def tspRepeats(G, start):
#make a graph out of the matrix
all_distances = dict(nx.floyd_warshall(G))
#initialize graph of distances (complete graph with shortest paths as edges)
B = G.copy()
edges = {""}
edges.pop()
for _ in G.nodes:
for __ in G.nodes:
if not B.has_edge(_, __) and not __ == _:
edges.add((_, __, all_distances[_][__]))
B.add_weighted_edges_from(edges)
#predecessors = nx.floyd_warshall_predecessor_and_distance(B)
all_distances = dict(nx.floyd_warshall(B))
#creates returner, a two-opt algorithm version of TSP on the shortest paths graph
returner = two_opt(B)
#shifts the array so the starting node is at the beginning of the array
def shift(seq, n):
n = n % len(seq)
return seq[n:] + seq[:n]
for _ in range(len(returner)):
if returner[_] == int(start):
returner = shift(returner, _)
finalList = []
if len(returner) > 0:
finalList = [returner[0]]
for i in range(len(returner)-1):
finalList += nx.shortest_path(G, returner[i], returner[i+1], weight='weight')[1:]
finalList += nx.shortest_path(G, returner[-1], returner[0], weight='weight')[1:]
return finalList
def lab_5():
def graph(n, k, p):
G = nx.watts_strogatz_graph(n, k, p)
if not nx.is_connected(G):
return graph(size, k, p)
return G
iterations = 100
size = np.arange(1, 6)
data = np.zeros((iterations, len(size)))
for i in trange(iterations):
for j in size:
G = graph(j * 100, 10, 0.5)
t = time()
nx.floyd_warshall(G)
data[i][j - 1] = time() - t
np.save('out/lab5.npy', data)
x = np.arange(100, 600, 100)
data = np.load('out/lab5.npy')
y = np.zeros(5)
for i in range(5):
y[i] = np.average(data[:, i])
matplotlib.rc('font', **{'size': 24})
plt.figure(figsize=(12, 9))
plt.title('Average Time')
plt.plot(x, y, color='#FA816D', linewidth=3)
plt.xlabel('Network Size')
plt.xticks(x)
plt.ylabel('Seconds')
plt.show()
def test_zero_weight(self):
G = nx.DiGraph()
edges = [(1,2,-2), (2,3,-4), (1,5,1), (5,4,0), (4,3,-5), (2,5,-7)]
G.add_weighted_edges_from(edges)
dist = nx.floyd_warshall(G)
assert_equal(dist[1][3], -14)
G = nx.MultiDiGraph()
edges.append( (2,5,-7) )
G.add_weighted_edges_from(edges)
dist = nx.floyd_warshall(G)
assert_equal(dist[1][3], -14)
def test_zero_weight(self):
G = nx.DiGraph()
edges = [(1,2,-2), (2,3,-4), (1,5,1), (5,4,0), (4,3,-5), (2,5,-7)]
G.add_weighted_edges_from(edges)
dist = nx.floyd_warshall(G)
assert_equal(dist[1][3], -14)
G = nx.MultiDiGraph()
edges.append( (2,5,-7) )
G.add_weighted_edges_from(edges)
dist = nx.floyd_warshall(G)
assert_equal(dist[1][3], -14)
def condense_graph(subG,clusterlabelfile, num_levels, level,nodeL):
with open(clusterlabelfile,"r+") as f:
lines = f.readlines()
line = lines[level]
num_communs = int(re.findall(r'(\d+) nodes',line)[0])
if level < 0:
hier = num_levels + level
else:
hier = level
with open("clusters.csv","w+") as f:
subprocess.check_call([r"./DirectedLouvain/bin/hierarchy","subG.tree","-l",str(hier)], stdout=f)
cluster_df = pd.read_csv('clusters.csv',index_col = False, names = ['node','community'],sep=' ')
def convert_inds(ind):
return nodeL[ind]
cluster_df['node'] = cluster_df['node'].map(convert_inds)
for i, tup in cluster_df.iterrows():
node, comm = tup
subG.nodes[node]['community'] = comm
print("Condensing graph...")
tic = timemod.clock()
condensed_G = nx.DiGraph()
for i in range(0,num_communs):
condensed_G.add_node(i)
nodes = list(cluster_df[cluster_df['community'] == i]['node'])
condensed_G.nodes[i]['squished_nodes'] = nodes
temp = subG.subgraph(nodes)
distances = nx.floyd_warshall(temp,weight='pace')
avg_pace = np.nanmean([t for src,tardict in distances.items() for dest,t in tardict.items() if src in nodes and dest in nodes and np.isfinite(t)])
if np.isfinite(avg_pace):
condensed_G.add_edge(i,i,pace=avg_pace)
for start,end in itertools.permutations(condensed_G.nodes,2):
clus1 = cluster_df[cluster_df['community']==start]
clus2 = cluster_df[cluster_df['community']==end]
temp = subG.subgraph(list(clus1['node'])+list(clus2['node']))
distances = nx.floyd_warshall(temp,weight='pace')
edges_12_pace = np.nanmean([t for src,tardict in distances.items() for dest,t in tardict.items()
if src in set(clus1['node']) and dest in set(clus2['node']) and np.isfinite(t)])
if np.isfinite(edges_12_pace):
condensed_G.add_edge(start,end,pace=edges_12_pace)
toc = timemod.clock()
print("Graph condensed in " + str(toc-tic) + " seconds.")
