def test_directed(self):
"""Tests that each pair of nodes in the directed graph is
counted once when computing the Wiener index.
"""
G = complete_graph(3)
H = DiGraph(G)
eq_(2 * wiener_index(G), wiener_index(H))
def test_directed(self):
"""Tests that each pair of nodes in the directed graph is
counted once when computing the Wiener index.
"""
G = complete_graph(3)
H = DiGraph(G)
eq_(2 * wiener_index(G), wiener_index(H))
def ustrezna_drevesa(sez):
#funkcija, ki iz seznama dreves pobere tista, ki se jim index spremeni za ena pri zamenjavi ene povezave pri listu
novi = []
for T in sez:
w = nx.wiener_index(T, weight=None)
for lis in listi(T):
for vozlisce in T:
G = T.copy()
G.remove_node(lis)
G.add_node(lis)
G.add_edge(lis, vozlisce)
v = nx.wiener_index(G, weight=None)
if abs(w - v) == 1:
novi.append(G)
return novi
def networkx_to_outp_format(graph, index, type):
return {
"index": index,
"graph_type": type,
"wiener_index": nx.wiener_index(graph, weight='weight'),
"edges": list(graph.edges())
}
def wiener_impact_e_removal(g: nx.Graph) -> List[float]:
"""
Calcula os impactos de Wiener para cada remoção de arestas possível em um grafo.
"""
M = g.number_of_edges()
return wiener_indices_e_removal(g) - nx.wiener_index(g) * np.ones(M)
def test_path_graph(self):
"""Tests that the Wiener index of the path graph is correctly
computed.
"""
# In P_n, there are n - 1 pairs of vertices at distance one, n -
# 2 pairs at distance two, n - 3 at distance three, ..., 1 at
# distance n - 1, so the Wiener index should be
#
# 1 * (n - 1) + 2 * (n - 2) + ... + (n - 2) * 2 + (n - 1) * 1
#
# For example, in P_5,
#
# 1 * 4 + 2 * 3 + 3 * 2 + 4 * 1 = 2 (1 * 4 + 2 * 3)
#
# and in P_6,
#
# 1 * 5 + 2 * 4 + 3 * 3 + 4 * 2 + 5 * 1 = 2 (1 * 5 + 2 * 4) + 3 * 3
#
# assuming n is *odd*, this gives the formula
#
# 2 \sum_{i = 1}^{(n - 1) / 2} [i * (n - i)]
#
# assuming n is *even*, this gives the formula
#
# 2 \sum_{i = 1}^{n / 2} [i * (n - i)] - (n / 2) ** 2
#
n = 9
G = path_graph(n)
expected = 2 * sum(i * (n - i) for i in range(1, (n // 2) + 1))
actual = wiener_index(G)
eq_(expected, actual)
def test_path_graph(self):
"""Tests that the Wiener index of the path graph is correctly
computed.
"""
# In P_n, there are n - 1 pairs of vertices at distance one, n -
# 2 pairs at distance two, n - 3 at distance three, ..., 1 at
# distance n - 1, so the Wiener index should be
#
# 1 * (n - 1) + 2 * (n - 2) + ... + (n - 2) * 2 + (n - 1) * 1
#
# For example, in P_5,
#
# 1 * 4 + 2 * 3 + 3 * 2 + 4 * 1 = 2 (1 * 4 + 2 * 3)
#
# and in P_6,
#
# 1 * 5 + 2 * 4 + 3 * 3 + 4 * 2 + 5 * 1 = 2 (1 * 5 + 2 * 4) + 3 * 3
#
# assuming n is *odd*, this gives the formula
#
# 2 \sum_{i = 1}^{(n - 1) / 2} [i * (n - i)]
#
# assuming n is *even*, this gives the formula
#
# 2 \sum_{i = 1}^{n / 2} [i * (n - i)] - (n / 2) ** 2
#
n = 9
G = path_graph(n)
expected = 2 * sum(i * (n - i) for i in range(1, (n // 2) + 1))
actual = wiener_index(G)
eq_(expected, actual)
def test_complete_graph(self):
"""TestData that the Wiener index of the complete graph is simply
the number of edges.
"""
n = 10
G = complete_graph(n)
assert wiener_index(G) == (n * (n - 1) / 2)
def wiener_indices_v_removal(g: nx.Graph) -> List[int]:
"""
Calcula os índices de Wiener para cada remoção de vértice possível em um grafo.
"""
deck = deck_of_graphs(g)
wieners = np.squeeze(np.asarray([nx.wiener_index(x) for x in deck]))
return wieners
def test_complete_graph(self):
"""Tests that the Wiener index of the complete graph is simply
the number of edges.
"""
n = 10
G = complete_graph(n)
eq_(wiener_index(G), n * (n - 1) / 2)
def test_complete_graph(self):
"""Tests that the Wiener index of the complete graph is simply
the number of edges.
"""
n = 10
G = complete_graph(n)
eq_(wiener_index(G), n * (n - 1) / 2)
def compute_wiener_index(G):
'''If graph is not connected returns -1'''
projected_graph = projected_graph.project_oxygen_role_based_graph(G)
try:
wiener = nx.wiener_index(projected_graph)
return wiener
except:
return -1
def wiener_impact_v_removal(g: nx.Graph) -> List[float]:
"""
Calcula os impactos de Wiener para cada remoção de vértices possível em um grafo.
"""
n = g.number_of_nodes()
transmissions = np.squeeze(
np.asarray(np.dot(distance_matrix([g]), np.ones(n))))
return wiener_indices_v_removal(
g) + transmissions - nx.wiener_index(g) * np.ones(n)
def projected_oxygen_graph_metrics(projected_graph):
communities = community.greedy_modularity_communities(projected_graph)
mod_score = modularity(projected_graph, communities) #not returned
try:
aspl = nx.average_shortest_path_length(projected_graph)
wiener = nx.wiener_index(projected_graph)
except:
aspl = -1
wiener = -1
return aspl, wiener, len(communities), communities, mod_score
def get_structural_virality(self):
"""
Returns a measure of structural virality.
