def augmentNodes(g):
r1 = nx.eigenvector_centrality_numpy(g)
r2 = nx.degree_centrality(g) # DP MY
r3 = nx.betweenness_centrality(g)
r5 = nx.load_centrality(g,weight='weight') # DY, WY-writename # Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001).
r6 = nx.pagerank(g, alpha=0.85, personalization=None, max_iter=100, tol=1e-08, nstart=None, weight='weight')
if nx.is_directed(g) == True:
r8 = nx.in_degree_centrality(g)
r9 = nx.out_degree_centrality(g)
# r10 = nx.hits(g, max_iter=100, tol=1e-08, nstart=None)
else:
r4 = nx.communicability_centrality(g)
r7 = nx.clustering(g, weight='weight')
for x in g.nodes():
g.node[x]['eigenvector_centrality_numpy'] = r1[x]
g.node[x]['degree_centrality'] = r2[x]
g.node[x]['betweenness_centrality'] = r3[x]
g.node[x]['load_centrality'] = r5[x]
g.node[x]['pagerank'] = r6[x]
if nx.is_directed(g) == True:
g.node[x]['in_degree_centrality'] = r8[x]
g.node[x]['out_degree_centrality'] = r9[x]
# g.node[x]['hits'] = r10[x]
else:
g.node[x]['communicability_centrality'] = r4[x]
g.node[x]['clustering'] = r7[x]
return g
def _create_flow_graph(G, H, infcapFlows):
"""Creates the flow graph on G corresponding to the auxiliary
digraph H and infinite capacity edges flows infcapFlows.
"""
if nx.is_directed(G):
flowGraph = nx.DiGraph(G)
else:
flowGraph = nx.Graph(G)
for (u, v) in flowGraph.edges():
if H.has_edge(u, v):
try:
flowGraph[u][v]['flow'] = abs(G[u][v]['capacity']
- H[u][v]['capacity'])
except KeyError: # (u, v) has infinite capacity
try:
flowGraph[u][v]['flow'] = H[v][u]['capacity']
except KeyError:
# Infinite capacity digon in the original graph.
if nx.is_directed(G):
flowGraph[u][v]['flow'] = max(infcapFlows[(u, v)]
- infcapFlows[(v, u)], 0)
else:
flowGraph[u][v]['flow'] = abs(infcapFlows[(u, v)]
- infcapFlows[(v, u)])
else:
flowGraph[u][v]['flow'] = G[u][v]['capacity']
return flowGraph
def calculate_network_measures(net, analyser):
deg=nx.degree_centrality(net)
clust=[]
if(net.is_multigraph()):
net = analyser.flatGraph(net)
if(nx.is_directed(net)):
tmp_net=net.to_undirected()
clust=nx.clustering(tmp_net)
else:
clust=nx.clustering(net)
if(nx.is_directed(net)):
tmp_net=net.to_undirected()
paths=nx.shortest_path(tmp_net, source=None, target=None, weight=None)
else:
paths=nx.shortest_path(net, source=None, target=None, weight=None)
lengths = [map(lambda a: len(a[1]), x[1].items()[1:]) for x in paths.items()]
all_lengths=[]
for a in lengths:
all_lengths.extend(a)
max_value=max(all_lengths)
#all_lengths = [x / float(max_value) for x in all_lengths]
return deg.values(),clust.values(),all_lengths
def _create_auxiliary_digraph(G):
"""Initialize an auxiliary digraph and dict of infinite capacity
edges for a given graph G.
Ignore edges with capacity <= 0.
"""
auxiliary = nx.DiGraph()
infcapFlows = {}
if nx.is_directed(G):
for edge in G.edges(data = True):
if edge[2].has_key('capacity'):
if edge[2]['capacity'] > 0:
auxiliary.add_edge(*edge)
else:
auxiliary.add_edge(*edge)
infcapFlows[(edge[0], edge[1])] = 0
else:
for edge in G.edges(data = True):
if edge[2].has_key('capacity'):
if edge[2]['capacity'] > 0:
auxiliary.add_edge(*edge)
auxiliary.add_edge(edge[1], edge[0], edge[2])
else:
auxiliary.add_edge(*edge)
auxiliary.add_edge(edge[1], edge[0], edge[2])
infcapFlows[(edge[0], edge[1])] = 0
infcapFlows[(edge[1], edge[0])] = 0
return auxiliary, infcapFlows
def _create_flow_dict(G, H, infcapFlows, capacity="capacity"):
"""Creates the flow dict of dicts on G corresponding to the
auxiliary digraph H and infinite capacity edges flows infcapFlows.
"""
flowDict = {}
for u in G.nodes_iter():
if not u in flowDict:
flowDict[u] = {}
for v in G.neighbors(u):
if H.has_edge(u, v):
try:
flowDict[u][v] = abs(G[u][v][capacity] - H[u][v][capacity])
except KeyError: # (u, v) has infinite capacity
try:
flowDict[u][v] = H[v][u][capacity]
except KeyError:
try: # Infinite capacity digon in the original graph.
if nx.is_directed(G):
flowDict[u][v] = max(infcapFlows[(u, v)] - infcapFlows[(v, u)], 0)
else:
flowDict[u][v] = abs(infcapFlows[(u, v)] - infcapFlows[(v, u)])
except KeyError: # Zero flow
flowDict[u][v] = 0
else:
flowDict[u][v] = G[u][v][capacity]
return flowDict
def attack_based_max_closeness(G):
""" Recalcuat closeness attack
"""
n = G.number_of_nodes()
tot_ND = [0] * (n+1)
tot_T = [0] * (n+1)
ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
tot_ND[0] = ND
tot_T[0] = 0
# remember when all the closeness have been zero for all nodes
for i in range(1, n+1):
all_closeness = nx.closeness_centrality(G)
# get node with max betweenness
node = max(all_closeness, key=all_closeness.get)
# remove all the edges adjacent to node
if not nx.is_directed(G): # undirected graph
for key in G[node].keys():
G.remove_edge(node, key)
else: # directed graph
for x in [v for u, v in G.out_edges_iter(node)]:
G.remove_edge(node, x)
for x in [u for u, v in G.in_edges_iter(node)]:
G.remove_edge(x, node)
# calculate driver node number ND
ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
tot_ND[i] = ND
tot_T[i] = i
return (tot_ND, tot_T, Max_Betweenness_Zero_T)
def random_rewiring(network):
"""
Rewires a pair of edges such that the degree sequence is preserved.
Arguments:
network => The input network.
Returns:
A network with one pair of edges randomly rewired.
"""
# Don't terminate until the rewiring is performed.
while True:
# Store the number of edges in the network to avoid repeated computation.
network_edges = nx.edges(network)
# If there isn't at least 1 edge, break out and return.
if len(network_edges) == 0:
break
# Randomly selected a link from the network.
link1 = (source1, target1) = random.choice(network_edges)
# Find all the edges that share no nodes with link1.
disjoint_links = [link for link in network_edges if not any(node in link for node in link1)]
# If there are no disjoint links, it would be impossible to randomize the network while
# still preserving the degree sequence, so break out and return.
if len(disjoint_links) == 0:
break
# Randomly selected a DIFFERENT link from the network (no sharing of nodes allowed).
link2 = (source2, target2) = random.choice(disjoint_links)