return cluster_df, condensed_G
def test(adj_mat, elapsed_time, i):
G = ntx.Graph(adj_mat)
ntx.draw_networkx(G, pos=ntx.kamada_kawai_layout(G), node_size=50, with_labels=True, font_size=4, width=0.5)
plt.savefig("graph"+i+".png", dpi=1000, quality=95)
plt.show()
t0 = time.perf_counter()
ntx.floyd_warshall(G)
elapsed_time[0].append(time.perf_counter() - t0)
t0 = time.perf_counter()
ntx.johnson(G)
elapsed_time[1].append(time.perf_counter() - t0)
print("finished_test")
return elapsed_time
def ich(M, colNames=[], dictDefault=-1, useFullDistance=True, name='', stateFile='', randOrder=True, procs=1):
progressFile = name+'_ich_progress'
if name: saveState({}, [], progressFile, overwrite=True)
if isinstance(M, nx.classes.graph.Graph) and useFullDistance:
nodes = sorted(M.nodes())
M = nx.floyd_warshall(M)
M = [[int(M[u][v]) if (v in M and M[u][v]!=np.inf) else -1 for v in nodes] for u in nodes]
distr = {}
tags = {}
chosen = []
if stateFile:
(tags, chosen) = readState(stateFile)[-1]
for t in tags:
if tags[t] not in distr: distr[tags[t]] = []
distr[tags[t]].append(t)
elif isinstance(M, list): tags = {i:'' for i in range(len(M))}
elif isinstance(M, dict): tags = {i:'' for i in M}
elif isinstance(M, nx.classes.graph.Graph): tags = {i:'' for i in M.nodes()}
n = len(tags)
check = colNames if (isinstance(M, dict) and colNames) else (sorted(M[M.keys()[0]].keys()) if isinstance(M, dict) else sorted(tags.keys()))
for col in chosen: check.remove(col)
check = list(np.random.permutation(check)) if randOrder else sorted(check)
while len(distr) < n and len(chosen) < n:
(distr, tags, _, chosen) = pickColumn(M, tags, check, chosen=chosen, dictDefault=dictDefault, procs=procs)
check.remove(chosen[-1])
if name: saveState(tags, chosen, progressFile, overwrite=True)
if len(distr) < n and len(chosen) == n: return 'NO SOLUTION EXISTS'
return chosen
def __init__(self, file_name):
"""Sets up basic Information about the graph
graph.labels = [all original labels with index = network x node number] (i.e graph.labels[0] == 'soda')
graph.homes = [node numbers of homes] with len() = k
graph.nxgraph = network x graph with number [1, 2, ..., n]
graph.num_houses = number of TAs (k)
graph.num_locs = number of locations (n)
graph.dist = shorest all paths computed dynamically by floyd_warshall
(i.e graph.dist[0][0] == 0)
"""
data = read_file(file_name)
parsed = data_parser(data)
self.parsed = parsed
self.num_locs = parsed[0]
self.num_houses = parsed[1]
self.labels = parsed[2]
homes = parsed[3]
start = parsed[4]
matrix = parsed[5]
self.homes = [self.labels.index(node) for node in homes]
self.start = self.labels.index(start)
self.nxgraph = adjacency_matrix_to_graph(matrix)[0]
self.dist = nx.floyd_warshall(self.nxgraph)
def moving(G, F):
d = nx.floyd_warshall(G, weight='weight')
# res[i - 1][0]: the result to unload ith item w/o carrying the (i + 1)th item
# res[i - 1][1]: the result to unload ith item w carrying the (i + 1)th item
res = [[]]
try:
res[0].append(d['1'][F[0][0]] + d[F[0][0]][F[0][1]])
if len(F) == 1:
return res[0][0]
res[0].append(d['1'][F[0][0]] + d[F[0][0]][F[1][0]] +
d[F[1][0]][F[0][1]])
for i in range(1, len(F)):
res.append([])
res[i].append(
min(
res[i - 1][0] + d[F[i - 1][1]][F[i][0]] +
d[F[i][0]][F[i][1]],
res[i - 1][1] + d[F[i - 1][1]][F[i][1]]))
if i == len(F) - 1:
return res[i][0]
res[i].append(
min(
res[i - 1][0] + d[F[i - 1][1]][F[i][0]] +
d[F[i][0]][F[i + 1][0]] + d[F[i + 1][0]][F[i][1]],
res[i - 1][1] + d[F[i - 1][1]][F[i + 1][0]] +
d[F[i + 1][0]][F[i][1]]))
except:
return -1
def expected_time(nodes, edges, p, g):
G = nx.Graph()
G.add_weighted_edges_from(g)
lengths = nx.floyd_warshall(G)
node_sum = {
node: sum(d.values())
for node, d in lengths.items()
}
cache = {}
def recurse(last, depth):
if (last, depth) not in cache:
if depth == 1:
cache[(last, depth)] = node_sum[last]
else:
cache[(last, depth)] = sum(
recurse(n, depth - 1)
for n in range(1, nodes + 1)
if n != last
) + node_sum[last]
cache[(last, depth)] /= (nodes - 1)
return cache[(last, depth)]
#pprint(cache)
return recurse(1, p)
def construct_diff(self):
# real knowledge structure obtained by using IITA, without transitive closure
real_knowledge_structure = nx.DiGraph(self.load_ks(self.e_ks.get()))
# print(real_knowledge_structure.nodes())
# transitive closure of the real knowledge structure
tc_knowledge_structure = nx.DiGraph([(u, v, {
'd': l
}) for u, adj in nx.floyd_warshall(real_knowledge_structure).items()
for v, l in adj.items()
if l > 0 and l < float('inf')])
# if there is any predecessor to the given node, than it is not in the fringe
def in_fringe(node, graph):
for edge in graph.edges():
if edge[1] == node:
return False
return True
fringe = []
complexity = []
level = 1
while tc_knowledge_structure.nodes():
for node in tc_knowledge_structure.nodes():
if in_fringe(node, tc_knowledge_structure):
fringe.append(node)
complexity.append((node, level))
tc_knowledge_structure.remove_nodes_from(fringe)
fringe = []
level += 1
self.txt_diff.delete(1.0, END)
self.txt_diff.insert(END, "" + str(complexity))
def __init__(self, train, test, path_feature=False):
self.train = train
self.test = test
self.info = json.load(open("attributes.json"))
if path_feature:
self.shortest_path = dict(nx.floyd_warshall(train,