Returns
--------
Structural virality: float
"""
import networkx as nx
from networkx.algorithms.wiener import wiener_index
n = self.diffusion_tree.number_of_nodes()
return nx.wiener_index(self.diffusion_tree) / (n * (n - 1))
def moc_mnozice_novih_indeksov(graf):
n = len(graf)
osnovni_index = nx.wiener_index(graf)
najkrajse_poti = nx.all_pairs_shortest_path(graf)
I = set()
for i in range(n):
vozlisce, slovar_poti = next(najkrajse_poti)
vsota_poti_iz_vozlisca = sum(
len(slovar_poti[kljuc]) for kljuc in slovar_poti) - n
nov_index = osnovni_index + vsota_poti_iz_vozlisca + n
I.add(int(nov_index))
return len(I)
def nodal_wiener_impact(self) -> Tuple[List[float], float]:
"""
Calcula o impacto nodal de Wiener para o grafo.
"""
impacts: List[float] = []
for i in range(self.graph.number_of_nodes()):
T_v = 0.0
graph_copy = deepcopy(self.graph)
for j in range(self.graph.number_of_nodes()):
T_v += self.distances[i][j]
graph_copy.remove_node(i)
W_v = nx.wiener_index(graph_copy)
I_v = W_v + T_v - self.wiener
impacts.append(I_v)
return (impacts, sum(impacts))
def _graph(self, graph):
"""Generate graph-based attributes."""
graph_attr = pd.DataFrame()
graph_attr['number_of_nodes'] = [nx.number_of_nodes(graph)]
graph_attr['number_of_edges'] = [nx.number_of_edges(graph)]
graph_attr['number_of_selfloops'] = [nx.number_of_selfloops(graph)]
graph_attr['graph_number_of_cliques'] = [
nx.graph_number_of_cliques(graph)
]
graph_attr['graph_clique_number'] = [nx.graph_clique_number(graph)]
graph_attr['density'] = [nx.density(graph)]
graph_attr['transitivity'] = [nx.transitivity(graph)]
graph_attr['average_clustering'] = [nx.average_clustering(graph)]
graph_attr['radius'] = [nx.radius(graph)]
graph_attr['is_tree'] = [1 if nx.is_tree(graph) else 0]
graph_attr['wiener_index'] = [nx.wiener_index(graph)]
return graph_attr
def compute_features(self):
wiener_index = lambda graph: nx.wiener_index(graph)
self.add_feature(
"wiener index",
wiener_index,
"The wiener index is defined as the sum of the lengths of the shortest paths between all pairs of vertices",
InterpretabilityScore(4),
)
estrada_index = lambda graph: nx.estrada_index(graph)
self.add_feature(
"estrada_index",
estrada_index,
"The Estrada Index is a topological index of protein folding or 3D compactness",
InterpretabilityScore(4),
)
def add_features(G):
L = nx.laplacian_matrix(G).todense()
eig = LA.eigvals(L)
avg_deg = 2 * (G.number_of_edges() / G.number_of_nodes())
lap_energy = sum([abs(i - avg_deg) for i in eig])
dist_matrix = np.array(
nx.floyd_warshall_numpy(G, nodelist=sorted(G.nodes())))
eccentricity = dist_matrix * (dist_matrix >= np.sort(
dist_matrix, axis=1)[:, [-1]]).astype(int)
e_vals = LA.eigvals(eccentricity)
largest_eig = np.real(max(e_vals))
energy = np.real(sum([abs(x) for x in e_vals]))
wiener_index = nx.wiener_index(G)
trace_DS = trace_deq_seq(G)
return {
'lap_energy': lap_energy,
'ecc_spectrum': largest_eig,
'ecc_energy': energy,
'wiener_index': wiener_index,
'trace_deg_seq': trace_DS
}
def get_subgraph_features(self, atoms_idx, name_space):
'''
:param atoms_idx: subgraph node indices
:param name_space: name space
:return: features dict
'''
res = {}
res[f'{name_space}#atoms_num'] = len(atoms_idx)
res[f'{name_space}#electronegativity_sum'] = np.sum(
self.electron[atoms_idx])
atoms_num_dict = {'C': 0, 'H': 0, 'O': 0, 'N': 0, 'F': 0}
for i in atoms_idx:
atoms_num_dict[self.atoms[i]] += 1
for atom_type, num in atoms_num_dict.items():
res[f'{name_space}#{atom_type}_num'] = num
s = np.linalg.eigvalsh(np.cov(self.coordinates[atoms_idx, :].T))[::-1]
eigen_ratio = np.cumsum(s) / np.sum(s)
res[f'{name_space}#eigen_ratio_1d'] = eigen_ratio[0]
res[f'{name_space}#eigen_ratio_2d'] = eigen_ratio[1]
sub_dist_matrix = self.dist_matrix[atoms_idx][:, atoms_idx]
res[f'{name_space}#bond_length_max'] = np.max(sub_dist_matrix)
subgraph = nx.Graph(self.graph_edges[atoms_idx][:, atoms_idx])
res[f'{name_space}#edges_num'] = len(subgraph.edges)
cycle_basis = nx.cycle_basis(subgraph)
res[f'{name_space}#cycle_basis_num'] = len(cycle_basis)
res[f'{name_space}#triangle_num'] = sum(
len(cycle) == 3 for cycle in cycle_basis)
res[f'{name_space}#wiener_index'] = nx.wiener_index(subgraph)
res[f'{name_space}#algebraic_connectivity'] = \
np.linalg.eigvalsh(nx.laplacian_matrix(subgraph).toarray())[1]
res[f'{name_space}#algebraic_connectivity_normalized'] = \
np.linalg.eigvalsh(nx.normalized_laplacian_matrix(subgraph).toarray())[1]
bond_length = [sub_dist_matrix[i1, i2] for i1, i2 in subgraph.edges]
res[f'{name_space}#bond_length_mean'] = np.mean(bond_length)
res[f'{name_space}#bond_length_max'] = np.max(bond_length)
res[f'{name_space}#bond_length_min'] = np.min(bond_length)
res[f'{name_space}#bond_length_std'] = np.std(bond_length)
return res
def calculate_features(filename):
graph = open(filename, "r")
G = nx.Graph()
nbColors = 0
nbPrecolor = 0
for line in graph:
split = line.split(' ')
if split[0] == 'p':
nbColors = int(split[4])
for i in range(int(split[2])):
G.add_node(i)
elif split[0] == 'e':
n1 = int(split[1]) - 1
n2 = int(split[2]) - 1
G.add_edge(n1, n2)
elif split[0] == 'n':
nbPrecolor += 1
graph.close()
degrees = np.array(G.degree)
centrality = np.fromiter(nx.betweenness_centrality(G).values(), dtype=int)
eigenvalues = np.linalg.eigvals(nx.to_numpy_matrix(G))
try:
eigenvector_centrality = np.fromiter(
nx.eigenvector_centrality(G).values(), dtype=float)
except nx.PowerIterationFailedConvergence:
eigenvector_centrality = np.array([0.])