# If the graph is directed, there is only one option.
# If the graph is undirected, there are two options, each with a 50-50 chance.
if not nx.is_directed(network) and random.random() < 0.5:
# Rewire links A-B and C-D to A-C and B-D.
new_link1 = (source1, source2)
new_link2 = (target1, target2)
else:
# Rewire links A-B and C-D to A-D and C-B.
new_link1 = (source1, target2)
new_link2 = (source2, target1)
# If the new links aren't in the network already, replace the old links with the new links.
if not network.has_edge(*new_link1) and not network.has_edge(*new_link2):
# Remove the old links.
network.remove_edges_from([link1, link2])
# Add the new links.
network.add_edges_from([new_link1, new_link2])
# Returned the slightly altered new network.
return network
def estimate_joint_dist(graph, nsteps):
assert(not nx.is_directed(graph))
assert('labeled' in graph.graph and graph.graph['labeled'])
n = nsteps #total num seen
n_iod = {} #total seen with indeg i, outdeg o, deg d
# random initial node; don't include in estimator
node = random.choice(graph.nodes())
# rw
for i in xrange(nsteps):
node = random.choice(list(nx.all_neighbors(graph, node)))
iod_tuple = (graph.node[node]['in-degree'],
graph.node[node]['out-degree'],
graph.node[node]['degree'])
n_iod[iod_tuple] = n_iod.get(iod_tuple,0) + 1
# degree distribution parameters
max_indeg = max([graph.node[k]['in-degree'] for k in graph.node.keys()])
max_outdeg = max([graph.node[k]['out-degree'] for k in graph.node.keys()])
deg_par = np.zeros((max_indeg + 1, max_outdeg + 1))
for (indeg, outdeg, deg) in n_iod.keys():
val = n_iod[(indeg, outdeg, deg)]
deg_par[indeg, outdeg] += float(val) / float(n * deg)
#deg_par[indeg, outdeg] += float(val) / float(deg)
# normalize
deg_par /= deg_par.sum()
np.savetxt("deg_par.csv", deg_par, delimiter=",")
return deg_par
def prepare_visjs_data(g):
nodes = []
for node in g.nodes_iter():
new = {'id': str(node),
'label': str(g.node[node]['label']) if 'label' in g.node[node] else str(node),
'shape': 'box'
}
nodes.append(new)
edges = []
for fromnode, tonode, etype in g.edges_iter(keys=True):
if 'label' in g[fromnode][tonode][etype]:
label = str(g[fromnode][tonode][etype]['label'])
elif 'weight' in g[fromnode][tonode][etype]:
label = str(g[fromnode][tonode][etype]['weight'])
else:
#label = str(etype)
label = ''
new = {'from': str(fromnode),
'to': str(tonode),
'label': label,
'color': {'color': 'black', 'highlight': 'blue', 'hover': 'blue'},
}
if nx.is_directed(g):
new['arrows'] = 'to'
edges.append(new)
return {'nodes': nodes,
'edges': edges}
def DFS(G, s):
cor = {}
pred = {}
d = {}
f = {}
tempo = 0
for v in G.nodes():
cor[v] = "branco" # cores possíveis: branco cinza e preto
pred[v] = None
for v in G.nodes():
if cor[v] == "branco":
tempo = visit(G, v, cor, pred, d, f, tempo)
H = nx.create_empty_copy(G)
for v1, v2, data in G.edges(data=True):
if (pred[v2] is v1) or (pred[v1] is v2 and not nx.is_directed(H)):
H.add_edge(v1, v2, data)
H.node[v1]["begin_time"] = d[v1]
H.node[v2]["begin_time"] = d[v2]
H.node[v1]["finish_time"] = f[v1]
H.node[v2]["finish_time"] = f[v2]
return H
def Prim(G = nx.Graph(), R = None):
# Q é a lista de vértices que não estão na árvore
Q = {}
# pred armazenará o predecessor de cada vértice
pred = {}
# Inicializamos Q com todos os vértices com valor infinito, pois neste
# ponto ainda não há ligação entre nenhum vértice. Igualmente, nenhum
# vértice tem predecessor, portanto utilizamos o valor 'null'.
for v,data in G.nodes(data=True):
Q[v] = n.inf
pred[v] = 'null'
# Caso não haja pesos definidos para os vértices, atribuímos o valor 1.0.
# Esta é uma abordagem alternativa à que usamos em Kruskal, de utilizar uma
# variável para verificar se estamos levando em conta o peso ou não.
for e,x in G.edges():
if ('weight' not in G[e][x]):
G[e][x]['weight'] = 1.0
# Inicializamos a raiz da árvore com valor 0, e criamos uma árvore chamada
# MST apenas com os vértices de G.
Q[R] = 0.0
MST = nx.create_empty_copy(G)
while Q:
# u := índice do menor elemento de Q
# pois queremos o vértice de menor peso
u = min(Q,key=Q.get)
# removemos de Q, pois ele será adicionado na árvore
del Q[u]
# guardamos os pesos mínimos de cada vizinho de u em Q, se forem
# menores do que os já armazenados
for vizinho in G[u]:
if vizinho in Q:
if G[u][vizinho]['weight'] < Q[vizinho]:
pred[vizinho] = u
Q[vizinho] = G[u][vizinho]['weight']
# Se existirem predecessores para u, então adicionaremos as arestas
# conectando o vértice u a seus predecessores
if pred[u] is not 'null':
for v1,v2,data in G.edges(data=True):
# para preservar os dados da aresta, foi necessário esse loop
# que verifica todas as arestas do grafo e procura a aresta
# (pred(u),u), porém, como um grafo não direcionado da
# biblioteca não duplica a existência de suas arestas no
# conjunto de arestas, isto é, se tem (u,v) não tem (v,u), há a
# necessidade de verificar, no caso de grafos não direcionados,
# se há a existência da aresta (u,pred(u)) ao invés de
# (pred(u),u)
if ( v1 is pred[u] and v2 is u ):
MST.add_edge(pred[u],u,data)
elif ( ( v1 is u and v2 is pred[u] ) and
( not nx.is_directed(G) ) ):
MST.add_edge(pred[u],u,data)
return MST
def _create_auxiliary_digraph(G, capacity="capacity"):
"""Initialize an auxiliary digraph and dict of infinite capacity
edges for a given nxgraph G.
Ignore edges with capacity <= 0.
"""
auxiliary = nx.DiGraph()
auxiliary.add_nodes_from(G)
inf_capacity_flows = {}
if nx.is_directed(G):
for edge in G.edges(data=True):
if capacity in edge[2]:
if edge[2][capacity] > 0:
auxiliary.add_edge(*edge)
else:
auxiliary.add_edge(*edge)
inf_capacity_flows[(edge[0], edge[1])] = 0
else:
for edge in G.edges(data=True):
if capacity in edge[2]:
if edge[2][capacity] > 0:
auxiliary.add_edge(*edge)
auxiliary.add_edge(edge[1], edge[0], edge[2])
else:
auxiliary.add_edge(*edge)
auxiliary.add_edge(edge[1], edge[0], edge[2])
inf_capacity_flows[(edge[0], edge[1])] = 0
inf_capacity_flows[(edge[1], edge[0])] = 0
return auxiliary, inf_capacity_flows
def output_graph_sgf(G):
print("# Simple Graph Format")
print("# name:", G.name)
if nx.is_directed(G):
d = "d"
else:
d = "u"
print(d, G.number_of_nodes(), G.number_of_edges())
cnt = 0
for node in G.nodes_iter(data=True):
node_id = node[0]
if node_id != cnt:
raise ("non-consecutive node exception")
# if 'weight' in node[1]:
cnt += 1
# print(G.out_edges([node[0]]))
print(node_id, end="|")
edges = []
# edges = [str(edge[1]) for edge in nx.edges_iter(G, [node[0]])]
for edge in G.edges_iter([node[0]], data="weight"):
# print('edge', edge)
src = edge[0]
dst = edge[1]
weight = edge[2]
if src != node_id:
raise ("invalid link")
if weight != None:
edges.append(str(dst) + ":" + str(weight))
else:
edges.append(str(dst))
print(",".join(edges))
if cnt != G.number_of_nodes():
raise ("non-consecutive node exception")
def scaling_mincostflow(G, s, t, capacity='capacity', weight='weight',
demand='demand', refine_scaling_constant=2):
"""Find a minimum cost flow solution using the push-relabel
algorithm/successive approximation algorithm
"""
if G.is_multigraph():
raise nx.NetworkXError(
'MultiGraph and MultiDiGraph not supported (yet).')
if not nx.is_directed(G):
raise nx.NetworkXError(
'Undirected graphs are not supported (yet).')