weight='weight'))
def cost_of_solution_no_print(G, car_cycle, dropoff_mapping):
cost = 0
dropoffs = dropoff_mapping.keys()
if not is_valid_walk(G, car_cycle):
print('This is not a valid walk for the given graph.\n')
sys.exit()
if not car_cycle[0] == car_cycle[-1]:
print('The start and end vertices are not the same.\n')
sys.exit()
if cost != 'infinite':
if len(car_cycle) == 1:
car_cycle = []
else:
car_cycle = get_edges_from_path(
car_cycle[:-1]) + [(car_cycle[-2], car_cycle[-1])]
if len(car_cycle) != 1:
driving_cost = sum([G.edges[e]['weight']
for e in car_cycle]) * 2 / 3
else:
driving_cost = 0
walking_cost = 0
shortest = dict(nx.floyd_warshall(G))
for drop_location in dropoffs:
for house in dropoff_mapping[drop_location]:
walking_cost += shortest[drop_location][house]
cost = driving_cost + walking_cost
return cost
def plot_path_length(g, directory):
fig1, ax1 = plt.subplots()
fig1.subplots_adjust(left=0.15)
hist = []
am = {}
table = nx.floyd_warshall(g)
for n in list(table.values()):
#print(n.values())
for k in list(n.values()):
#hist[int(k)] = hist.get(int(k), 0) + 1
if k < 10000:
if int(k) != 0:
hist.append(k)
am[int(k)] = am.get(int(k), 0) + 1
plt.hist(hist,
len(am.values()) - 1,
facecolor='blue',
edgecolor='darkblue',
alpha=0.75,
align='left')
ax1.set_xlabel("Path length")
ax1.set_ylabel("Paths")
plt.savefig("plots/{}/histogram_shortest_path".format(directory))
print("AVERAGE: ", sum(hist) / len(hist))
def compute_greedy_heuristic(self): """ Computes WMSCP Greedy Heuristic. self.graph is the NetworkX graph. self.clusters is a list of lists of node incides where each list corresponds to the list of nodes in each cluster (so [[0,1,2,3],[4,5,6,7]] would be two clusters with 0-3 in one cluster and 4-7 in other). """ controller_set = [] # Stores controller indices distances = nx.floyd_warshall(self.graph, 'weight') # Stores distances between every node weights_index = 0 # Converts index of minimum weight to actual node index (only works because clusters are in-order and sorted for i in range(len(self.clusters)): # Go through each node in cluster and compute weights weights = [] for node in self.clusters[i]: # Go through every cluster and find shortest distance, shortest distance to controller weight = 0 # Stores weight of this node for j in range(len(self.clusters)): if i == j: # Matching cluster, ignore continue cluster_distance = 1e6 controller_distance = 0 for cluster_node in self.clusters[j]: # Go through every node in other clusters and compute distance to find shortest node per cluster cluster_distance = min(cluster_distance, distances[node][cluster_node]) if cluster_node in controller_set: # If node is a controller, add its distance a "second" time to correspond # to second sigma-sum of weight calculation assert controller_distance == 0, print(cluster_node, controller_set) controller_distance = distances[node][cluster_node] assert cluster_distance != 1e6, "Cluster distance was too low, it was not modified" weight += cluster_distance + controller_distance # Add to node weight weight /= len(self.clusters[i]) + 1 # Divide by nodes covered (the length of cluster upcoming controller is in) weights.append(weight) controller_set.append(weights.index(min(weights)) + weights_index) # Add node index to controller list weights_index += len(self.clusters[i]) return controller_set, super().step(controller_set) # Return controller list and corresponding cost (minimum distance between all controllers)
def cost_of_solution(G, car_cycle, dropoff_mapping):
cost = 0
message = ''
dropoffs = dropoff_mapping.keys()
if not is_valid_walk(G, car_cycle):
message += 'This is not a valid walk for the given graph.\n'
cost = 'infinite'
if not car_cycle[0] == car_cycle[-1]:
message += 'The start and end vertices are not the same.\n'
cost = 'infinite'
if cost != 'infinite':
if len(car_cycle) == 1:
car_cycle = []
else:
car_cycle = get_edges_from_path(car_cycle[:-1]) + [(car_cycle[-2], car_cycle[-1])]
driving_cost = sum([G.edges[e]['weight'] for e in car_cycle]) * 2 / 3
walking_cost = 0
shortest = dict(nx.floyd_warshall(G))
for drop_location in dropoffs:
for house in dropoff_mapping[drop_location]:
walking_cost += shortest[drop_location][house]
message += f'The driving cost of your solution is {driving_cost}.\n'
message += f'The walking cost of your solution is {walking_cost}.\n'
cost = driving_cost + walking_cost
message += f'The total cost of your solution is {cost}.\n'
return cost, message
def eloc_node(G, xNode):
'''
A function to calculate the nodal local efficiency
from a node xNode.
input parameters:
G: A graph in networkX format.
xNode: The node where the nodal global efficiency is calculated.
returns:
Eloc: The nodal local efficiency at node xNode.
'''
subG = subgraph(G, xNode)
#Eloc, tmpEloci, tmpNodes = eglob_net(subG)
NNodes = len(subG.nodes())
if NNodes>1:
#Dij = nx.all_pairs_shortest_path_length(subG)
Dij = nx.floyd_warshall(subG)
D = [Dij[i].values() for i in subG.nodes()]
cD = []
for irow in D:
cD += irow
NZD = np.array(cD)[np.nonzero(cD)]
if len(NZD)>0:
Eloc = (1.0/(NNodes*(NNodes-1.0))) * np.sum(1.0/NZD)
else:
Eloc = 0
else:
Eloc = 0
return Eloc
def WD(self) -> (np.array, np.array):
"""
Creates the matrices W and D.