cycles = list(map(lambda x: len(x), nx.cycle_basis(G)))
components = [nx.subgraph(G, comp) for comp in nx.connected_components(G)]
return G.number_of_nodes(), G.number_of_edges(), nx.density(G), np.mean(degrees, axis=0)[1], \
np.std(degrees, axis=0)[1], sum([nx.average_shortest_path_length(g) for g in components]), \
sum([nx.diameter(g) for g in components]), "inf" if len(cycles) == 0 else min(cycles), np.mean(
centrality), np.std(centrality), nx.average_clustering(G), nx.wiener_index(G), np.mean(
np.fromiter(map(lambda x: abs(x), eigenvalues), dtype=float)), np.std(eigenvalues), -1, \
np.mean(eigenvector_centrality), np.std(eigenvector_centrality), \
nbColors, nbPrecolor / float(G.number_of_nodes())
def _graph(self):
"""Generate graph-based attributes."""
self.graph_attr['number_of_nodes'] = [nx.number_of_nodes(self.graph)]
self.graph_attr['number_of_edges'] = [nx.number_of_edges(self.graph)]
self.graph_attr['number_of_selfloops'] = [
nx.number_of_selfloops(self.graph)
]
self.graph_attr['graph_number_of_cliques'] = [
nx.graph_number_of_cliques(self.graph)
]
self.graph_attr['graph_clique_number'] = [
nx.graph_clique_number(self.graph)
]
self.graph_attr['density'] = [nx.density(self.graph)]
self.graph_attr['transitivity'] = [nx.transitivity(self.graph)]
self.graph_attr['average_clustering'] = [
nx.average_clustering(self.graph)
]
self.graph_attr['radius'] = [nx.radius(self.graph)]
self.graph_attr['is_tree'] = [1 if nx.is_tree(self.graph) else 0]
self.graph_attr['wiener_index'] = [nx.wiener_index(self.graph)]
return self.graph_attr
def cpip_stats(filepath, core):
# Read in the network data for the full network
W = __pd__.read_csv(filepath)
# Rename columns to match pulp formatting
cc = list(W.columns)
for c in range(len(cc)):
cc[c] = __pulp_names__(cc[c])
W.columns = cc
# Create the core and periphery of the network
c_ids = [list(W.columns).index(c) for c in core]
p_ids = [i for i in range(len(W.columns)) if W.columns[i] not in core]
C = W
P = W
for c in [c_ids[len(c_ids) - 1 - i] for i in range(len(c_ids))]:
P = P.drop(P.columns[c], axis=1).drop(c, axis=0)
for p in [p_ids[len(p_ids) - 1 - i] for i in range(len(p_ids))]:
C = C.drop(C.columns[p], axis=1).drop(p, axis=0)
# Preparing some arrays of binary adjacency matrices for generating function outputs
M = W.values
MC = C.values
MP = P.values
for row in range(len(M)):
for col in range(len(M)):
if W.values[row][col] > 0:
M[row][col] = 1
for row in range(len(C)):
for col in range(len(C)):
if C.values[row][col] > 0:
MC[row][col] = 1
for row in range(len(P)):
for col in range(len(P)):
if P.values[row][col] > 0:
MP[row][col] = 1
# Creating the output object
output = __network_object__()
# Number of vertices
output.order = __network_object__()
output.order.network = len(M)
output.order.core = len(c_ids)
output.order.periphery = len(p_ids)
# Number of edges
output.size = __network_object__()
output.size.network = sum(sum(M)) / 2
output.size.core = sum(sum(MC)) / 2
output.size.periphery = sum(sum(MP)) / 2
output.size.between = output.size.network - output.size.core - output.size.periphery
# Ratios of order and size
output.ratio_v = __network_object__()
output.ratio_v.network = 1
output.ratio_v.core = output.order.core / output.order.network
output.ratio_v.periphery = 1 - output.ratio_v.core
output.ratio_e = __network_object__()
output.ratio_e.network = 1
output.ratio_e.core = output.size.core / output.size.network
output.ratio_e.periphery = output.size.periphery / output.size.network
output.ratio_e.between = 1 - output.ratio_e.core - output.ratio_e.periphery
# Densities
output.density = __network_object__()
output.density.network = output.size.network / ((len(M) *
(len(M) - 1)) / 2)
output.density.core = output.size.core / ((len(MC) * (len(MC) - 1)) / 2)
output.density.periphery = output.size.periphery / ((len(MP) *
(len(MP) - 1)) / 2)
# Degree statistics (mean, min, max)
output.within_degrees = __network_object__()
output.total_degrees = __network_object__()
output.within_degrees.average = __network_object__()
output.within_degrees.average.network = sum(sum(M)) / len(M)
output.within_degrees.average.core = sum(sum(MC)) / len(MC)
output.within_degrees.average.periphery = sum(sum(MP)) / len(MP)
output.within_degrees.min = __network_object__()
output.within_degrees.min.network = min(sum(M))
output.within_degrees.min.core = min(sum(MC))
output.within_degrees.min.periphery = min(sum(MP))
output.within_degrees.max = __network_object__()
output.within_degrees.max.network = max(sum(M))
output.within_degrees.max.core = max(sum(MC))
output.within_degrees.max.periphery = max(sum(MP))
output.total_degrees.average = __network_object__()
output.total_degrees.average.network = output.within_degrees.average.network
output.total_degrees.average.core = sum([sum(M)[c]
for c in c_ids]) / len(c_ids)
output.total_degrees.average.periphery = sum([sum(M)[p]
