def alp_katz(g, subgraphs, func=max):
import operator
landmarks = []
for sub in subgraphs.values():
if g.is_directed():
g_s = list(nx.strongly_connected_component_subgraphs(g.subgraph(sub)))[0]
else:
g_s = list(nx.connected_component_subgraphs(g.subgraph(sub), False))[0]
n_len = nx.number_of_nodes(g_s)
if n_len < 10:
landmarks.append(g_s.nodes()[0])
else:
try:
bc = nx.katz_centrality(g_s, max_iter=100000, normalized=True)
except:
try:
print "Running Katz centrality again for tolerance = ", str(.001)
bc = nx.katz_centrality(g_s, max_iter=100000, normalized=True, tol=.001)
except:
print "Katz Centrality returned nothing."
return []
if func == mode:
landmarks.append(mode(bc))
else:
landmarks.append(func(bc.iteritems(), key=operator.itemgetter(1))[0])
return landmarks
def katz(graph_data):
graph = graph_data['net']
w_label = graph_data['w_label']
# sem peso e sem direção
graph_simply = dir2undir(graph, w_label).simplify(
multiple=True, loops=False, combine_edges=graph_data['simply_method2'])
# sem peso e sem direção
undir_unweig = sorted(networkx.katz_centrality(graph_simply, weight=None))
undir_unweig = list(undir_unweig.values())
# com peso
weig = sorted(networkx.katz_centrality(graph_simply, weight=w_label))
weig = list(weig.values())
# com direção
in_katz = sorted(networkx.katz_centrality(graph.to_networkx(),
weight=None))
in_katz = list(in_katz.values())
# com peso e com direção
in_weig_katz = sorted(
networkx.katz_centrality(graph.to_networkx(), weight=w_label))
in_weig_katz = list(in_weig_katz.values())
return undir_unweig, weig, in_katz, in_weig_katz
def compute_katz(self, graph_id):
"""
Computes the Katz coeffcient for every node in the indicated graph.
Ads the computed coefficient as property to nodes.
"""
if graph_id == 1:
rank = nx.katz_centrality(self.graph_icnet)
nx.set_node_attributes(self.graph_icnet, 'katz', rank)
if graph_id == 2:
rank = nx.katz_centrality(self.graph_aicnet)
nx.set_node_attributes(self.graph_aicnet, 'katz', rank)
def test_K5(self):
"""Katz centrality: K5"""
G = nx.complete_graph(5)
alpha = 0.1
b = nx.katz_centrality(G, alpha)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
nstart = {n: 1 for n in G}
b = nx.katz_centrality(G, alpha, nstart=nstart)
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
def test_K5(self):
"""Katz centrality: K5"""
G = nx.complete_graph(5)
alpha = 0.1
b = nx.katz_centrality(G, alpha)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n])
nstart = dict([(n, 1) for n in G])
b = nx.katz_centrality(G, alpha, nstart=nstart)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n])
def test_K5(self):
"""Katz centrality: K5"""
G = nx.complete_graph(5)
alpha = 0.1
b = nx.katz_centrality(G, alpha)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
nstart = {n: 1 for n in G}
b = nx.katz_centrality(G, alpha, nstart=nstart)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def centrality_algorithms(graph):
# Centrality functions return a dictionary of values
# Calculate the maximum and print node name with value
# Value stays the same for closness centrality, but the node itself changes
centrality_dict = nx.degree_centrality(graph)
print('Degree Centrality: ', max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
centrality_dict = nx.in_degree_centrality(graph)
print('In Degree Centrality: ',
max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
centrality_dict = nx.out_degree_centrality(graph)
print('Out Degree Centrality: ',
max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
centrality_dict = nx.eigenvector_centrality_numpy(graph)
print('Eigenvector Centrality: ',
max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
centrality_dict = nx.katz_centrality(graph)