getcontext().prec = 28
G_copy = nx.DiGraph(G)
max_cost = max([G_copy[u][v][weight] for u,v in G_copy.edges_iter()])
#initialization
price='price'
for v in G_copy:
G_copy.node[v][price] = 0
epsilon = Decimal(max_cost)
_get_maxflow(G_copy, s, t, capacity)
len_G = len(G_copy)
tol = Decimal(1/Decimal(len_G))
while epsilon >= tol:
epsilon = _refine(epsilon, G_copy, capacity, weight, refine_scaling_constant, s, t)
return _create_flow_dict(G, G_copy, t)
def __init__(
self,
graph,
weight='weight',
cap='capacity',
):
"""
Constructor
"""
self.wt = weight
self.cap = cap
self.g = graph
self.pathHeap = [] # Use the heapq module functions heappush(pathHeap, item) and heappop(pathHeap, item)
self.pathList = [] # Contains WeightedPath objects
self.deletedEdges = set()
self.deletedNodes = set()
self.kPath = None
# Make a copy of the graph tempG that we can manipulate
if isinstance(graph, nx.Graph):
# self.tempG = graph.copy()
if nx.is_directed(graph):
self.tempG = nx.DiGraph(graph)
else:
self.tempG = nx.Graph(graph)
else:
self.tempG = None
def WC_model(G, a): # a: the set of initial active nodes
# each edge from node u to v is assigned probability 1/in-degree(v) of activating v
A = set(a) # A: the set of active nodes, initially a
B = set(a) # B: the set of nodes activated in the last completed iteration
converged = False
if nx.is_directed(G):
my_degree_function = G.in_degree
else:
my_degree_function = G.degree
while not converged:
nextB = set()
for n in B:
for m in set(G.neighbors(n)) - A:
prob = random.random() # in the range [0.0, 1.0)
p = 1.0/my_degree_function(m)
if prob <= p:
nextB.add(m)
B = set(nextB)
if not B:
converged = True
A |= B
return len(A)
def attack_based_max_eigenvector(G):
""" Recalculate eigenvector centrality attack
"""
n = G.number_of_nodes()
tot_ND = [0] * (n+1)
tot_T = [0] * (n+1)
ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
tot_ND[0] = ND
tot_T[0] = 0
for i in range(1, n+1):
# calculate all nodes' eigenvector centrality
allEigenvectorCentrality = nx.eigenvector_centrality(G, max_iter=1000, weight=None)
# get node with max eigenvector centrality
node = max(allEigenvectorCentrality, key=allEigenvectorCentrality.get)
# remove all the edges adjacent to node
if not nx.is_directed(G): # undirected graph
for key in G[node].keys():
G.remove_edge(node, key)
else: # directed graph
for x in [v for u, v in G.out_edges_iter(node)]:
G.remove_edge(node, x)
for x in [u for u, v in G.in_edges_iter(node)]:
G.remove_edge(x, node)
ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
tot_ND[i] = ND
tot_T[i] = i
return (tot_ND, tot_T)
def single_discount_high_degree_nodes_gen(k, G):
if nx.is_directed(G):
my_degree_function = G.out_degree
else:
my_degree_function = G.degree
D = []
for i in range(k):
# find the node of max out_degree, discounting any out-edge
# to a node already in D
maxoutdeg_i = -1
v_i = -1
for v in list(set(G.nodes()) - set(D)):
outdeg = my_degree_function(v)
for u in D:
if G.has_edge(v, u):
outdeg -= 1
if outdeg > maxoutdeg_i:
maxoutdeg_i = outdeg
v_i = v
D.append(v_i)
yield D
def add_graph(canvas: CanvasSelection,
graph,
weight: Union[str, None] = 'weight') -> CanvasSelection:
"""
Adds all nodes and edges from a NetworkX graph to the given canvas.
Edges will automatically set the :meth:`~graphics.EdgeSelection.directed`
attribute and/or add a weight :meth:`~graphics.EdgeSelection.label`
depending on the provided graph.
:param canvas: The CanvasSelection onto which the graph should be added.
:type canvas: :class:`~graphics.CanvasSelection`
:param graph: The NetworkX graph
:type graph: Any type of NetworkX graph
:param weight: The name of the attribute which describes edge weight in the the
NetworkX graph. Edges without the attribute will not display a weight,
and a value of ``None`` will prevent any weight from being displayed.
Defaults to "weight".
:type weight: Union[str, None]
:return: The provided CanvasSelection with animations disabled, allowing
initial attributes to be configured.
:rtype: :class:`~graphics.CanvasSelection`
"""
weighted_edges = []
unweighted_edges = []
for e in graph.edges:
if weight in graph.edges[e]:
weighted_edges.append(e)
else:
unweighted_edges.append(e)
canvas.nodes(graph.nodes).add()
if len(unweighted_edges) > 0:
init_edges = canvas.edges(unweighted_edges).add()
if is_directed(graph):
init_edges.directed(True)
if len(weighted_edges) > 0:
init_edges = canvas.edges(weighted_edges).add()
if is_directed(graph):
init_edges.directed(True)
init_edges.label().add().text(lambda e: graph.edges[e][weight])
return canvas.duration(0)
def matchingVertices(self, graph, trie_node, nodes_used, states):
candidates = []
if not trie_node.areConditionsRespectedWeak(nodes_used):
return candidates
min_value = trie_node.getMinLabelForCurrentPos(nodes_used)
if nodes_used == []:
candidates = [x for x in graph.nodes() if x >= min_value]
else:
cand_graph = graph.to_undirected() if networkx.is_directed(graph) else graph
connections = [set(cand_graph.neighbors(x)) for x in nodes_used]
if trie_node.getGraph().degree(trie_node.getGraph().nodes()[len(nodes_used)]) == 0:
connections.append(set([x for x, y in graph.degree_iter() if y == 0]))
connections = list(set.union(*connections))
connections = [x for x in connections if x >= min_value]
candidates = [x for x in connections if x not in nodes_used]
#Testing the space reduction
#candidates.sort(key=lambda x: len(graph.neighbors(x)))
#candidates = [x for x in candidates if len(graph.neighbors(x)) == len(graph.neighbors(candidates[0]))]
#candidates = [x for x in candidates if x not in nodes_used]
#candidates = []
#if len(connections) > 0:
#candidates = [x for x in graph.neighbors(connections[0]) if x not in nodes_used]
vertices = []
for node in candidates:
cand_test = []
test_nodes = copy.deepcopy(nodes_used)
test_nodes.append(node)
if states:
if graph.node[node] == trie_node.getNodeStates()[len(nodes_used)]:
for i in range(0, len(trie_node.getInLinks())):
if ((trie_node.getInLinks()[i] == 1 and node in graph.edge[test_nodes[i]] and
trie_node.getInLinkStates()[i] == graph.edge[test_nodes[i]][node]) or
(trie_node.getInLinks()[i] == 0 and node not in graph.edge[test_nodes[i]])) and \
((trie_node.getOutLinks()[i] == 1 and test_nodes[i] in graph.edge[node] and
trie_node.getOutLinkStates()[i] == graph.edge[node][test_nodes[i]]) or
(trie_node.getOutLinks()[i] == 0 and test_nodes[i] not in graph.edge[node])):
cand_test.append(True)
else:
cand_test.append(False)
if False not in cand_test:
vertices.append(node)
else:
for i in range(0, len(trie_node.getInLinks())):
if ((trie_node.getInLinks()[i] == 1 and node in graph.edge[test_nodes[i]]) or
(trie_node.getInLinks()[i] == 0 and node not in graph.edge[test_nodes[i]])) and \
((trie_node.getOutLinks()[i] == 1 and test_nodes[i] in graph.edge[node]) or
(trie_node.getOutLinks()[i] == 0 and test_nodes[i] not in graph.edge[node])):
cand_test.append(True)
else:
cand_test.append(False)
if False not in cand_test:
vertices.append(node)
return vertices
def evaluate(input_graph,
lst,
teleportation_vector,
r,
alpha=0.85,
element='edge',
max_iter=100,
tol=1e-3):
"""
evaluation
:param input_graph: a networkx graph
:param lst: list of selected edges/nodes, or the list of nodes in induced-subgraph
:param teleportation_vector: teleportation vector
:param r: ranking vector before elements removal
:param alpha: damping factor
:param element: edge, node, or subgraph
:param max_iter: maximum number of iterations
:param tol: tolerance
:return: value for evaluation metric
"""
graph = deepcopy(input_graph)
directed = nx.is_directed(graph)
r_change = list()
if element == 'edge':
graph.remove_edges_from(lst)
r_change = power_method_left(graph,
teleportation_vector,
alpha=alpha,
max_iter=max_iter,
tol=tol)
if element == 'node':
if directed:
edge_vertices = list(graph.out_edges(
lst, data='weight', default=1)) + list(
graph.in_edges(lst, data='weight', default=1))
else:
edge_vertices = list(graph.edges(lst, data='weight', default=1))
graph.remove_edges_from(edge_vertices)
r_change = power_method_left(graph,
teleportation_vector,
alpha=alpha,
max_iter=max_iter,
tol=tol)
if element == 'subgraph':
subgraph = nx.subgraph(graph, lst)
if directed:
edge_subgraph = list(subgraph.out_edges(
data='weight', default=1)) + list(
subgraph.in_edges(data='weight', default=1))
else:
edge_subgraph = list(subgraph.edges(data='weight', default=1))
graph.remove_edges_from(edge_subgraph)
r_change = power_method_left(graph,
teleportation_vector,
alpha=alpha,
max_iter=max_iter,
tol=tol)
change = abs(norm(r) - norm(r_change))
return change
def Prim(G=nx.Graph(), R=None):