:return: W, D matrices as 2D np.array
"""
# makes a copy of the original graph
# could it be expensive?
new_g = nx.DiGraph()
n_vertices = self.g.number_of_nodes()
W = np.empty((n_vertices, n_vertices), dtype=np.int)
D = np.empty((n_vertices, n_vertices))
# 1. Weight each edge u-e->_ in E with the ordered
# pair (w(e), -d(u))
new_g.add_weighted_edges_from([
(u, v, CustomWeight(self.g.edges[u, v]["weight"], -self.delay[u]))
for (u, v) in self.g.edges
])
# 2. compute the all-pairs shortest paths
# add of the weights: componentwise addition
# comparison of the weights: lexicographic order
path_len = dict(nx.floyd_warshall(new_g))
# 3. For each u,v vertices, their shortest path weight is (x,y)
# set W(u,v) = x, D(u,v) = d(v) - y
for u in new_g.nodes:
for v in new_g.nodes:
cw = path_len[u][v]
W[int(u), int(v)] = cw.x
D[int(u), int(v)] = self.delay[v] - cw.y
return W, D
def eloc_node(G, xNode):
'''
A function to calculate the nodal local efficiency
from a node xNode.
input parameters:
G: A graph in networkX format.
xNode: The node where the nodal global efficiency is calculated.
returns:
Eloc: The nodal local efficiency at node xNode.
'''
subG = subgraph(G, xNode)
#Eloc, tmpEloci, tmpNodes = eglob_net(subG)
NNodes = len(subG.nodes())
if NNodes > 1:
#Dij = nx.all_pairs_shortest_path_length(subG)
Dij = nx.floyd_warshall(subG)
D = [Dij[i].values() for i in subG.nodes()]
cD = []
for irow in D:
cD += irow
NZD = np.array(cD)[np.nonzero(cD)]
if len(NZD) > 0:
Eloc = (1.0 / (NNodes * (NNodes - 1.0))) * np.sum(1.0 / NZD)
else:
Eloc = 0
else:
Eloc = 0
return Eloc
def is_metricFlexible(G):
shortest = dict(nx.floyd_warshall(G))
for u, v, datadict in G.edges(data=True):
if abs(shortest[u][v] - datadict["weight"]) >= 0.00001:
print(u, v, shortest[u][v])
return False
return True
def is_metric(G):
shortest = dict(nx.floyd_warshall(G))
for u, v, datadict in G.edges(data=True):
assert shortest[u][v] == datadict[
'weight'], 'Direct path from {} to {} (weight {}) is not shortest path (weight {})'.format(
u, v, datadict['weight'], shortest[u][v])
return True
def chinese_postman(g, weight="weight"):
"""
中国人郵便配達問題
入力
g: 無向グラフ
weight: 重みの属性文字
出力
距離と頂点リスト
"""
import networkx as nx
from itertools import combinations
assert not g.is_directed()
g = nx.MultiGraph(g)
subnd = [nd for nd, dg in g.degree() if dg % 2 == 1] # 奇数次数ノード群
dd = nx.floyd_warshall(g, weight=weight) # 完全距離表
mx = max(d for dc in dd.values() for d in dc.values()) # 最大距離
h = nx.Graph()
for i, j in combinations(subnd, 2):
h.add_edge(i, j, weight=mx - dd[i][j])
for i, j in nx.max_weight_matching(h, True): # 最大重み最大マッチング問題
g.add_edge(i, j, weight=dd[i][j])
return (
sum(d[weight] for (i, j, _), d in g.edges.items()),
list(nx.eulerian_circuit(g)),
)
def hierarchy_clustering(G):
N = len(G)
S = np.zeros((N, N))
floyd = nx.floyd_warshall(G)
for i in range(N):
for j in range(N):
S[i, j] = floyd[i][j]
# print(S)
Y = squareform(S)
Z = hierarchy.linkage(Y, method='average')
hierarchy.dendrogram(Z)
plt.show()
clusters = hierarchy.fcluster(Z, 3.25, criterion='distance')
n_clusters = max(clusters)
print(n_clusters)
nodes = np.arange(N)
for i in range(1, n_clusters + 1):
GG = G.subgraph(nodes[clusters == i])
# print(len(GG), GG.edges())
nx.draw(GG)
plt.show()
return clusters
def MakeCostMatrix(d):
""" Make a ransom metrix matrix as described in Cuturi 2013 (Figure 4) """
G = nx.erdos_renyi_graph(d, 0.5)
for u, v, w in G.edges(data=True):
w['weight'] = np.random.uniform(0, 1)
# All pair shortest path
M = nx.floyd_warshall(G)
return M
def run(self):
start = time.time()
answer = nx.floyd_warshall(self.data['g'])
if self.verbose:
print('FloydWarshall took %.2f s.' % (time.time() - start))
return answer
def computeGraphDistances(G):
'''
Computes all pairs shortest paths on the given graph.