print('Katz Centrality: ', max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
centrality_dict = nx.closeness_centrality(graph)
print('Closeness Centrality: ',
max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
centrality_dict = nx.betweenness_centrality(graph)
print('Betweenness Centrality: ',
max(centrality_dict, key=centrality_dict.get),
max(centrality_dict.values()))
def centrality_calculation_by_networkx(G):
'''
使用 networkx 计算 Centrality
'''
d_c = nx.degree_centrality(G)
k_z = nx.katz_centrality(
G=G,
alpha=0.3,
beta=0.3,
max_iter=1000,
tol=1.0e-6,
nstart=None,
normalized=True)
# 归一化，每个元素除以集合中最大元素
max_item = max([d_c[item] for item in d_c])
degree_centrality = [round(d_c[item] / max_item, 4) for item in d_c]
max_item = max([k_z[item] for item in k_z])
katz_centrality = [round(k_z[item] / max_item, 4) for item in k_z]
nx_list = [{'Degree': degree_centrality}, {'Katz': katz_centrality}]
return nx_list
def test_katz_centrality_nx(graph_file):
gc.collect()
NM = utils.read_csv_for_nx(graph_file)
Gnx = nx.from_pandas_edgelist(NM,
create_using=nx.DiGraph(),
source="0",
target="1")
G = cugraph.utilities.convert_from_nx(Gnx)
largest_out_degree = G.degrees().nlargest(n=1, columns="out_degree")
largest_out_degree = largest_out_degree["out_degree"].iloc[0]
katz_alpha = 1 / (largest_out_degree + 1)
nk = nx.katz_centrality(Gnx, alpha=katz_alpha)
ck = cugraph.katz_centrality(Gnx, alpha=None, max_iter=1000)
# Calculating mismatch
nk = sorted(nk.items(), key=lambda x: x[0])
ck = sorted(ck.items(), key=lambda x: x[0])
err = 0
assert len(ck) == len(nk)
for i in range(len(ck)):
if (abs(ck[i][1] - nk[i][1]) > 0.1 and ck[i][0] == nk[i][0]):
err = err + 1
print("Mismatches:", err)
assert err < (0.1 * len(ck))
def centrality_histogram(g, c): # Creates the centrality histogram specified
if c == 'degree':
degree_sequence = sorted(
[val for key, val in nx.degree_centrality(g).items()])
elif c == 'in_degree':
degree_sequence = sorted(
[val for key, val in nx.in_degree_centrality(g).items()])
elif c == 'out_degree':
degree_sequence = sorted(
[val for key, val in nx.out_degree_centrality(g).items()])
elif c == 'closeness':
degree_sequence = sorted(
[val for key, val in nx.closeness_centrality(g).items()])
elif c == 'betweenness':
degree_sequence = sorted(
[val for key, val in nx.betweenness_centrality(g).items()])
elif c == 'eigenvector':
degree_sequence = sorted(
[val for key, val in nx.eigenvector_centrality(g).items()])
elif c == 'katz':
degree_sequence = sorted(
[val for key, val in nx.katz_centrality(g).items()])
degree_count = col.Counter(degree_sequence)
deg, cnt = zip(*degree_count.items())
plt.bar(deg, cnt, width=0.01, color='b')
plt.title('Degree Histogram')
plt.ylabel('Count')
plt.xlabel('Degree')
plt.show()
def relevant_stats(G): cloC = nx.closeness_centrality(G, distance = 'distance') betC = nx.betweenness_centrality(G, weight = 'distance') katC = nx.katz_centrality(G) eigC = nx.eigenvector_centrality(G) return
def most_central(self,F=1,cent_type='betweenness'):
if cent_type == 'betweenness':
ranking = nx.betweenness_centrality(self.G).items()
elif cent_type == 'closeness':
ranking = nx.closeness_centrality(self.G).items()
elif cent_type == 'eigenvector':
ranking = nx.eigenvector_centrality(self.G).items()
elif cent_type == 'harmonic':
ranking = nx.harmonic_centrality(self.G).items()
elif cent_type == 'katz':
ranking = nx.katz_centrality(self.G).items()
elif cent_type == 'load':
ranking = nx.load_centrality(self.G).items()
elif cent_type == 'degree':
ranking = nx.degree_centrality(self.G).items()
ranks = [r for n,r in ranking]
cent_dict = dict([(self.lab[n],r) for n,r in ranking])
m_centrality = sum(ranks)
if len(ranks) > 0:
m_centrality = m_centrality/len(ranks)
#Create a graph with the nodes above the cutoff centrality- remove the low centrality nodes