# Q é a lista de vértices que não estão na árvore
Q = {}
# pred armazenará o predecessor de cada vértice
pred = {}
# Inicializamos Q com todos os vértices com valor infinito, pois neste
# ponto ainda não há ligação entre nenhum vértice. Igualmente, nenhum
# vértice tem predecessor, portanto utilizamos o valor 'null'.
for v, data in G.nodes(data=True):
Q[v] = n.inf
pred[v] = 'null'
# Caso não haja pesos definidos para os vértices, atribuímos o valor 1.0.
# Esta é uma abordagem alternativa à que usamos em Kruskal, de utilizar uma
# variável para verificar se estamos levando em conta o peso ou não.
for e, x in G.edges():
if ('weight' not in G[e][x]):
G[e][x]['weight'] = 1.0
# Inicializamos a raiz da árvore com valor 0, e criamos uma árvore chamada
# MST apenas com os vértices de G.
Q[R] = 0.0
MST = nx.create_empty_copy(G)
while Q:
# u := índice do menor elemento de Q
# pois queremos o vértice de menor peso
u = min(Q, key=Q.get)
# removemos de Q, pois ele será adicionado na árvore
del Q[u]
# guardamos os pesos mínimos de cada vizinho de u em Q, se forem
# menores do que os já armazenados
for vizinho in G[u]:
if vizinho in Q:
if G[u][vizinho]['weight'] < Q[vizinho]:
pred[vizinho] = u
Q[vizinho] = G[u][vizinho]['weight']
# Se existirem predecessores para u, então adicionaremos as arestas
# conectando o vértice u a seus predecessores
if pred[u] is not 'null':
for v1, v2, data in G.edges(data=True):
# para preservar os dados da aresta, foi necessário esse loop
# que verifica todas as arestas do grafo e procura a aresta
# (pred(u),u), porém, como um grafo não direcionado da
# biblioteca não duplica a existência de suas arestas no
# conjunto de arestas, isto é, se tem (u,v) não tem (v,u), há a
# necessidade de verificar, no caso de grafos não direcionados,
# se há a existência da aresta (u,pred(u)) ao invés de
# (pred(u),u)
if (v1 is pred[u] and v2 is u):
MST.add_edge(pred[u], u, data)
elif ((v1 is u and v2 is pred[u]) and (not nx.is_directed(G))):
MST.add_edge(pred[u], u, data)
return MST
def adjacency_embedding(G, max_dim=2, elb=1, get_lcc=True, weightcol='weight', svd_seed=None):
"""
Inputs
G - A networkx graph
Outputs
eig_vectors - The scaled (or unscaled) eigenvectors
"""
# if get_lcc==True:
# #print("extracting largest_connected_component")
# G_lcc = lcc_BNU.extract_lcc(G)
# else:
# G_lcc = G.copy()
# weightcolumn = weightcol
# print("pass_to_ranks")
# G_ptr = ptr.pass_to_ranks(G_lcc, weightcol=weightcolumn)
# print ("diagonoal augmentation")
# G_aug_ptr= cvec.diag_aug(G_ptr, weightcol=weightcolumn)
sorted_vertex = sorted(G.nodes())
A = nx.to_scipy_sparse_matrix(G, nodelist=sorted_vertex)
row, col = A.shape
n = min(row, col)
#print ("spectral embedding into %d dimensions" %max_dim)
U, Sigma, VT = randomized_svd(A,
n_components=min(max_dim, n - 1),
n_iter=50,
random_state=svd_seed)
#print ("dimension reduction (elbow selection)")
rank_graph = getElbows_BNU.getElbows(Sigma, n_elbows=elb)
reduced_dim = rank_graph[(elb-1)]
#print ("elbow is %d" %reduced_dim)
s_sqrt = np.sqrt(Sigma) #[np.newaxis] Zeinab commented this out
s_sqrt_dim_reduced = s_sqrt[:reduced_dim]
U_dim_reduced = U[:, :reduced_dim ]
VT_dim_reduced =VT[:reduced_dim, :]
Xhat1 = np.multiply( s_sqrt_dim_reduced, U_dim_reduced)
if nx.is_directed(G) == False:
Xhat2 = np.array([]).reshape(Xhat1.shape[0],0)
else:
Xhat2 = np.multiply( np.transpose(VT_dim_reduced), s_sqrt_dim_reduced)
Xhat = np.concatenate((Xhat1, Xhat2), axis=1)
embedded = collections.namedtuple('embedded', 'X vertex_labels')
result = embedded(X = Xhat, vertex_labels = sorted_vertex)
return result
def train(self, G):
self.G = G
node2id = dict([(node, vid) for vid, node in enumerate(G.nodes())])
self.is_directed = nx.is_directed(self.G)
self.num_node = self.G.number_of_nodes()
self.num_edge = G.number_of_edges()
self.edges = [[node2id[e[0]], node2id[e[1]]] for e in self.G.edges()]
id2node = dict(zip(node2id.values(), node2id.keys()))
self.num_neigh = np.asarray([len(list(self.G.neighbors(id2node[i]))) for i in range(self.num_node)])
self.neighbors = [[node2id[v] for v in self.G.neighbors(id2node[i])]
for i in range(self.num_node)]
s = time.time()
self.alias_nodes = {}
self.node_weight = {}
for i in range(self.num_node):
unnormalized_probs = [G[id2node[i]][nbr].get("weight", 1.0) for nbr in G.neighbors(id2node[i])]
norm_const = sum(unnormalized_probs)
normalized_probs = [float(u_prob)/norm_const for u_prob in unnormalized_probs]
self.alias_nodes[i] = alias_setup(normalized_probs)
self.node_weight[i] = dict(zip([node2id[nbr] for nbr in G.neighbors(id2node[i])],unnormalized_probs))
t = time.time()
print('alias_nodes', t-s)
# run netsmf algorithm with multiprocessing and apply randomized svd
print("number of sample edges ", self.num_round * self.num_edge * self.window_size)
print("random walk start...")
t0 = time.time()
results = []
pool = Pool(processes=self.worker)
for i in range(self.worker):
results.append(pool.apply_async(func=self._random_walk_matrix, args=(i,)))
pool.close()
pool.join()
print('random walk time', time.time() - t0)
matrix = sp.lil_matrix((self.num_node, self.num_node))
A = sp.csr_matrix(nx.adjacency_matrix(self.G))
degree = sp.diags(np.array(A.sum(axis=0))[0], format="csr")
degree_inv = degree.power(-1)
t1 = time.time()
for res in results:
matrix += res.get()
print('number of nzz', matrix.nnz)
t2 = time.time()
print('construct random walk matrix time', time.time() - t1)
L = sp.csgraph.laplacian(matrix, normed=False, return_diag=False)
M = degree_inv.dot(degree - L).dot(degree_inv)
M = M * A.sum() / self.negative
M.data[M.data <= 1] = 1
M.data = np.log(M.data)
print('construct matrix sparsifier time', time.time() - t2)
embedding = self._get_embedding_rand(M)
return embedding
def test_graph_extract(self):
"""
Make sure that extract graph does not error
"""
G = self.reader.extract_graph()
self.assertEqual(nx.number_of_nodes(G), 7)
self.assertEqual(nx.number_of_edges(G), 6)
self.assertFalse(nx.is_directed(G))
def is_directed_graph(graph):
"""
Get whether the graph has directed edges.