'''
G_undirected = nx.Graph(G)
distances = nx.floyd_warshall(G_undirected)
return distances
def test_floyd_warshall_predecessor_and_distance(self):
XG = nx.DiGraph()
XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
('u', 'v', 1), ('u', 'x', 2),
('v', 'y', 1), ('x', 'u', 3),
('x', 'v', 5), ('x', 'y', 2),
('y', 's', 7), ('y', 'v', 6)])
path, dist = nx.floyd_warshall_predecessor_and_distance(XG)
assert dist['s']['v'] == 9
assert path['s']['v'] == 'u'
assert (dist ==
{'y': {'y': 0, 'x': 12, 's': 7, 'u': 15, 'v': 6},
'x': {'y': 2, 'x': 0, 's': 9, 'u': 3, 'v': 4},
's': {'y': 7, 'x': 5, 's': 0, 'u': 8, 'v': 9},
'u': {'y': 2, 'x': 2, 's': 9, 'u': 0, 'v': 1},
'v': {'y': 1, 'x': 13, 's': 8, 'u': 16, 'v': 0}})
GG = XG.to_undirected()
# make sure we get lower weight
# to_undirected might choose either edge with weight 2 or weight 3
GG['u']['x']['weight'] = 2
path, dist = nx.floyd_warshall_predecessor_and_distance(GG)
assert dist['s']['v'] == 8
# skip this test, could be alternate path s-u-v
# assert_equal(path['s']['v'],'y')
G = nx.DiGraph() # no weights
G.add_edges_from([('s', 'u'), ('s', 'x'),
('u', 'v'), ('u', 'x'),
('v', 'y'), ('x', 'u'),
('x', 'v'), ('x', 'y'),
('y', 's'), ('y', 'v')])
path, dist = nx.floyd_warshall_predecessor_and_distance(G)
assert dist['s']['v'] == 2
# skip this test, could be alternate path s-u-v
# assert_equal(path['s']['v'],'x')
# alternate interface
dist = nx.floyd_warshall(G)
assert dist['s']['v'] == 2
# floyd_warshall_predecessor_and_distance returns
# dicts-of-defautdicts
# make sure we don't get empty dictionary
XG = nx.DiGraph()
XG.add_weighted_edges_from([('v', 'x', 5.0), ('y', 'x', 5.0),
('v', 'y', 6.0), ('x', 'u', 2.0)])
path, dist = nx.floyd_warshall_predecessor_and_distance(XG)
inf = float("inf")
assert (dist ==
{'v': {'v': 0, 'x': 5.0, 'y': 6.0, 'u': 7.0},
'x': {'x': 0, 'u': 2.0, 'v': inf, 'y': inf},
'y': {'y': 0, 'x': 5.0, 'v': inf, 'u': 7.0},
'u': {'u': 0, 'v': inf, 'x': inf, 'y': inf}})
assert (path ==
{'v': {'x': 'v', 'y': 'v', 'u': 'x'},
'x': {'u': 'x'},
'y': {'x': 'y', 'u': 'x'}})
def is_metric(G):
shortest = dict(nx.floyd_warshall(G))
answer = True
for u, v, datadict in G.edges(data=True):
if abs(shortest[u][v] - datadict['weight']) >= 0.00001:
print(shortest[u][v])
print(datadict['weight'])
answer = False
return answer
def check_triangle(adj):
matrix = np.matrix(adj)
G = nx.from_numpy_matrix(matrix)
shortest = dict(nx.floyd_warshall(G))
for u, v, datadict in G.edges(data=True):
val = datadict['weight']
if not isinstance(val, str) and abs(shortest[u][v] - datadict['weight']) >= 0.00001:
assert False
print("Adjacency matrix satisfies triangle inequality")
def __init__(self, G=None):
self.G = G if G else self.createGraph()
self.nodes = list(self.G.nodes)
self.number_of_nodes = self.G.number_of_nodes
self.edges = sorted(graph, key=lambda x: x[2])
print('networkx: ', nx.floyd_warshall(self.G))
self.floyd()
self.draw()
def floyd_warshall(distance):
'''
:param distance: distance model with maxsize
:return: shortest_dis, predecessors
'''
G = nx.DiGraph(distance)
shortest_dis = nx.floyd_warshall(G)
predecessors, _ = nx.floyd_warshall_predecessor_and_distance(G)
return shortest_dis, predecessors
def get_pred_path(G,v1,v2):
pred = nx.floyd_warshall(G)[1]
edges = deque([])
u = v2
while u != v1:
edges.appendleft((pred[v1][u],u,G[pred[v1][u]][u]['e']))
u = pred[v1][u]
return edges
def makeMetricCompleteFlexible(graph):
data = graph['data']
npy = np.array(data)
shortest = dict(nx.floyd_warshall(nx.from_numpy_matrix(npy)))
for i in range(len(data)):
for j in range(i, len(data)):
if (data[i][j] == graph['header'][3]):
data[i][j], data[j][
i] = shortest[i][j] - .0001, shortest[i][j] - .0001,
def get_paths(data, edgeDict=None, graph=None, algorithm='Floyd', weights='aff',
saveResults=False, filepathDist=None):
'''
a function that computes all pairwise distances (shortest paths)
and puts it into a dictionary.
Input: graph with edges as distances OR
(default) dict with pairwise affinities (not distances)
Output: shortest paths in a dict of dicts.
'''
unmatched = []
distGraph = nx.Graph()
if weights == 'aff':
print "computing 1/affinities..."
for i in data:
matched = 0
if i in edgeDict:
distGraph.add_node(i)
matched = 1
for j in edgeDict[i]:
if edgeDict[i][j] == 0:
distGraph.add_edge(i, j, weight='inf')
else:
distGraph.add_edge(i, j, weight=1.0 / edgeDict[i][j])
if matched == 0: unmatched.append(i)
elif weights == 'dist':
distGraph = graph
else:
print "Error: weight should be either 'aff' or 'dist'"
return 1
print "number of unmatched nodes: ", len(unmatched)
print unmatched
if algorithm == 'Floyd':
print "\ncomputing all shortest paths with Floyd-Warshall algorithm..."
dist = nx.floyd_warshall(distGraph)
print "pairwise distances obtained"
elif algorithm == "Dijkstra":
print "\ncomputing all shortest paths with Dijkstra algorithm..."
