graph.number_of_nodes()
while len(nlist) < nodes:
x0 = float("-inf")
for r in nlist:
(x, index) = g.farthest(r, exclude=nlist)
if x > x0:
x0 = x
index0 = index
s0 = float("inf")
nelem = len(nlist)
for t in range(nelem):
s = g.savings(nlist[t], nlist[(t + 1) % nelem], index0)
if s < s0:
s0 = s
ind_s = t
nlist.insert((ind_s + 1) % nelem, index0)
g.route = nlist
return nlist
def nearest(self, g): #nearest method, factor=2
graph = g.graph
nlist = [0]
nlist.append(g.nearest(nlist[0], exclude=nlist)[1])
nodes = graph.number_of_nodes()
while len(nlist) < nodes:
x0 = float("inf")
for r in nlist:
(x, index) = g.nearest(r, exclude=nlist)
if x < x0:
x0 = x
index0 = index
s0 = float("inf")
nelem = len(nlist)
for t in range(nelem):
s = g.savings(nlist[t], nlist[(t + 1) % nelem], index0)
if s < s0:
s0 = s
ind_s = t
nlist.insert(
(ind_s + 1) % nelem, index0
) # default inserts BEFORE the elem, here modified to AFTER the elem
g.route = nlist
return nlist
def symmetric_gamma_node(graph, node, formulas_in):
value_list = graph.node[node]
size = len(value_list)
index = 0
for i in range(index,size):
value = value_list[i]
if value[0] == 'box':
formula = value[1]
if value not in formulas_in[node]:
formulas_in[node].append(value)
try:
graph.successors(node)
except:
break
next_node = graph.successors(node)
for single_node in next_node:
if single_node < node:
#take the initial size of list to check whether it expanded
initial_size = len(graph.node[single_node])
if formula not in graph.node[single_node]:
graph.node[single_node].append(formula)
alpha_node_solve(graph,single_node)
beta_node_solve(graph,single_node, formulas_in)
final_size = len(graph.node[single_node])
#take diff to scan for these new entries
diff_size = final_size-initial_size
if diff_size > 0:
value_list_single_node_initial= graph.node[single_node]
value_list_single_node = value_list_single_node_initial[-diff_size:]
for value in value_list_single_node:
if isinstance(value,tuple) and value[0] == 'box':
part = value[1]
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'diamond':
part = ('not',value[1][1])
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value, tuple) and value[0] == 'diamond':
part = value[1]
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
#expand new delta formulae
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][1] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
elif isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'box':
part = ('not', value[1][1])
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][1] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
elif value[0] == 'not' and value[1][0] == 'diamond':
formula = ('not', value[1][1])
if value not in formulas_in[node]:
formulas_in[node].append(value)
try:
graph.successors(node)
except:
break
next_node = graph.successors(node)
for single_node in next_node:
if single_node < node:
#take the initial size of list to check whether it expanded
initial_size = len(graph.node[single_node])
if formula not in graph.node[single_node]:
graph.node[single_node].append(formula)
alpha_node_solve(graph, single_node)
beta_node_solve(graph, single_node, formulas_in)
final_size = len(graph.node[single_node])
#take diff to scan for these new entries
diff_size = final_size-initial_size
if diff_size > 0:
value_list_single_node_initial= graph.node[single_node]
value_list_single_node = value_list_single_node_initial[-diff_size:]
for value in value_list_single_node:
if isinstance(value,tuple) and value[0] == 'box':
part = value[1]
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'diamond':
part = ('not',value[1][1])
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value, tuple) and value[0] == 'diamond':
part = value[1]
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][0] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
elif isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'box':
part = ('not', value[1][1])
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][0] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph,new_node)
beta_node_solve(graph,new_node, formulas_in)
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
def delta_node_solve(graph, node, formulas_in):
delta_list = graph.node[node]
for i in range(len(delta_list)-1,-1,-1):
part1 = delta_list[i][0]
if part1 == 'diamond':
sub = delta_list[i]
if sub not in formulas_in[node]:
formulas_in[node].append(sub)
part2 = delta_list[i][1]
new_node= graph.number_of_nodes()+1
graph.add_edge(node,(new_node)) #adding new world and relation Rxx'
graph.add_edge((new_node), node) #add symmetric edge
graph.node[node] = delta_list
graph.node[new_node] = [part2]
formulas_in[new_node] = []
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][1] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
elif part1 == 'not' and delta_list[i][1][0] == 'box':
sub = delta_list[i]
if sub not in formulas_in[node]:
formulas_in[node].append(sub)
part2 = ('not', delta_list[i][1][1])
new_node= graph.number_of_nodes()+1
graph.add_edge(node,(new_node)) #adding new world and relation Rxx'
graph.add_edge((new_node), node) #add symmetric edge
graph.node[node] = delta_list
graph.node[new_node] = [part2]
formulas_in[new_node] = []
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][1] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