thresh = F*m_centrality
lab = {}
for k in self.lab:
lab[k] = self.lab[k]
g = Graph(self.adj.copy(),self.char_list)
for n,r in ranking:
if r < thresh:
g.G.remove_node(n)
del g.lab[n]
return (cent_dict,thresh,g)
def nextBestNode(self, state): #Finds the next best spot for a station
graph = state.get_graph()
nodeScores = []
centrality = nx.katz_centrality(graph)
for i in centrality:
nodeScores.append(centrality[i])
bestNode = 0
bestScore = nodeScores[0]
for i in range(len(nodeScores)):
if (nodeScores[i] > bestScore and (i not in self.stations)):
bestNode = i
bestScore = nodeScores[i]
#print("bestNode=",(bestScore,bestNode))
#Factor in distance from each station
for i in range(len(nodeScores)):
if (i not in self.stations):
distanceScore = 1.0 / self.closestStation(graph, i)[1]
#print("distanceScore=",distanceScore)
nodeScores[i] -= distanceScore * self.distanceWeight
#Get the node with the best score
bestNode = 0
bestScore = nodeScores[0]
for i in range(len(nodeScores)):
if (nodeScores[i] > bestScore and (i not in self.stations)):
bestNode = i
bestScore = nodeScores[i]
#print("bestNode=",(bestScore,bestNode))
return bestNode
def centralities(self):
'''
Get info on centralities of data
Params:
None
Returns:
dictionary of centrality metrics with keys(centralities supported):
degree - degree centrality
betweeness - betweeness centrality
eigenvector - eigenvector centrality
hub - hub scores - not implemented
authority - authority scores - not implemented
katz - katz centrality with params X Y
pagerank - pagerank centrality with params X Y
'''
output = {}
output['degree'] = nx.degree_centrality(self.G)
output['betweeness'] = nx.betweenness_centrality(self.G)
try:
output['eigenvector'] = nx.eigenvector_centrality(self.G)
output['katz'] = nx.katz_centrality(self.G)
except:
output['eigenvector'] = 'empty or exception'
output['katz'] = 'empty or exception'
# output['hub'] = 'Not implemented'
# output['authority'] = 'Not implemented'
# output['pagerank'] = 'Not implemented'
return output
def centrality(self, c_type='degree'):
"""计算整个网络的所有节点的中心度，返回一个dict"""
if c_type not in self._centrality.keys(): # 检测输入类型不正确的异常
raise ValueError(
"输入类型不正确！type请输入degree/indegree/outdegree/eigenvector/katz/pagerank/betweenness/closeness！")
if not self._centrality[c_type]:
if c_type == 'degree': # 因为networkx的度数中心度计算不带权重，故自制了一个
if self.weight_type:
weight = [edge[2][self.weight_type] for edge in self.network.edges(data=True)]
s = 1.0 / sum(weight)
else:
s = 1.0 / (len(self.network) - 1.0)
self._centrality[c_type] = {n: d * s for n, d in self.network.degree(weight=self.weight_type)}
elif c_type == 'indegree':
s = 1.0 / (len(self.network) - 1.0)
self._centrality[c_type] = {n: d * s for n, d in self.network.in_degree(weight=self.weight_type)}
elif c_type == 'outdegree':
s = 1.0 / (len(self.network) - 1.0)
self._centrality[c_type] = {n: d * s for n, d in self.network.out_degree(weight=self.weight_type)}
elif c_type == 'eigenvector':
self._centrality[c_type] = nx.eigenvector_centrality(self.network, max_iter=1000,
weight=self.weight_type)
elif c_type == 'katz':
self._centrality[c_type] = nx.katz_centrality(self.network, max_iter=1000, weight=self.weight_type)
elif c_type == 'pagerank':
pr = nx.pagerank(self.network, weight=self.weight_type)
self._centrality[c_type] = {node: pr[node] for node in pr}
elif c_type == 'betweenness':
self._centrality[c_type] = nx.betweenness_centrality(self.network, weight=self.weight_type)
elif c_type == 'closeness':
self._centrality[c_type] = nx.closeness_centrality(self.network)
return self._centrality[c_type]
def get_hubs(c, method):
try:
if method == 'eigenvector':
centralities = nx.eigenvector_centrality(c, weight='weight', max_iter=1000)