:param graph: The graph.
:return: True if the graph has directed edges.
"""
return nx.is_directed(graph)
def extract_ipc(self, dependency_graph):
if nx.is_directed(dependency_graph):
self.log_handler.info("Extracting IPC...")
lng_path = nx.dag_longest_path(dependency_graph)
if self.log_output:
self.log_handler.info("Longest path:%s\n" % str(lng_path))
self.longest_path = str(lng_path)
self.IPC = float(dependency_graph.order()) / (len(lng_path))
def jaccard_coefficient(graph, author_osn_id, labeled_author_osn_id):
if not nx.is_directed(graph):
pair = [(author_osn_id, labeled_author_osn_id)]
jaccard_coefficient_iterator = nx.jaccard_coefficient(graph, pair)
jaccard_coefficient_score = LinkPredictionStaticFunctions.get_score_from_iterator(
jaccard_coefficient_iterator)
return jaccard_coefficient_score
return 0
def __init__(self, p, q, num_runs, g=nx.gnm_random_graph(10000, 30000)):
if not nx.is_directed(g):
self.g = g.to_directed()
else:
self.g = g
self.p = p
self.q = q
self.num_runs = num_runs
def adamic_adar_index(graph, author_osn_id, labeled_author_osn_id):
if not nx.is_directed(graph):
pair = [(author_osn_id, labeled_author_osn_id)]
adamic_adar_iterator = nx.adamic_adar_index(graph, pair)
adamic_adar_score = LinkPredictionStaticFunctions.get_score_from_iterator(
adamic_adar_iterator)
return adamic_adar_score
return 0
def dist(self, G1, G2):
"""A scalable approach to network similarity.
A network similarity measure based on node signature distrubtions.
Params
------
G1, G2 (nx.Graph): two undirected networkx graphs to be compared.
Returns
-------
dist (float): the distance between G1 and G2.
"""
# NOTE: the measure only works for undirected
# graphs. For now we will silently convert a
# directed graph to be undirected.
directed_flag = False
if nx.is_directed(G1):
G1 = nx.to_undirected(G1)
directed_flag = True
if nx.is_directed(G2):
G2 = nx.to_undirected(G2)
directed_flag = True
if directed_flag:
warnings.warn("Coercing directed graph to undirected.", RuntimeWarning)
# find the graph node feature matrices
G1_node_features = feature_extraction(G1)
G2_node_features = feature_extraction(G2)
# get the graph signature vectors
G1_signature = graph_signature(G1_node_features)
G2_signature = graph_signature(G2_node_features)
# the final distance is the absolute canberra distance
dist = abs(canberra(G1_signature, G2_signature))
self.results['dist'] = dist
return dist
def _check_directedness(self, graph):
"""Checking the undirected nature of a single graph."""
try:
directed = nx.is_directed(graph)
if directed:
raise ValueError("Graph is directed. Please see requirements.")
except:
exit("Graph is directed. Please see requirements.")
def disparity_filter(G, weight='weight'):
from scipy import integrate
'''
Compute significance scores (alpha) for weighted edges in G as defined in Serrano et al. 2009
Args
G: Weighted NetworkX graph
Returns
Weighted graph with a significance score (alpha) assigned to each edge
References
M. A. Serrano et al. (2009) Extracting the Multiscale backbone of complex weighted networks. PNAS, 106:16,
pp. 6483-6488.
'''
if nx.is_directed(G): # directed case
N = nx.DiGraph()
for u in G:
k_out = G.out_degree(u)
k_in = G.in_degree(u)
if k_out > 1:
sum_w_out = sum(np.absolute(G[u][v][weight]) for v in G.successors(u))
for v in G.successors(u):
w = G[u][v][weight]
p_ij_out = float(np.absolute(w)) / sum_w_out
alpha_ij_out = 1 - (k_out - 1) * integrate.quad(lambda x: (1 - x) ** (k_out - 2), 0, p_ij_out)[0]
N.add_edge(u, v, weight=w, alpha_out=float('%.4f' % alpha_ij_out))
elif k_out == 1 and G.in_degree(G.successors(u)[0]) == 1:
# we need to keep the connection as it is the only way to maintain the connectivity of the network
v = G.successors(u)[0]
w = G[u][v][weight]
N.add_edge(u, v, weight=w, alpha_out=0., alpha_in=0.)
# there is no need to do the same for the k_in, since the link is built already from the tail
if k_in > 1:
sum_w_in = sum(np.absolute(G[v][u][weight]) for v in G.predecessors(u))
for v in G.predecessors(u):
w = G[v][u][weight]
p_ij_in = float(np.absolute(w)) / sum_w_in
alpha_ij_in = 1 - (k_in - 1) * integrate.quad(lambda x: (1 - x) ** (k_in - 2), 0, p_ij_in)[0]
N.add_edge(v, u, weight=w, alpha_in=float('%.4f' % alpha_ij_in))
return N
else: # undirected case
B = nx.Graph()
for u in G:
k = len(G[u])
if k > 1:
sum_w = sum(np.absolute(G[u][v][weight]) for v in G[u])
for v in G[u]:
w = G[u][v][weight]
p_ij = float(np.absolute(w)) / sum_w
alpha_ij = 1 - (k - 1) * integrate.quad(lambda x: (1 - x) ** (k - 2), 0, p_ij)[0]
B.add_edge(u, v, weight=w, alpha=float('%.4f' % alpha_ij))
else:
B.add_node(u)
return B
def main():
args = parse_args()
args.directed = True
seed = args.seed
training_edgelist_dir = os.path.join(args.output,
"seed={:03d}".format(seed),
"training_edges")
removed_edges_dir = os.path.join(args.output, "seed={:03d}".format(seed),
"removed_edges")
if not os.path.exists(training_edgelist_dir):
os.makedirs(training_edgelist_dir, exist_ok=True)
if not os.path.exists(removed_edges_dir):
os.makedirs(removed_edges_dir, exist_ok=True)
training_edgelist_fn = os.path.join(training_edgelist_dir, "edgelist.tsv")
val_edgelist_fn = os.path.join(removed_edges_dir, "val_edges.tsv")
val_non_edgelist_fn = os.path.join(removed_edges_dir, "val_non_edges.tsv")
test_edgelist_fn = os.path.join(removed_edges_dir, "test_edges.tsv")
test_non_edgelist_fn = os.path.join(removed_edges_dir,
"test_non_edges.tsv")
graph, _ = load_data(args)
print("loaded dataset")
assert nx.is_directed(graph)
edges = list(graph.edges())
print("enumerated edges")
(training_edges, (val_edges, val_non_edges),
(test_edges, test_non_edges)) = split_edges(graph,
edges,
seed,
val_split=0)
print("number of val edges", len(val_edges), "number of val non edges",
len(val_edges))
print("number of test edges", len(test_edges), "number of test non edges",
len(test_edges))
N = len(graph)
graph.remove_edges_from(val_edges +
test_edges) # remove val and test edges
assert len(nx.DiGraph(training_edges)) == N
print("removed edges")
nx.write_edgelist(graph,
training_edgelist_fn,
delimiter="\t",
data=["weight"])
write_edgelist_to_file(val_edges, val_edgelist_fn)
write_edgelist_to_file(val_non_edges, val_non_edgelist_fn)
write_edgelist_to_file(test_edges, test_edgelist_fn)
write_edgelist_to_file(test_non_edges, test_non_edgelist_fn)
print("done")
def from_nx(graph, any_hashable=True):
"""Create a graph from a NetworkX graph.
:param graph: a graph
:type graph: nx graph
:param any_hashable: if true the returned graph uses the same objects as the nx graph,
otherwise integers are used. In the later case a renumbering is performed independently from
any possible ordering in the original graph.