for p in p_ids]) / len(p_ids)
output.total_degrees.min = __network_object__()
output.total_degrees.min.network = output.within_degrees.min.network
output.total_degrees.min.core = min([sum(M)[c] for c in c_ids])
output.total_degrees.min.periphery = min([sum(M)[p] for p in p_ids])
output.total_degrees.max = __network_object__()
output.total_degrees.max.network = output.within_degrees.max.network
output.total_degrees.max.core = max([sum(M)[c] for c in c_ids])
output.total_degrees.max.periphery = max([sum(M)[p] for p in p_ids])
# Number of connected components
output.components = __network_object__()
output.components.network = __nx__.number_connected_components(
__nx__.Graph(M))
output.components.core = __nx__.number_connected_components(
__nx__.Graph(MC))
output.components.periphery = __nx__.number_connected_components(
__nx__.Graph(MP))
# Radius and diameter
output.radius = __network_object__()
output.diameter = __network_object__()
if output.components.network != 1:
output.radius.network = 'inf'
output.diameter.network = 'inf'
else:
output.radius.network = __nx__.radius(__nx__.Graph(M))
output.diameter.network = __nx__.diameter(__nx__.Graph(M))
if output.components.core != 1:
output.radius.core = 'inf'
output.diameter.core = 'inf'
else:
output.radius.core = __nx__.radius(__nx__.Graph(MC))
output.diameter.core = __nx__.diameter(__nx__.Graph(MC))
if output.components.periphery != 1:
output.radius.periphery = 'inf'
output.diameter.periphery = 'inf'
else:
output.radius.periphery = __nx__.radius(__nx__.Graph(MP))
output.diameter.periphery = __nx__.diameter(__nx__.Graph(MP))
# Maximium clique size
output.clique = __network_object__()
output.clique.network = len(max(__nx__.find_cliques(__nx__.Graph(M))))
output.clique.core = len(max(__nx__.find_cliques(__nx__.Graph(MC))))
output.clique.periphery = len(max(__nx__.find_cliques(__nx__.Graph(MP))))
# Global clustering
output.clustering = __network_object__()
output.clustering.network = __nx__.average_clustering(__nx__.Graph(M))
output.clustering.core = __nx__.average_clustering(__nx__.Graph(MC))
output.clustering.periphery = __nx__.average_clustering(__nx__.Graph(MP))
# Connectivity statistics
output.connectivity = __network_object__()
output.edge_connectivity = __network_object__()
output.algebraic_connectivity = __network_object__()
if output.components.network > 1:
output.connectivity.network = 0
output.edge_connectivity.network = 0
else:
output.connectivity.network = __nx__.node_connectivity(__nx__.Graph(M))
output.edge_connectivity.network = __nx__.edge_connectivity(
__nx__.Graph(M))
if output.components.core > 1:
output.connectivity.core = 0
output.edge_connectivity.core = 0
else:
output.connectivity.core = __nx__.node_connectivity(__nx__.Graph(MC))
output.edge_connectivity.core = __nx__.edge_connectivity(
__nx__.Graph(MC))
if output.components.periphery > 1:
output.connectivity.periphery = 0
output.edge_connectivity.periphery = 0
else:
output.connectivity.periphery = __nx__.node_connectivity(
__nx__.Graph(MP))
output.edge_connectivity.periphery = __nx__.edge_connectivity(
__nx__.Graph(MP))
output.algebraic_connectivity.network = __nx__.algebraic_connectivity(
__nx__.Graph(M))
output.algebraic_connectivity.core = __nx__.algebraic_connectivity(
__nx__.Graph(MC))
output.algebraic_connectivity.periphery = __nx__.algebraic_connectivity(
__nx__.Graph(MP))
# Energies and Laplacian energies
output.energy = __network_object__()
output.laplacian_energy = __network_object__()
output.energy.network = sum(abs(__nx__.adjacency_spectrum(
__nx__.Graph(M))))
output.energy.core = sum(abs(__nx__.adjacency_spectrum(__nx__.Graph(MC))))
output.energy.periphery = sum(
abs(__nx__.adjacency_spectrum(__nx__.Graph(MP))))
output.laplacian_energy.network = sum(
abs(__nx__.laplacian_spectrum(__nx__.Graph(M))))
output.laplacian_energy.core = sum(
abs(__nx__.laplacian_spectrum(__nx__.Graph(MC))))
output.laplacian_energy.periphery = sum(
abs(__nx__.laplacian_spectrum(__nx__.Graph(MP))))
# Transitivity
output.transitivity = __network_object__()
output.transitivity.network = __nx__.transitivity(__nx__.Graph(M))
output.transitivity.core = __nx__.transitivity(__nx__.Graph(MC))
output.transitivity.periphery = __nx__.transitivity(__nx__.Graph(MP))
# Wiener index
output.wiener = __network_object__()
output.wiener.network = __nx__.wiener_index(__nx__.Graph(M))
output.wiener.core = __nx__.wiener_index(__nx__.Graph(MC))
output.wiener.periphery = __nx__.wiener_index(__nx__.Graph(MP))
# Check if the core is a dominating set
output.dom_set = __network_object__()
output.dom_set.core = __nx__.is_dominating_set(__nx__.Graph(M), c_ids)
output.dom_set.periphery = __nx__.is_dominating_set(__nx__.Graph(M), p_ids)
return output
def test_disconnected_graph(self):
"""Tests that the Wiener index of a disconnected graph is
positive infinity.