elif method == 'pagerank':
centralities = nx.pagerank(c, max_iter=1000)
elif method == 'hits_hub':
centralities = nx.hits(c, max_iter=1000)[1]
elif method == 'hits_authority':
centralities = nx.hits(c, max_iter=1000)[0]
elif method == 'betweenness':
centralities = nx.betweenness_centrality(c, weight='weight')
elif method == 'katz':
centralities = nx.katz_centrality(c, weight='weight', max_iter=10000)
else:
raise NameError
except nx.PowerIterationFailedConvergence:
return None
max_hub = max(centralities.items(), key=itemgetter(1))[1]
hubs = [node for node in centralities if abs(centralities[node]-max_hub)<=0.001]
if len(hubs) == len(c.nodes()):
return 'all nodes'
else:
return (', '.join(hubs))
def most_central(self, F=1, cent_type='betweenness'):
if cent_type == 'betweenness':
ranking = nx.betweenness_centrality(self.G).items()
elif cent_type == 'closeness':
ranking = nx.closeness_centrality(self.G).items()
elif cent_type == 'eigenvector':
ranking = nx.eigenvector_centrality(self.G).items()
elif cent_type == 'harmonic':
ranking = nx.harmonic_centrality(self.G).items()
elif cent_type == 'katz':
ranking = nx.katz_centrality(self.G).items()
elif cent_type == 'load':
ranking = nx.load_centrality(self.G).items()
elif cent_type == 'degree':
ranking = nx.degree_centrality(self.G).items()
ranks = [r for n, r in ranking]
cent_dict = dict([(self.lab[n], r) for n, r in ranking])
m_centrality = sum(ranks)
if len(ranks) > 0:
m_centrality = m_centrality / len(ranks)
#Create a graph with the nodes above the cutoff centrality- remove the low centrality nodes
thresh = F * m_centrality
lab = {}
for k in self.lab:
lab[k] = self.lab[k]
g = Graph(self.adj.copy(), self.char_list)
for n, r in ranking:
if r < thresh:
g.G.remove_node(n)
del g.lab[n]
return (cent_dict, thresh, g)
def print_graph_stats(self, G):
print('average clustering: ', nx.average_clustering(G))
degrees = [val for (node, val) in G.degree()]
print('average degree: ', sum(degrees) / float(len(G)))
print('density: ', nx.density(G))
print('assortativity coefficient (Pearson\'s rho): ',
nx.degree_pearson_correlation_coefficient(G))
print('(should be negative according to Gonzalez et al., 2007)')
import operator
x = nx.betweenness_centrality(G)
sorted_x = sorted(x.items(), key=operator.itemgetter(1))
print('betweenness centrality', sorted_x)
x = nx.degree_centrality(G)
sorted_x = sorted(x.items(), key=operator.itemgetter(1))
print('degree centrality:', sorted_x)
x = nx.eigenvector_centrality(G)
sorted_x = sorted(x.items(), key=operator.itemgetter(1))
print('eigenvector centrality:', sorted_x)
x = nx.katz_centrality(G)
sorted_x = sorted(x.items(), key=operator.itemgetter(1))
print('Katz centrality:', sorted_x)
x = nx.closeness_centrality(G)
sorted_x = sorted(x.items(), key=operator.itemgetter(1))
print('closeness centrality:', sorted_x)
print('\n')
def create_metric_column(G, metric, year=None):
"""
Returns an array of the pageranks for vertices in a network G
Parameters
------------
G: igraph network object where each node has a time attribute
metric: string of the vertex metrics we want to compute
(pagerank, indegree, etc)
year: is year of the network if we are passing a time truncated network
- katz
d_ means for directed graph
u_ means for undirected graph
Output
-------
metric: an array of size G.vs that contains the metric for G's vertices
or does not return value on invalid metric parameter
"""
try:
# calculates metric which matched parameter
if metric == 'katz':
metric_column = nx.katz_centrality(Gnx)
except Exception:
print 'problem with %s' % metric
metric_column = metric_column = [np.nan] * len(G.vs)
return metric_column
def CentralityPoint2D(graph, numberOfPoints, typePlot):
"""Plot 3D centrality based on type."""