:type any_hashable: boolean
:returns: a new graph
:type: jgrapht graph
"""
try:
import networkx as nx
except ImportError:
raise ImportError("NetworkX required")
is_directed = nx.is_directed(graph)
is_weighted = any("weight" in data for u, v, data in graph.edges(data=True))
allowing_multiple_edges = isinstance(graph, (nx.MultiGraph, nx.MultiDiGraph))
result = _create_graph(
directed=is_directed,
weighted=is_weighted,
allowing_self_loops=True,
allowing_multiple_edges=allowing_multiple_edges,
any_hashable=any_hashable,
)
if any_hashable:
# copy graph topology and attributes
result.graph_attrs.update(**graph.graph)
for v in graph.nodes:
result.add_vertex(vertex=v)
result.vertex_attrs[v].update(**graph.nodes[v])
try:
for u, v, k in graph.edges(keys=True):
e = result.add_edge(u, v)
result.edge_attrs[e].update(**graph.edges[u,v,k])
except TypeError:
for u, v in graph.edges():
e = result.add_edge(u, v)
result.edge_attrs[e].update(**graph.edges[u,v])
else:
# copy graph topology only
vmap = {}
for v in graph.nodes:
vmap[v] = result.add_vertex()
for u, v, d in graph.edges(data=True):
if 'weight' in d:
result.add_edge(vmap[u], vmap[v], weight=d['weight'])
else:
result.add_edge(vmap[u], vmap[v])
return result
def print_node_edge_data(DG):
print '#Source----Destination---weight#'
if(nx.is_directed(DG)):
for node in DG.nodes_iter():
for item in DG.adjacency_iter():
if item[1].has_key(node):
print str(item[0])+'--->'+str(node)+' : '+str(item[1][node])
else:
print 'Not a Directed Graph'
def preferential_attachment(graph, author_osn_id, labeled_author_osn_id):
if not nx.is_directed(graph):
pair = [(author_osn_id, labeled_author_osn_id)]
preferential_attachment_iterator = nx.preferential_attachment(
graph, pair)
preferential_attachment_score = LinkPredictionStaticFunctions.get_score_from_iterator(
preferential_attachment_iterator)
return preferential_attachment_score
return 0
def common_neighbors(graph, author_osn_id, labeled_author_osn_id):
if not nx.is_directed(graph):
pair = [(author_osn_id, labeled_author_osn_id)]
common_neighbors_iterator = nx.nx.cn_soundarajan_hopcroft(
graph, pair)
common_neighbors_score = LinkPredictionStaticFunctions.get_score_from_iterator(
common_neighbors_iterator)
return common_neighbors_score
return 0
def scIndex(g, alpha=-1./2., _isWeightedCalc=True):
res=0.
#res=np.zeros(4);
weights=nx.get_edge_attributes(g,'weight')
for pair in weights.keys():
if _isWeightedCalc:
if nx.is_directed(g):
res+= (weights[pair])*np.power( ( g.out_degree(pair[0])+g.in_degree(pair[1]) ) ,alpha)
else:
res+= (weights[pair])*np.power( ( g.degree(pair[0])+g.degree(pair[1]) ) ,alpha)
else:
if nx.is_directed(g):
res+= (1)*np.power( ( g.out_degree(pair[0])+g.in_degree(pair[1]) ) ,alpha)
else:
res+= (1)*np.power( ( g.degree(pair[0])+g.degree(pair[1]) ) ,alpha)
return res
def display_node_attributes(node):
"""Accepts a node, calculates various attributes, and formats it into a string"""
text = G[node]["name"] if hasattr(G[node], "name") else "Node: " + str(node)
if nx.is_directed(G):
text += ", In Degree: " + str(G.in_degree[node])
text += ", Out Degree: " + str(G.out_degree[node])
else:
text += "Degree: " + str(G.degree[node])
eccentricity = max(nx.single_source_shortest_path_length(G, node))
text += ", Ecentricity: " + str(eccentricity)
if nx.is_directed(G):
text += ", Reciprocity: {:.2f}".format(reciprocities[node])
return text
def makeAllDirected( *graphs ):
"""If any one of the input graphs is directed, make directed versions of all
of the inputs and return them. Otherwise, return the input unchanged."""
someDirected = reduce( lambda x, y: x or y, map( nx.is_directed, graphs ) )
if someDirected:
return [ ( g.to_directed() if (not nx.is_directed( g )) else g )
for g in graphs ]
else:
return graphs
def draw_top_size_cliques(graph, top=10, layout="spring"):
if nx.is_directed(graph):
print("Err, only graph undirected")
return
print("Showing the top " + str(top) + " for size")
top_n_size_cliques = []
all_cliques = list(nx.algorithms.clique.enumerate_all_cliques(graph))
cliques = []
for i in range(len(all_cliques)):
k = sorted(all_cliques[i], key=lambda j: j)
if k not in cliques:
cliques.append(k)
s = []
for i in cliques:
s.append((i, len(i)))
s = sorted(s, key=lambda i: i[1])
s.reverse()
max_size = int(s[0][1])
print("Max Size: ", str(max_size))
clique_for_size = dict()
for i in range(1, max_size + 1):
clique_for_size[i] = []
for i in s:
clique_for_size[i[1]] += i[0]
if top > max_size:
top = max_size
a = []
for i in range(max_size, max_size - top, -1):
a += clique_for_size[i]
for n in graph:
if n in a and n not in top_n_size_cliques:
top_n_size_cliques.append(n)
graph = graph.subgraph(top_n_size_cliques)
coords = layout_dealer(graph, layout)
cliques = [
clique for clique in nx.find_cliques(graph)
if len(clique) >= max_size - top
]
print("Number of Cliques: " + str(len(cliques)))
for clique in cliques:
if len(clique) > max_size - top:
plt.figure()
nx.draw(graph, pos=coords, with_labels=graph.nodes().values())
print("Clique to appear: ", clique, " length: ", str(len(clique)))
nx.draw_networkx_nodes(graph,
pos=coords,
nodelist=clique,
node_color=next(colors))
plt.show()
def __check_type(self):
if isinstance(self.graph, nx.Graph):
self.directed = nx.is_directed(self.graph)
self.tp = 0
elif ig is not None and isinstance(self.graph, ig.Graph):
self.directed = self.graph.is_directed()
self.tp = 1
else:
raise ValueError("Graph model not supported")
def independent_numbers(G, nodes=None, seed=None):
if not G:
raise Exception("You must provice path graph value")
if nx.is_directed(G):
C = G.to_undirected()
else:
C = G
return nx.maximal_independent_set(C, nodes=None, seed=None)
def check_graph(G, **kwargs):
out = True
if 'node_number' in kwargs:
if len(G) is not kwargs['node_number']:
out = False
if 'directed' in kwargs:
if nx.is_directed(G) is not kwargs['directed']:
out = False
return out
def calculate_shortest_paths_lengths(graph: Union[nx.Graph, nx.DiGraph],
shortest_paths_path: Union[str, Path]):
if nx.is_directed(graph):
graph = nx.DiGraph(graph)
else:
graph = nx.Graph(graph)
serializer.save(dict(nx_sp.shortest_path_length(graph)),
shortest_paths_path)
def signed_degrees(G, n):
in_pos, in_neg = signed_in_degrees(G, n)
pos = in_pos
neg = in_neg
if nx.is_directed(G):
out_pos, out_neg = signed_out_degrees(G, n)
pos += out_pos
neg += out_neg
return pos, neg
def deg_of_net(G):
print 'Is the karate club network graph directed ? : ', nx.is_directed(G)
all_degrees = [] # List containing degree of each individual nodes
for i in nx.degree(G):
all_degrees.append(i[1])
sum_degrees = 0 # Sum of degree of all nodes
for i in all_degrees:
sum_degrees = sum_degrees + i
print 'Degree of the network is : ', sum_degrees / nx.number_of_nodes(G)
def Dijkstra(G, s):
Lambda = {} # valores de "peso" para cada vértice
pred = {} # predecessores
Q = G.nodes() # vértices que ainda não estão na árvore de
# caminhos mínimos
# inicializamos todos os lambdas com infinito
for v in G.nodes():
Lambda[v] = n.inf
# Caso não haja pesos definidos para os vértices, atribuímos o valor 1
for v1,v2 in G.edges():
if ('weight' not in G[v1][v2]):
G[v1][v2]['weight'] = 1
Lambda[s] = 0
pred[s] = None
while Q:
# encontramos o menor valor de Lambda pertencente a Q
menor = n.inf
u = Q[0]
if sys.version_info[0] < 3:
for k,v in Lambda.iteritems():
if (v < menor) and (k in Q):
menor = v
u = k
else:
for k,v in Lambda.items():
if (v < menor) and (k in Q):
menor = v
u = k
# removemos o item de Q, já que está sendo inserido na árvore
u_index = Q.index(u)
del Q[u_index]
# percorremos a vizinhança de u procurando pesos menores
for v in G[u]:
if (v in Q) and (Lambda[v] > Lambda[u] + G[u][v]['weight']):
Lambda[v] = Lambda[u] + G[u][v]['weight']
pred[v] = u
# Criamos um novo grafo vazio do mesmo tipo de G
H = nx.create_empty_copy(G)
# Adicionamos os vértices de acordo com os dados de G
for v1,v2,data in G.edges(data=True):
if (pred[v2] is v1) or (pred[v1] is v2 and not nx.is_directed(H)):
H.add_edge( v1, v2, data )
H.node[v1]['lambda'] = Lambda[v1]
H.node[v2]['lambda'] = Lambda[v2]
# Retornamos a árvore de predecessores com a informação de Lambda[v]
return H
def iteration(self, node_status=True):
"""
Execute a single model iteration
:return: Iteration_id, Incremental node status (dictionary node->status)
"""
self.clean_initial_status(self.available_statuses.values())
actual_status = {node: nstatus for node, nstatus in future.utils.iteritems(self.status)}
if self.actual_iteration == 0:
self.actual_iteration += 1
delta, node_count, status_delta = self.status_delta(actual_status)
if node_status:
return {"iteration": 0, "status": actual_status.copy(),
"node_count": node_count.copy(), "status_delta": status_delta.copy()}
else:
return {"iteration": 0, "status": {},
"node_count": node_count.copy(), "status_delta": status_delta.copy()}
for u in self.graph.nodes():
if self.status[u] != 1:
continue
neighbors = list(self.graph.neighbors(u)) # neighbors and successors (in DiGraph) produce the same result
# Standard threshold
if len(neighbors) > 0:
threshold = 1.0/len(neighbors)
for v in neighbors:
if actual_status[v] == 0:
key = (u, v)
# Individual specified thresholds
if 'threshold' in self.params['edges']:
if key in self.params['edges']['threshold']:
threshold = self.params['edges']['threshold'][key]
elif (v, u) in self.params['edges']['threshold'] and not nx.is_directed(self.graph):
threshold = self.params['edges']['threshold'][(v, u)]
flip = np.random.random_sample()
if flip <= threshold:
actual_status[v] = 1
actual_status[u] = 2
delta, node_count, status_delta = self.status_delta(actual_status)
self.status = actual_status
self.actual_iteration += 1
if node_status:
return {"iteration": self.actual_iteration - 1, "status": delta.copy(),
"node_count": node_count.copy(), "status_delta": status_delta.copy()}
else:
return {"iteration": self.actual_iteration - 1, "status": {},
"node_count": node_count.copy(), "status_delta": status_delta.copy()}
def _decompress(self, focus_frame, change_frame):
""" Decompression function that takes the compressed graph: changeFrame, and "unpacks" it
into the focusFrame.
"""
# Loop over the nodes in the compressed frame
for nodes in change_frame.nodes_iter():
change = change_frame.node[nodes].pop(compressState.tag)
# If the change state is 'Added', add node
if change == compressState.added:
add_node = nodes
if nodes in focus_frame.nodes_iter():
add_node = max(focus_frame.nodes())+1
while add_node in change_frame.node:
add_node += 1
update_map = {nodes: add_node}
focus_frame.add_node(add_node, change_frame.node[nodes])
change_frame = nx.relabel_nodes(change_frame, update_map)
else:
focus_frame.add_node(add_node, change_frame.node[nodes])
# If the change state is 'Deleted', delete node
elif change == compressState.deleted:
focus_frame.remove_node(nodes)
# If the change state is 'StateChanged', update with changed state
elif change == compressState.stateChange:
state_name = change_frame.node[nodes][compressState.stateChangedName]
assert (focus_frame.node[nodes][state_name] == change_frame.node[nodes][compressState.stateChangedFrom])
focus_frame.node[nodes][state_name] = change_frame.node[nodes][compressState.stateChangedTo]
processed = []
# Loop over the edges in the compressed frame
for edges in change_frame.edges_iter():
# Extract start and end nodes for the edge
start = edges[0]
end = edges[1]
change = change_frame.edge[start][end].pop(compressState.tag)
#skip undirected edges that have already been changed
if not nx.is_directed(focus_frame) and (end, start) in processed:
continue
# Was this edge added
if change == compressState.added:
focus_frame.add_edge(start, end, change_frame.edge[start][end])
# Or was it deleted
elif change == compressState.deleted:
# If it was deleted check to make sure the deletion of the nodes didn't already
# clean the edges
if start in focus_frame.edge and end in focus_frame.edge[start]:
focus_frame.remove_edge(start, end)
# If the change state is 'StateChanged', update with changed state
elif change == compressState.stateChange:
state_name = change_frame.edge[start][end][compressState.stateChangedName]
assert (focus_frame.edge[start][end][state_name] == change_frame.edge[start][end][compressState.stateChangedFrom])
focus_frame.edge[start][end][state_name] = change_frame.edge[start][end][compressState.stateChangedTo]
processed.append((start, end))
def disparity_filter(G, weight='weight'):
''' Compute significance scores (alpha) for weighted edges in G as defined in Serrano et al. 2009
Args
G: Weighted NetworkX graph
Returns
Weighted graph with a significance score (alpha) assigned to each edge
References
M. A. Serrano et al. (2009) Extracting the Multiscale backbone of complex weighted networks. PNAS, 106:16, pp. 6483-6488.
'''
if nx.is_directed(G): #directed case
N = nx.DiGraph()
for u in G:
k_out = G.out_degree(u)
k_in = G.in_degree(u)
if k_out > 1:
sum_w_out = sum(np.absolute(G[u][v][weight]) for v in G.successors(u))
for v in G.successors(u):
w = G[u][v][weight]
p_ij_out = float(np.absolute(w))/sum_w_out
alpha_ij_out = 1 - (k_out-1) * integrate.quad(lambda x: (1-x)**(k_out-2), 0, p_ij_out)[0]
N.add_edge(u, v, weight = w, alpha_out=float('%.4f' % alpha_ij_out))
elif k_out == 1 and G.in_degree(G.successors(u)[0]) == 1:
#we need to keep the connection as it is the only way to maintain the connectivity of the network
v = G.successors(u)[0]
w = G[u][v][weight]
N.add_edge(u, v, weight = w, alpha_out=0., alpha_in=0.)
#there is no need to do the same for the k_in, since the link is built already from the tail
if k_in > 1:
sum_w_in = sum(np.absolute(G[v][u][weight]) for v in G.predecessors(u))
for v in G.predecessors(u):
w = G[v][u][weight]
p_ij_in = float(np.absolute(w))/sum_w_in
alpha_ij_in = 1 - (k_in-1) * integrate.quad(lambda x: (1-x)**(k_in-2), 0, p_ij_in)[0]
N.add_edge(v, u, weight = w, alpha_in=float('%.4f' % alpha_ij_in))
return N
else: #undirected case
B = nx.Graph()
for u in G:
k = len(G[u])
if k > 1:
sum_w = sum(np.absolute(G[u][v][weight]) for v in G[u])
for v in G[u]:
w = G[u][v][weight]
p_ij = float(np.absolute(w))/sum_w
alpha_ij = 1 - (k-1) * integrate.quad(lambda x: (1-x)**(k-2), 0, p_ij)[0]
B.add_edge(u, v, weight = w, alpha=float('%.4f' % alpha_ij))
return B
def high_degree_nodes_gen(k, G):
if nx.is_directed(G):
my_degree_function = G.out_degree
else:
my_degree_function = G.degree
V = [(my_degree_function(i), i) for i in G.nodes()]
V.sort(reverse=True)
N = [t[1] for t in V]
for i in range(1, min(k, len(N)) + 1):
yield N[:i]
def choose_most_inter_used_nodes(G, I, node_cnt, role, secondary_sort, seed=None):
# select nodes with the specified role from graph G and create a list of tuples with their in-degree in graph I
rank_node_pairs = list()
for node in G.nodes():
node_role = G.node[node]['role']
if node_role == role:
if nx.is_directed(I):
rank = I.in_degree(node)
else:
rank = I.degree(node)
rank_node_pairs.append((rank, node))
return choose_nodes_by_rank(rank_node_pairs, node_cnt, secondary_sort, seed)
def _create_auxiliary_anti_parallel_digraph(G, capacity, preflow='preflow'):
"""
Converts the input graph to an anti parallel digraph which is
amenable to simple implementations of the push-relabel
algorithm variants.