"""
eq_(wiener_index(empty_graph(2)), float('inf'))
import networkx as nx n = 10 G = nx.complete_graph(n) print(nx.wiener_index(G) == n * (n - 1) / 2)
def test_disconnected_graph(self):
"""Tests that the Wiener index of a disconnected graph is
positive infinity.
"""
eq_(wiener_index(empty_graph(2)), float('inf'))
def compute_summaries(G):
""" Compute network features, computational times and their nature.
Evaluate 54 summary statistics of a network G, plus 4 noise variables,
store the computational time to evaluate each summary statistic, and keep
track of their nature (discrete or not).
Args:
G (networkx.classes.graph.Graph):
an undirected networkx graph.
Returns:
resDicts (tuple):
a tuple containing the elements:
- dictSums (dict): a dictionary with the name of the summaries
as keys and the summary statistic values as values;
- dictTimes (dict): a dictionary with the name of the summaries
as keys and the time to compute each one as values;
- dictIsDist (dict): a dictionary indicating if the summary is
discrete (True) or not (False).
"""
dictSums = dict() # Will store the summary statistic values
dictTimes = dict() # Will store the evaluation times
dictIsDisc = dict() # Will store the summary statistic nature
# Extract the largest connected component
Gcc = sorted(nx.connected_components(G), key=len, reverse=True)
G_lcc = G.subgraph(Gcc[0])
# Number of edges
start = time.time()
dictSums["num_edges"] = G.number_of_edges()
dictTimes["num_edges"] = time.time() - start
dictIsDisc["num_edges"] = True
# Number of connected components
start = time.time()
dictSums["num_of_CC"] = nx.number_connected_components(G)
dictTimes["num_of_CC"] = time.time() - start
dictIsDisc["num_of_CC"] = True
# Number of nodes in the largest connected component
start = time.time()
dictSums["num_nodes_LCC"] = nx.number_of_nodes(G_lcc)
dictTimes["num_nodes_LCC"] = time.time() - start
dictIsDisc["num_nodes_LCC"] = True
# Number of edges in the largest connected component
start = time.time()
dictSums["num_edges_LCC"] = G_lcc.number_of_edges()
dictTimes["num_edges_LCC"] = time.time() - start
dictIsDisc["num_edges_LCC"] = True
# Diameter of the largest connected component
start = time.time()
dictSums["diameter_LCC"] = nx.diameter(G_lcc)
dictTimes["diameter_LCC"] = time.time() - start
dictIsDisc["diameter_LCC"] = True
# Average geodesic distance (shortest path length in the LCC)
start = time.time()
dictSums["avg_geodesic_dist_LCC"] = nx.average_shortest_path_length(G_lcc)
dictTimes["avg_geodesic_dist_LCC"] = time.time() - start
dictIsDisc["avg_geodesic_dist_LCC"] = False
# Average degree of the neighborhood of each node
start = time.time()
dictSums["avg_deg_connectivity"] = np.mean(
list(nx.average_degree_connectivity(G).values()))
dictTimes["avg_deg_connectivity"] = time.time() - start
dictIsDisc["avg_deg_connectivity"] = False
# Average degree of the neighbors of each node in the LCC
start = time.time()
dictSums["avg_deg_connectivity_LCC"] = np.mean(
list(nx.average_degree_connectivity(G_lcc).values()))
dictTimes["avg_deg_connectivity_LCC"] = time.time() - start
dictIsDisc["avg_deg_connectivity_LCC"] = False
# Recover the degree distribution
start_degree_extract = time.time()
degree_vals = list(dict(G.degree()).values())
degree_extract_time = time.time() - start_degree_extract
# Entropy of the degree distribution
start = time.time()
dictSums["degree_entropy"] = ss.entropy(degree_vals)
dictTimes["degree_entropy"] = time.time() - start + degree_extract_time
dictIsDisc["degree_entropy"] = False
# Maximum degree
start = time.time()
dictSums["degree_max"] = max(degree_vals)
dictTimes["degree_max"] = time.time() - start + degree_extract_time
dictIsDisc["degree_max"] = True
# Average degree
start = time.time()
dictSums["degree_mean"] = np.mean(degree_vals)
dictTimes["degree_mean"] = time.time() - start + degree_extract_time
dictIsDisc["degree_mean"] = False
# Median degree
start = time.time()
dictSums["degree_median"] = np.median(degree_vals)
dictTimes["degree_median"] = time.time() - start + degree_extract_time
dictIsDisc["degree_median"] = False
# Standard deviation of the degree distribution
start = time.time()
dictSums["degree_std"] = np.std(degree_vals)
dictTimes["degree_std"] = time.time() - start + degree_extract_time
dictIsDisc["degree_std"] = False
# Quantile 25%
start = time.time()
dictSums["degree_q025"] = np.quantile(degree_vals, 0.25)
dictTimes["degree_q025"] = time.time() - start + degree_extract_time
dictIsDisc["degree_q025"] = False
# Quantile 75%
start = time.time()
dictSums["degree_q075"] = np.quantile(degree_vals, 0.75)
dictTimes["degree_q075"] = time.time() - start + degree_extract_time
dictIsDisc["degree_q075"] = False
# Average geodesic distance
start = time.time()
dictSums["avg_shortest_path_length_LCC"] = nx.average_shortest_path_length(
G_lcc)