dist = nx.all_pairs_dijkstra_path_length(distGraph)
print "pairwise distances obtained"
else:
print "\nError: cannot recognize what algorithm to use"
return 1
print "num of rows in dist matrix: ", len(dist.keys())
# print dist.keys()
if saveResults:
if filepathDist == None:
#filepathDist = "/home/krybachuk/SHORTESTPATH_" + VersionTime
filepathDist = "SHORTESTPATH_" + "latest"
json.dump(dist, open(filepathDist, 'w'))
print "shortest path dict saved\n\n"
return dist
def test_shortest_path_all_pairs(iterations=20):
for i in range(iterations):
g = SmallWorldGraph(20, 4, 0.5)
print("Finding my results: ")
my_results = g.shortest_path_all_pairs()
print("Finding nx results: ")
nx_results = nx.floyd_warshall(g)
for key in my_results:
my_res = my_results[key]
nx_res = nx_results[key[0]][key[1]]
if not my_res == nx_res:
print("Mismatch!")
def prob_err(tree, leaves, budget):
assert budget >= 2
distance_matrix = nx.floyd_warshall(tree)
opt_err = 2
opt_sensors = []
for sensors in itertools.combinations(leaves, budget):
(classes, cardinalities) = equivalence_classes(distance_matrix, sensors)
err = prob_err_from_cardinalities(cardinalities)
if err < opt_err:
opt_err = err
opt_sensors = sensors
return (opt_err, opt_sensors)
def exp_dist(tree, leaves, budget):
assert budget >= 2
distance_matrix = nx.floyd_warshall(tree)
opt_exp_dist = sum([sum(distance_matrix[u].values()) for u in
distance_matrix])
opt_sensors = []
for sensors in itertools.combinations(leaves, budget):
(classes, cardinalities) = equivalence_classes(distance_matrix, sensors)
exp_dist = exp_dist_from_classes(distance_matrix, classes)
if exp_dist < opt_exp_dist:
opt_exp_dist = exp_dist
opt_sensors = sensors
return (opt_exp_dist, opt_sensors)
def floyd_warshall_solution_remove_stations(cityMap):
nodes = cityMap.g.nodes()
for v in nodes:
if v not in cityMap.rv:
cityMap.g.remove_node(v)
all_short = networkx.floyd_warshall(cityMap.g)
route = []
for v in cityMap.g.nodes():
route.append(min([node for node in all_short[v] if node not in route], key=lambda x: all_short[v][x]))
routes = []
segment = int(len(route) / cityMap.number_of_busses) + 1
for i in range(segment):
routes.append(route[i*segment: i*segment + segment])
cityMap.set_route(i+1, route[i*segment: i*segment + segment + 1])
return cityMap
def inverse_weight_shortest_path(G,weight_name='weight',dir='./',filename=' '):
if G.is_directed():
T=nx.DiGraph();
else:
T=nx.Graph();
T.add_nodes_from(G.nodes(data=True));
T.add_edges_from(G.edges());
for e in G.edges(data=True):
T[e[0]][e[1]][weight_name]=float(1/float(G[e[0]][e[1]][weight_name]));
distances=nx.floyd_warshall(T, weight=weight_name);
if filename!=' ':
nx.write_gexf(T,dir+filename.split('.')[-2]+'_inverse_edge_weight.gexf');
pickle.dump(distances,open(dir+filename+'_inverse_weight_shortest_path.pck','w'));
print 'Distance file saved to '+dir+filename+'_inverse_weight_shortest_path.pck'
return distances;
def test_floyd_warshall(self):
XG=nx.DiGraph()
XG.add_weighted_edges_from([('s','u',10) ,('s','x',5) ,
('u','v',1) ,('u','x',2) ,
('v','y',1) ,('x','u',3) ,
('x','v',5) ,('x','y',2) ,
('y','s',7) ,('y','v',6)])
dist, path =nx.floyd_warshall(XG)
assert_equal(dist['s']['v'],9)
assert_equal(path['s']['v'],'u')
assert_equal(dist,
{'y': {'y': 0, 'x': 12, 's': 7, 'u': 15, 'v': 6},
'x': {'y': 2, 'x': 0, 's': 9, 'u': 3, 'v': 4},
's': {'y': 7, 'x': 5, 's': 0, 'u': 8, 'v': 9},
'u': {'y': 2, 'x': 2, 's': 9, 'u': 0, 'v': 1},
'v': {'y': 1, 'x': 13, 's': 8, 'u': 16, 'v': 0}})
GG=XG.to_undirected()
dist, path = nx.floyd_warshall(GG)
assert_equal(dist['s']['v'],8)
assert_equal(path['s']['v'],'y')
G=nx.DiGraph() # no weights
G.add_edges_from([('s','u'), ('s','x'),
('u','v'), ('u','x'),
('v','y'), ('x','u'),
('x','v'), ('x','y'),
('y','s'), ('y','v')])
dist, path = nx.floyd_warshall(G)
assert_equal(dist['s']['v'],2)
assert_equal(path['s']['v'],'x')
dist, path = nx.floyd_warshall(self.cycle)
assert_equal(dist[0][3],3)
assert_equal(path[0][3],2)
assert_equal(dist[0][4],3)
XG3=nx.Graph()
XG3.add_weighted_edges_from([ [0,1,2],[1,2,12],[2,3,1],
[3,4,5],[4,5,1],[5,0,10] ])