"""
if not nx.is_directed(G):
G_copy = nx.DiGraph()
#Transform graph to anti-parallel digraph
for u, v in G.edges_iter():
auxiliary_node = str(u)+'-'+str(v)
if capacity in G.get_edge_data(u,v):
edge_cap = G[u][v][capacity]
G_copy.add_edge(u,v)
G_copy.add_edge(v,auxiliary_node)
G_copy.add_edge(auxiliary_node,u)
G_copy[u][v][capacity] = edge_cap
G_copy[v][auxiliary_node][capacity] = edge_cap
G_copy[auxiliary_node][u][capacity] = edge_cap
else:
G_copy.add_edge(u,v)
G_copy.add_edge(v,auxiliary_node)
G_copy.add_edge(auxiliary_node,u)
G_copy[u][v][preflow] = 0
G_copy[v][auxiliary_node][preflow] = 0
G_copy[auxiliary_node][u][preflow] = 0
else:
G_copy = nx.DiGraph()
for u, v in G.edges_iter():
if G_copy.has_edge(v,u):
auxiliary_node = str(u)+'-'+str(v)
if capacity in G.get_edge_data(u,v):
edge_cap = G[u][v][capacity]
G_copy.add_edge(u,auxiliary_node)
G_copy.add_edge(auxiliary_node,v)
G_copy[u][auxiliary_node][capacity] = edge_cap
G_copy[auxiliary_node][v][capacity] = edge_cap
else:
G_copy.add_edge(u,auxiliary_node)
G_copy.add_edge(auxiliary_node,v)
G_copy[u][auxiliary_node][preflow] = 0
G_copy[auxiliary_node][v][preflow] = 0
else:
if capacity in G.get_edge_data(u,v):
G_copy.add_edge(u, v)
edge_cap = G[u][v][capacity]
G_copy[u][v][capacity] = G[u][v][capacity]
else:
G_copy.add_edge(u, v)
G_copy[u][v][preflow] = 0
return G_copy
def compute_normalized_triad_motif_z_scores(network, num_rand_instances=10, num_rewirings=None):
"""
Computes the normalized triad motif z-score for each connected non-isomorphic triadic subgraph
in the input network.
Arguments:
network => The input network (can be directed or undirected).
num_rand_instances => The number of randomly-rewired network instances used when computing
z-score values.
num_rewirings => The number of edge rewirings performed when randomizing the network.
Returns:
A fixed-size numpy array where each index corresponds to a predefined unique triad motif
and where the value at each index represents the normalized z-score for the average
over- or underexpression of a triad motif in the network.
"""
# Determine if the network is directed or not (store to avoid recalculation).
directed = nx.is_directed(network)
# Count the number of occurences of each triad motif.
original_motif_counts = count_triad_motifs(network, directed=directed)
# Initialize an array for storing motif counts in randomized instances.
rand_motif_counts = []
# Iterate through random instances.
for _ in range(num_rand_instances):
# Randomize the network.
rand_network = randomize(network, num_rewirings=num_rewirings)
# Store the number of occurences of each motif in the randomized instance.
rand_motif_counts.append(count_triad_motifs(rand_network, directed=directed))
# Stack the counts as an array.
rand_motif_counts = np.vstack(rand_motif_counts)
# Divide the random motif counts by the number of instances to make them into average counts.
avg_rand_motif_counts = np.mean(rand_motif_counts, axis=0)
# Compute the random motif standard deviation.
rand_motif_std_dev = np.std(rand_motif_counts, axis=0)
# Compute the z-scores (ignoring division by 0 warnings and place the resulting NaNs/infs with 0s).
with np.errstate(divide="ignore", invalid="ignore"):
motif_z_scores = (original_motif_counts - avg_rand_motif_counts) / rand_motif_std_dev
motif_z_scores[motif_z_scores == np.inf] = 0
motif_z_scores = np.nan_to_num(motif_z_scores)
return motif_z_scores
def attack_based_max_betweenness(G):
""" Recalculate betweenness attack
Basic Idea:
----------
Every time we remove the node with max betweeneness-centrality, then
recalcuate all nodes' betweenness NOTE that here remove a node only
remove all the edges adjacent to it.
Parameters:
----------
G: graph (directed or undirected)
Returns:
-------
tot_ND: the number of driver nodes after every node removed
tot_T: the number of removed nodes
Max_Betweenness_Zero_T: the number of removed nodes such that
all nodes' betweenness centrality have been zeros
"""
n = G.number_of_nodes()
tot_ND = [0] * (n+1)
tot_T = [0] * (n+1)
ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
tot_ND[0] = ND
tot_T[0] = 0
# remember when all the betweenness have been zero for all nodes
Max_Betweenness_Zero_T = -1
for i in range(1, n+1):
all_betweenness = nx.betweenness_centrality(G)
# get node with max betweenness
node = max(all_betweenness, key=all_betweenness.get)
if Max_Betweenness_Zero_T == -1 and abs(all_betweenness[node] - 0.0) < 1E-8:
Max_Betweenness_Zero_T = i
# remove all the edges adjacent to node
if not nx.is_directed(G): # undirected graph
for key in G[node].keys():
G.remove_edge(node, key)
else: # directed graph
for x in [v for u, v in G.out_edges_iter(node)]:
G.remove_edge(node, x)
for x in [u for u, v in G.in_edges_iter(node)]:
G.remove_edge(x, node)
# calculate driver node number ND
ND, ND_lambda = ECT.get_number_of_driver_nodes(G)
tot_ND[i] = ND
tot_T[i] = i
return (tot_ND, tot_T, Max_Betweenness_Zero_T)
def addNode_degree(G):
"""
Add strength, general and specific degree of nodes
:param G: directed or undirected Graph
:return: G
"""
# add strength degree
for n in G.nodes():
G.node[n]['N'] = G.degree(n, weight='weight')
G.node[n]['n'] = float(G.degree(n))
if G.node[n]['N']<=0.0:
raise TypeError('find isolated node, or negative weight:{}-{}'.format(n,G.node[n]['label']))
#--------------
if nx.is_directed(G):
G_nei_iter = PF.genChain(G.successors_iter, G.predecessors_iter)
else:
G_nei_iter = G.neighbors_iter
def getMaxMinStrength():
node = G.nodes_iter().next()
max_S = G.node[node]['N']
min_S = G.node[node]['N']
for n in G.nodes_iter():
s = G.node[n]['N']
if s > max_S:
max_S = s
if s < min_S:
min_S = s
return max_S,min_S
def getNeiStrength(x):
s=0
for n in G_nei_iter(x):
s = s + G.node[n]['N']
return s
maxS,minS = getMaxMinStrength()
arrayForpercentile = [ G.node[n]['N'] for n in G.nodes() ]+[maxS]
percdict = PF.listtopercentiles( arrayForpercentile )
# calculate general and specific degree
for n in G.nodes():
strength = G.node[n]['N']
#general degree
G.node[n]['G_r'] = strength / ( getNeiStrength(n) + 0.1 )
G.node[n]['G_n'] = PF.scaling( maxS + 0.1, minS - 0.1, strength)
G.node[n]['G_p'] = percdict[strength]
#specific degree
G.node[n]['SP_r'] = 1.0 - G.node[n]['G_r']
G.node[n]['SP_n'] = 1.0 - G.node[n]['G_n']
G.node[n]['SP_p'] = 1.0 - G.node[n]['G_p']
return G