dictTimes["avg_shortest_path_length_LCC"] = time.time() - start
dictIsDisc["avg_shortest_path_length_LCC"] = False
# Average global efficiency:
# The efficiency of a pair of nodes in a graph is the multiplicative
# inverse of the shortest path distance between the nodes.
# The average global efficiency of a graph is the average efficiency of
# all pairs of nodes.
start = time.time()
dictSums["avg_global_efficiency"] = nx.global_efficiency(G)
dictTimes["avg_global_efficiency"] = time.time() - start
dictIsDisc["avg_global_efficiency"] = False
# Harmonic mean which is 1/avg_global_efficiency
start = time.time()
dictSums["harmonic_mean"] = nx.global_efficiency(G)
dictTimes["harmonic_mean"] = time.time() - start
dictIsDisc["harmonic_mean"] = False
# Average local efficiency
# The local efficiency of a node in the graph is the average global
# efficiency of the subgraph induced by the neighbors of the node.
# The average local efficiency is the average of the
# local efficiencies of each node.
start = time.time()
dictSums["avg_local_efficiency_LCC"] = nx.local_efficiency(G_lcc)
dictTimes["avg_local_efficiency_LCC"] = time.time() - start
dictIsDisc["avg_local_efficiency_LCC"] = False
# Node connectivity
# The node connectivity is equal to the minimum number of nodes that
# must be removed to disconnect G or render it trivial.
# Only on the largest connected component here.
start = time.time()
dictSums["node_connectivity_LCC"] = nx.node_connectivity(G_lcc)
dictTimes["node_connectivity_LCC"] = time.time() - start
dictIsDisc["node_connectivity_LCC"] = True
# Edge connectivity
# The edge connectivity is equal to the minimum number of edges that
# must be removed to disconnect G or render it trivial.
# Only on the largest connected component here.
start = time.time()
dictSums["edge_connectivity_LCC"] = nx.edge_connectivity(G_lcc)
dictTimes["edge_connectivity_LCC"] = time.time() - start
dictIsDisc["edge_connectivity_LCC"] = True
# Graph transitivity
# 3*times the number of triangles divided by the number of triades
start = time.time()
dictSums["transitivity"] = nx.transitivity(G)
dictTimes["transitivity"] = time.time() - start
dictIsDisc["transitivity"] = False
# Number of triangles
start = time.time()
dictSums["num_triangles"] = np.sum(list(nx.triangles(G).values())) / 3
dictTimes["num_triangles"] = time.time() - start
dictIsDisc["num_triangles"] = True
# Estimate of the average clustering coefficient of G:
# Average local clustering coefficient, with local clustering coefficient
# defined as C_i = (nbr of pairs of neighbors of i that are connected)/(nbr of pairs of neighbors of i)
start = time.time()
dictSums["avg_clustering_coef"] = nx.average_clustering(G)
dictTimes["avg_clustering_coef"] = time.time() - start
dictIsDisc["avg_clustering_coef"] = False
# Square clustering (averaged over nodes):
# the fraction of possible squares that exist at the node.
# We average it over nodes
start = time.time()
dictSums["square_clustering_mean"] = np.mean(
list(nx.square_clustering(G).values()))
dictTimes["square_clustering_mean"] = time.time() - start
dictIsDisc["square_clustering_mean"] = False
# We compute the median
start = time.time()
dictSums["square_clustering_median"] = np.median(
list(nx.square_clustering(G).values()))
dictTimes["square_clustering_median"] = time.time() - start
dictIsDisc["square_clustering_median"] = False
# We compute the standard deviation
start = time.time()
dictSums["square_clustering_std"] = np.std(
list(nx.square_clustering(G).values()))
dictTimes["square_clustering_std"] = time.time() - start
dictIsDisc["square_clustering_std"] = False
# Number of 2-cores
start = time.time()
dictSums["num_2cores"] = len(nx.k_core(G, k=2))
dictTimes["num_2cores"] = time.time() - start
dictIsDisc["num_2cores"] = True
# Number of 3-cores
start = time.time()
dictSums["num_3cores"] = len(nx.k_core(G, k=3))
dictTimes["num_3cores"] = time.time() - start
dictIsDisc["num_3cores"] = True
# Number of 4-cores
start = time.time()
dictSums["num_4cores"] = len(nx.k_core(G, k=4))
dictTimes["num_4cores"] = time.time() - start
dictIsDisc["num_4cores"] = True
# Number of 5-cores
start = time.time()
dictSums["num_5cores"] = len(nx.k_core(G, k=5))
dictTimes["num_5cores"] = time.time() - start
dictIsDisc["num_5cores"] = True
# Number of 6-cores
start = time.time()
dictSums["num_6cores"] = len(nx.k_core(G, k=6))