dist, path = nx.floyd_warshall(XG3)
assert_equal(dist[0][3],15)
assert_equal(path[0][3],2)
XG4=nx.Graph()
XG4.add_weighted_edges_from([ [0,1,2],[1,2,2],[2,3,1],
[3,4,1],[4,5,1],[5,6,1],
[6,7,1],[7,0,1] ])
dist, path = nx.floyd_warshall(XG4)
assert_equal(dist[0][2],4)
assert_equal(path[0][2],1)
def process(filename):
edges, vertexesNumber, edgesNumber = read(filename)
G = nx.DiGraph()
G.add_nodes_from(xrange(1, vertexesNumber + 1))
G.add_weighted_edges_from(edges)
print "Graph %s formed" % filename
if nx.negative_edge_cycle(G):
print "Graph %s has negative cycle" % filename
return
print "Begin FW for %s" % filename
lengths = nx.floyd_warshall(G)
shortestPathLengths = map(dict.values, lengths.values())
shortestPathLength = min(min(raw) for raw in shortestPathLengths)
print "Shortest path for %s: %d" % (filename, shortestPathLength)
def test_floyd_warshall_predecessor_and_distance(self):
XG=nx.DiGraph()
XG.add_weighted_edges_from([('s','u',10) ,('s','x',5) ,
('u','v',1) ,('u','x',2) ,
('v','y',1) ,('x','u',3) ,
('x','v',5) ,('x','y',2) ,
('y','s',7) ,('y','v',6)])
path, dist =nx.floyd_warshall_predecessor_and_distance(XG)
assert_equal(dist['s']['v'],9)
assert_equal(path['s']['v'],'u')
assert_equal(dist,
{'y': {'y': 0, 'x': 12, 's': 7, 'u': 15, 'v': 6},
'x': {'y': 2, 'x': 0, 's': 9, 'u': 3, 'v': 4},
's': {'y': 7, 'x': 5, 's': 0, 'u': 8, 'v': 9},
'u': {'y': 2, 'x': 2, 's': 9, 'u': 0, 'v': 1},
'v': {'y': 1, 'x': 13, 's': 8, 'u': 16, 'v': 0}})
GG=XG.to_undirected()
# make sure we get lower weight
# to_undirected might choose either edge with weight 2 or weight 3
GG['u']['x']['weight']=2
path, dist = nx.floyd_warshall_predecessor_and_distance(GG)
assert_equal(dist['s']['v'],8)
# skip this test, could be alternate path s-u-v
# assert_equal(path['s']['v'],'y')
G=nx.DiGraph() # no weights
G.add_edges_from([('s','u'), ('s','x'),
('u','v'), ('u','x'),
('v','y'), ('x','u'),
('x','v'), ('x','y'),
('y','s'), ('y','v')])
path, dist = nx.floyd_warshall_predecessor_and_distance(G)
assert_equal(dist['s']['v'],2)
# skip this test, could be alternate path s-u-v
# assert_equal(path['s']['v'],'x')
# alternate interface
dist = nx.floyd_warshall(G)
assert_equal(dist['s']['v'],2)
def test_floyd_warshall_predecessor_and_distance(self):
XG=nx.DiGraph()
XG.add_weighted_edges_from([('s','u',10) ,('s','x',5) ,
('u','v',1) ,('u','x',2) ,
('v','y',1) ,('x','u',3) ,
('x','v',5) ,('x','y',2) ,
('y','s',7) ,('y','v',6)])
path, dist =nx.floyd_warshall_predecessor_and_distance(XG)
assert_equal(dist['s']['v'],9)
assert_equal(path['s']['v'],'u')
assert_equal(dist,
{'y': {'y': 0, 'x': 12, 's': 7, 'u': 15, 'v': 6},
'x': {'y': 2, 'x': 0, 's': 9, 'u': 3, 'v': 4},
's': {'y': 7, 'x': 5, 's': 0, 'u': 8, 'v': 9},
'u': {'y': 2, 'x': 2, 's': 9, 'u': 0, 'v': 1},
'v': {'y': 1, 'x': 13, 's': 8, 'u': 16, 'v': 0}})
GG=XG.to_undirected()
path, dist = nx.floyd_warshall_predecessor_and_distance(GG)
assert_equal(dist['s']['v'],8)
assert_equal(path['s']['v'],'y')
G=nx.DiGraph() # no weights
G.add_edges_from([('s','u'), ('s','x'),
('u','v'), ('u','x'),
('v','y'), ('x','u'),
('x','v'), ('x','y'),
('y','s'), ('y','v')])
path, dist = nx.floyd_warshall_predecessor_and_distance(G)
assert_equal(dist['s']['v'],2)
assert_equal(path['s']['v'],'x')
# alternate interface
dist = nx.floyd_warshall(G)
assert_equal(dist['s']['v'],2)
e = [(0, 1, 4), (2, 5, 4), (0, 7, 8), (3, 5, 14), (1, 2, 8), (3, 4, 9), (1, 7, 11), (4, 5, 10), (2, 8, 2),
(5, 6, 2), (2, 3, 7), (6, 8, 6), (6, 7, 1), (7, 8, 7), (9, 0, 6), (10, 3, 1), (10, 4, 1), (11, 12, 1),
(12, 13, 1), (11, 13, 1), (11, 3, 20), (13, 3, 20)]
#e = [(1, 2, 1), (2, 3, 1), (4, 2, 1), (4, 5, 1)]
G.add_weighted_edges_from(e)
pos = nx.spring_layout(G)
#############################################################################
#############################################################################
#############################################################################
density_q = G.degree(weight='weight') # Density function with respect to the node.
D = nx.floyd_warshall(G, 'weight') # Dictionary of shortest paths for each node.