dictTimes["num_6cores"] = time.time() - start
dictIsDisc["num_6cores"] = True
# Number of k-shells
# The k-shell is the subgraph induced by nodes with core number k.
# That is, nodes in the k-core that are not in the k+1-core
# Number of 2-shells
start = time.time()
dictSums["num_2shells"] = len(nx.k_shell(G, 2))
dictTimes["num_2shells"] = time.time() - start
dictIsDisc["num_2shells"] = True
# Number of 3-shells
start = time.time()
dictSums["num_3shells"] = len(nx.k_shell(G, 3))
dictTimes["num_3shells"] = time.time() - start
dictIsDisc["num_3shells"] = True
# Number of 4-shells
start = time.time()
dictSums["num_4shells"] = len(nx.k_shell(G, 4))
dictTimes["num_4shells"] = time.time() - start
dictIsDisc["num_4shells"] = True
# Number of 5-shells
start = time.time()
dictSums["num_5shells"] = len(nx.k_shell(G, 5))
dictTimes["num_5shells"] = time.time() - start
dictIsDisc["num_5shells"] = True
# Number of 6-shells
start = time.time()
dictSums["num_6shells"] = len(nx.k_shell(G, 6))
dictTimes["num_6shells"] = time.time() - start
dictIsDisc["num_6shells"] = True
start = time.time()
listOfCliques = list(nx.enumerate_all_cliques(G))
enum_all_cliques_time = time.time() - start
# Number of 4-cliques
start = time.time()
n4Clique = 0
for li in listOfCliques:
if len(li) == 4:
n4Clique += 1
dictSums["num_4cliques"] = n4Clique
dictTimes["num_4cliques"] = time.time() - start + enum_all_cliques_time
dictIsDisc["num_4cliques"] = True
# Number of 5-cliques
start = time.time()
n5Clique = 0
for li in listOfCliques:
if len(li) == 5:
n5Clique += 1
dictSums["num_5cliques"] = n5Clique
dictTimes["num_5cliques"] = time.time() - start + enum_all_cliques_time
dictIsDisc["num_5cliques"] = True
# Maximal size of a clique in the graph
start = time.time()
dictSums["max_clique_size"] = len(approximation.clique.max_clique(G))
dictTimes["max_clique_size"] = time.time() - start
dictIsDisc["max_clique_size"] = True
# Approximated size of a large clique in the graph
start = time.time()
dictSums["large_clique_size"] = approximation.large_clique_size(G)
dictTimes["large_clique_size"] = time.time() - start
dictIsDisc["large_clique_size"] = True
# Number of shortest path of size k
start = time.time()
listOfPLength = list(nx.shortest_path_length(G))
path_length_time = time.time() - start
# when k = 3
start = time.time()
n3Paths = 0
for node in G.nodes():
tmp = list(listOfPLength[node][1].values())
n3Paths += tmp.count(3)
dictSums["num_shortest_3paths"] = n3Paths / 2
dictTimes["num_shortest_3paths"] = time.time() - start + path_length_time
dictIsDisc["num_shortest_3paths"] = True
# when k = 4
start = time.time()
n4Paths = 0
for node in G.nodes():
tmp = list(listOfPLength[node][1].values())
n4Paths += tmp.count(4)
dictSums["num_shortest_4paths"] = n4Paths / 2
dictTimes["num_shortest_4paths"] = time.time() - start + path_length_time
dictIsDisc["num_shortest_4paths"] = True
# when k = 5
start = time.time()
n5Paths = 0
for node in G.nodes():
tmp = list(listOfPLength[node][1].values())
n5Paths += tmp.count(5)
dictSums["num_shortest_5paths"] = n5Paths / 2
dictTimes["num_shortest_5paths"] = time.time() - start + path_length_time
dictIsDisc["num_shortest_5paths"] = True
# when k = 6
start = time.time()
n6Paths = 0
for node in G.nodes():
tmp = list(listOfPLength[node][1].values())
n6Paths += tmp.count(6)
dictSums["num_shortest_6paths"] = n6Paths / 2
dictTimes["num_shortest_6paths"] = time.time() - start + path_length_time
dictIsDisc["num_shortest_6paths"] = True
# Size of the minimum (weight) node dominating set:
# A subset of nodes where each node not in the subset has for direct
# neighbor a node of the dominating set.
start = time.time()
T = approximation.min_weighted_dominating_set(G)
dictSums["size_min_node_dom_set"] = len(T)
dictTimes["size_min_node_dom_set"] = time.time() - start
dictIsDisc["size_min_node_dom_set"] = True
# Idem but with the edge dominating set
start = time.time()
T = approximation.min_edge_dominating_set(G)
dictSums["size_min_edge_dom_set"] = 2 * len(
T) # times 2 to have a number of nodes
dictTimes["size_min_edge_dom_set"] = time.time() - start
dictIsDisc["size_min_edge_dom_set"] = True
# The Wiener index of a graph is the sum of the shortest-path distances
# between each pair of reachable nodes. For pairs of nodes in undirected graphs,
# only one orientation of the pair is counted.
# (On LCC otherwise inf)
start = time.time()
dictSums["wiener_index_LCC"] = nx.wiener_index(G_lcc)
dictTimes["wiener_index_LCC"] = time.time() - start
dictIsDisc["wiener_index_LCC"] = True
# Betweenness node centrality (averaged over nodes):
# at node u it is defined as B_u = sum_i,j sigma(i,u,j)/sigma(i,j)
# where sigma is the number of shortest path between i and j going through u or not
start = time.time()
betweenness = list(nx.betweenness_centrality(G).values())
time_betweenness = time.time() - start
# Averaged across nodes
start = time.time()
dictSums["betweenness_centrality_mean"] = np.mean(betweenness)
dictTimes["betweenness_centrality_mean"] = time.time(
) - start + time_betweenness
dictIsDisc["betweenness_centrality_mean"] = False
# Maximum across nodes
start = time.time()
dictSums["betweenness_centrality_max"] = max(betweenness)
dictTimes["betweenness_centrality_max"] = time.time(
) - start + time_betweenness
dictIsDisc["betweenness_centrality_max"] = False
# Central point dominance
# CPD = sum_u(B_max - B_u)/(N-1)
start = time.time()
dictSums["central_point_dominance"] = sum(
max(betweenness) - np.array(betweenness)) / (len(betweenness) - 1)
dictTimes["central_point_dominance"] = time.time(
) - start + time_betweenness
dictIsDisc["central_point_dominance"] = False
# Estrata index : sum_i^n exp(lambda_i)
# with n the number of nodes, lamda_i the i-th eigen value of the adjacency matrix of G
start = time.time()
dictSums["Estrata_index"] = nx.estrada_index(G)
dictTimes["Estrata_index"] = time.time() - start
dictIsDisc["Estrata_index"] = False
# Eigenvector centrality
# For each node, it is the average eigenvalue centrality of its neighbors,
# where centrality of node i is taken as the i-th coordinate of x
# such that Ax = lambda*x (for the maximal eigen value)
# Averaged
start = time.time()
dictSums["avg_eigenvec_centrality"] = np.mean(
list(nx.eigenvector_centrality_numpy(G).values()))
dictTimes["avg_eigenvec_centrality"] = time.time() - start
dictIsDisc["avg_eigenvec_centrality"] = False
# Maximum
start = time.time()
dictSums["max_eigenvec_centrality"] = max(
list(nx.eigenvector_centrality_numpy(G).values()))
dictTimes["max_eigenvec_centrality"] = time.time() - start
dictIsDisc["max_eigenvec_centrality"] = False
### Noise generation ###
# Noise simulated from a Normal(0,1) distribution
start = time.time()
dictSums["noise_Gauss"] = ss.norm.rvs(0, 1)
dictTimes["noise_Gauss"] = time.time() - start
dictIsDisc["noise_Gauss"] = False
# Noise simulated from a Uniform distribution [0-50]
start = time.time()
dictSums["noise_Unif"] = ss.uniform.rvs(0, 50)
dictTimes["noise_Unif"] = time.time() - start
dictIsDisc["noise_Unif"] = False
# Noise simulated from a Bernoulli B(0.5) distribution
start = time.time()
dictSums["noise_Bern"] = ss.bernoulli.rvs(0.5)
dictTimes["noise_Bern"] = time.time() - start
dictIsDisc["noise_Bern"] = True
# Noise simulated from a discrete uniform distribution [0,50[
start = time.time()
dictSums["noise_disc_Unif"] = ss.randint.rvs(0, 50)
dictTimes["noise_disc_Unif"] = time.time() - start
dictIsDisc["noise_disc_Unif"] = True
resDicts = (dictSums, dictTimes, dictIsDisc)
return resDicts
def closeness_vitality(G, node=None, weight=None, wiener_index=None):
"""Returns the closeness vitality for nodes in the graph.
The *closeness vitality* of a node, defined in Section 3.6.2 of [1],
is the change in the sum of distances between all node pairs when
excluding that node.
Parameters
----------
G : NetworkX graph
A strongly-connected graph.
weight : string
The name of the edge attribute used as weight. This is passed
directly to the :func:`~networkx.wiener_index` function.
node : object
If specified, only the closeness vitality for this node will be
returned. Otherwise, a dictionary mappping each node to its
closeness vitality will be returned.
Other parameters
----------------
wiener_index : number
If you have already computed the Wiener index of the graph
``G``, you can provide that value here. Otherwise, it will be
computed for you.
Returns
-------
dictionary or float
If ``node`` is ``None``, this function returnes a dictionary
with nodes as keys and closeness vitality as the
value. Otherwise, it returns only the closeness vitality for the
specified ``node``.
The closeness vitality of a node may be negative infinity if
removing that node would disconnect the graph.
Examples
--------
>>> G = nx.cycle_graph(3)
>>> nx.closeness_vitality(G)
{0: 2.0, 1: 2.0, 2: 2.0}
See Also
--------
closeness_centrality
References
----------
.. [1] Ulrik Brandes, Thomas Erlebach (eds.).
*Network Analysis: Methodological Foundations*.
Springer, 2005.
<http://books.google.com/books?id=TTNhSm7HYrIC>
"""
if wiener_index is None:
wiener_index = nx.wiener_index(G, weight=weight)
if node is not None:
after = nx.wiener_index(G.subgraph(set(G) - {node}), weight=weight)
return wiener_index - after
vitality = partial(closeness_vitality, G, weight=weight,
wiener_index=wiener_index)
# TODO This can be trivially parallelized.
return {v: vitality(node=v) for v in G}
def getWienerD(self):
"""
Returns the Wiener distance for a graph.
"""
return NX.wiener_index(self)
'.json') and not pos_json.endswith('nodes.json')]
with open('./wienerIndexes.json', 'w') as wienerIndexes:
with open('./graphDegres.json', 'w') as graphDegres:
wienerIndexesDict = {}
graphDegreeDict = {}
for fileName in json_files:
print(fileName)
with open('./Topologias/' + fileName, 'r') as json_file:
JSONLinks = json.load(json_file)
G = nx.Graph()
G.add_weighted_edges_from(
(elem['From'], elem['To'], 1)
for elem in JSONLinks
)
wienerIndex = nx.wiener_index(G)
graphDegree = sum(
map(lambda v: v[1], G.degree())) / len(G.nodes)
wienerIndexesDict[fileName] = wienerIndex
graphDegreeDict[fileName] = graphDegree
json.dump(wienerIndexesDict, wienerIndexes, sort_keys=True)
json.dump(graphDegreeDict, graphDegres, sort_keys=True)
def __init__(self, graph: nx.Graph):
self.graph = graph
self.wiener = nx.wiener_index(graph)
self.distances = dict(nx.all_pairs_dijkstra_path_length(graph))
def calculate(graph):
if nx.is_connected(graph):
return Utils.approx_to_int(nx.wiener_index(graph))
else:
return 10**10
),
)
return edge_disjoint_shortest_paths
graph = nx.Graph()
with open("TopologiasRedesReais/scteste_nodes.csv") as nf:
with open("TopologiasRedesReais/scteste_links.csv") as ef:
nodes = list(map(lambda n: n["Id"], csv.DictReader(nf)))
edges = list(map(lambda e: (e["From"], e["To"], 1),
csv.DictReader(ef)))
graph.add_nodes_from(nodes)
graph.add_weighted_edges_from(edges)
print(nx.wiener_index(graph, weight='weight'))
# get_all_pairs_edge_disjoint_shortest_paths(graph.to_directed())
# graph = nx.Graph()
# graph.add_nodes_from(["s", "a", "b", "c", "d", "e", "f", "g"])
# graph.add_edges_from(
# [
# ("s", "a"),
# ("s", "b"),
# ("s", "d"),
# ("a", "c"),
# ("a", "d"),
# ("a", "e"),
# ("b", "e"),
# ("c", "f"),