n_k = 3 # Number of voroni nodes
#K = random.sample(G.nodes(), n_k)
K = [0, 8, 10, 12]
K = deque(K)
cont = 0
while cont < 10:
print "K vector: ", K
vor.parallel_dijkstra(G, K, 1)
vor_seg = groups(nx.get_node_attributes(G,'V'))
# if x == s1[y][0]:
# temp.append(s1[y][:])
# k=k+1
# print x
k,faltu = x.split()
data[k]=sd[k]
#if count == 50:
# break
fname = 'newcatalans.json'
f = open(fname, 'w')
data = json.dumps(data, indent=4)
f.write(data)
f.close()
h=open("newcatalans.json", 'r')
jd=json.loads(h.read())
G = nx.Graph(jd)
length = nx.floyd_warshall(G, weight='weight')
# print length
bname = 'fw_on_catalans.json'
b = open(bname, 'w')
data = json.dumps(length, indent=4)
b.write(data)
b.close()
def shortest_path_weight(G,v1,v2):
return nx.floyd_warshall(G)[0][v1][v2]
NOC.add_edges_from([(1,3),(3,1)],cost_per_bit=0.02,latency=0.01)
w=[[1,10,10,10],[10,10,10,10],[1,10,10,10],[10,10,10,10],[10,10,10,10]]
#w=[[1,10,10,10],[10,1,10,10],[1,10,10,10],[10,10,1,10],[10,10,10,1]]
N=5
M=4
###########################################################################
f=open('results.txt','w')
results={}
cnt=0
threshold=60
better_solns=0
total=24576
best_cost=threshold
E_c=nx.floyd_warshall(NOC,'cost_per_bit')
L_c=nx.floyd_warshall(NOC,'latency')
sorted_nodes=nx.topological_sort(TG)
def modify_time(node):
global t,Z,L_c,TG,h
Q= queue.Queue()
Q.put(node)
while not Q.empty():
i=Q.get()
for j in TG.successors(i):
m=Z[i].index(1)
n=Z[j].index(1)
t[j]=max(t[j],t[i]+h[i]+TG.edge[i][j]['volume']*L_c[m][n])
Q.put(j)
def main(path_nodes, path_edges, gid_nodes, gid_edges, weight_edges):
# ----------------------------------------------------------
# NetworkX
# ----------------------------------------------------------
# Import des données SHP à grapher:
G = nx.Graph(name="Floyd_Warshall_script", date=str(datetime.datetime.now()))
E = nx.read_shp(str(path_edges))
N = nx.read_shp(str(path_nodes))
G.add_nodes_from(N.nodes(data=True))
G.add_edges_from(E.edges(data=True))
# Changement de leur nom (pour l'instant, chaque valeur a le nom de ses coordonnées géographiques, c'est nul):
# ----------------------------------------------------------
# D'abord pour les edges:
x = 0
dict_edges = {}
total_edges = G.number_of_edges()
print("Processing Edges")
while x < total_edges:
try: # En raison de la structure possible des fichiers, on place un try qui propose [1] ou [2], histoire de parer à toute éventualité.
dict_edges[G.edges(data=True)[x][0]] = G.edges(data=True)[x][2][str(gid_edges)]
x = x + 1
except:
dict_edges[G.edges(data=True)[x][0]] = G.edges(data=True)[x][1][str(gid_edges)]
x = x + 1
# Maintenant pour les nodes:
x = 0
dict_nodes = {}
count_nodes = {}
total_nodes = G.number_of_nodes()
print("Processing Nodes")
while x < total_nodes:
try: # En raison de la structure possible des fichiers, on place un try qui propose [1] ou [2], histoire de parer à toute éventualité.
dict_nodes[G.nodes(data=True)[x][0]] = G.nodes(data=True)[x][1][str(gid_nodes)]
count_nodes[x] = G.nodes(data=True)[x][1][str(gid_nodes)]
x = x + 1
except:
dict_nodes[G.nodes(data=True)[x][0]] = G.nodes(data=True)[x][2][str(gid_nodes)]
count_nodes[x] = G.nodes(data=True)[x][1][str(gid_nodes)]
x = x + 1
# On renomme les nodes/edges par leur id/gid originels:
G = nx.relabel_nodes(G, dict_nodes)
print("Processing Graph")
# G=nx.relabel_edges(G,dict_edges) # Il semblerait que cette fonction n'existe pas... A rajouter manuellement, cela ne doit pas être bien dur.
# ----------------------------------------------------------
# On lance maintenant le calcul d'itinéraire pour l'ensemble des paires de noeuds du réseau:
starting_point = datetime.datetime.now()
results = nx.floyd_warshall(G, weight=str(weight_edges))
print(starting_point)
print(datetime.datetime.now())
print("Il aura fallu: " + str(datetime.datetime.now() - starting_point) + " pour effectuer le calcul")
text_file = open("Shitty_output.txt", "w")
text_file.write(str(results))
text_file.close()
open(
"Output.txt", "w"
).close() # On efface Output.txt avant de lancer des opérations "append" dessus, histoire d'eviter d'avoir un mélange de résultats de plusieurs fichiers.
with open("Output.txt", "a") as text_file:
gid = 0
i = 0
text_file.writelines("gid" + ";" + "Origin" + ";" + "Destination" + ";" + "FloydWarshall_Cost" + "\n")
while i < total_nodes:
origins = results[str(count_nodes[i])]
i1 = 0
for origin in origins:
while i1 < total_nodes:
gid = gid + 1
destinations = origins[str(count_nodes[i1])]
text_file.writelines(
str(gid)
+ ";"
+ str(count_nodes[i] + ";" + str(count_nodes[i1]) + ";" + str(destinations))
+ "\n"
)
i1 = i1 + 1
i = i + 1
text_file.close()
print(
'Un fichier .TXT nommé "Output" a maintenant du apparaitre dans le dossier depuis lequel nous avons chargé le shapefile'
)
#Calculate Betweenness Centrality bcdict = nx.betweenness_centrality(G, normalized=False, weighted_edges=True) for el1,el2 in bcdict.iteritems(): print "NODE: ",el1, "\t" + "BC",el2 print "\n" #Calculate NC ncdict = bcdict.copy() for el1 in ncdict.keys(): ncdict[el1]=ncdict[el1]+(len(ncdict)-1) print "NODE: ",el1, "\t" + "NC",ncdict[el1] print "\n" #Calculate F.W. fwdict = nx.floyd_warshall(G,huge=99) #print "FW",fwdict #create and init a vector with my pl to other nodes mypl = bcdict.copy() for i in mypl.iterkeys(): mypl[i]=9999 fcdict = bcdict.copy() for i in fcdict.iterkeys(): fcdict[i]=0 # Average path length that entering node would have by selecting the node #node, even considering the already selected nodes pldict = bcdict.copy() for i in pldict.iterkeys():
def bm_networkx(self): nx.floyd_warshall(self.nx_ER_G)