points = dict()
c_eigenvector = nx.katz_centrality(graph)
c_eigenvector = heapq.nlargest(numberOfPoints,
list(c_eigenvector.values()))
max_eigenvector = max(c_eigenvector)
points['Eigenvalues'] = c_eigenvector
c_betweenness = nx.betweenness_centrality(graph)
c_betweenness = heapq.nlargest(numberOfPoints,
list(c_betweenness.values()))
max_betweenness = max(c_betweenness)
points['Betweenness'] = c_betweenness
c_closeness = nx.closeness_centrality(graph)
c_closeness = heapq.nlargest(numberOfPoints, list(c_closeness.values()))
max_closeness = max(c_closeness)
points['Closeness'] = c_closeness
c_harmonic = nx.harmonic_centrality(graph)
c_harmonic = heapq.nlargest(numberOfPoints, list(c_harmonic.values()))
max_harmonic = max(c_harmonic)
points['Harmonic'] = c_harmonic
glCoe = GlobalClusteringCoefficient(graph)
points['Mix'] = (max_eigenvector, max_harmonic, max_betweenness)
points['Mix2'] = (max_eigenvector, glCoe, max_closeness)
points['Mix3'] = (max_eigenvector, glCoe, max_harmonic)
points['Mix4'] = (max_eigenvector, glCoe,
SquareClusteringCoefficient(graph))
return points[typePlot]
def test_dask_katz_centrality(client_connection):
gc.collect()
input_data_path = r"../datasets/karate.csv"
chunksize = dcg.get_chunksize(input_data_path)
ddf = dask_cudf.read_csv(
input_data_path,
chunksize=chunksize,
delimiter=" ",
names=["src", "dst", "value"],
dtype=["int32", "int32", "float32"],
)
df = cudf.read_csv(
input_data_path,
delimiter=" ",
names=["src", "dst", "value"],
dtype=["int32", "int32", "float32"],
)
g = cugraph.DiGraph()
g.from_cudf_edgelist(df, "src", "dst")
dg = cugraph.DiGraph()
dg.from_dask_cudf_edgelist(ddf, "src", "dst")
largest_out_degree = g.degrees().nlargest(n=1, columns="out_degree")
largest_out_degree = largest_out_degree["out_degree"].iloc[0]
katz_alpha = 1 / (largest_out_degree + 1)
mg_res = dcg.katz_centrality(dg, alpha=katz_alpha, tol=1e-6)
mg_res = mg_res.compute()
import networkx as nx
from cugraph.tests import utils
NM = utils.read_csv_for_nx(input_data_path)
Gnx = nx.from_pandas_edgelist(
NM, create_using=nx.DiGraph(), source="0", target="1"
)
nk = nx.katz_centrality(Gnx, alpha=katz_alpha)
import pandas as pd
pdf = pd.DataFrame(nk.items(), columns=['vertex', 'katz_centrality'])
exp_res = cudf.DataFrame(pdf)
err = 0
tol = 1.0e-05
compare_res = exp_res.merge(
mg_res, on="vertex", suffixes=["_local", "_dask"]
)
for i in range(len(compare_res)):
diff = abs(
compare_res["katz_centrality_local"].iloc[i]
- compare_res["katz_centrality_dask"].iloc[i]
)
if diff > tol * 1.1:
err = err + 1
assert err == 0
def test_P3(self):
"""Katz centrality: P3"""
alpha = 0.1
G = nx.path_graph(3)
b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
b = nx.katz_centrality(G, alpha)
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
def run(self,steps): for _ in xrange(steps): self.update() self.prs =nx.pagerank(self.G) self.close = nx.closeness_centrality(self.G) self.bet = nx.betweenness_centrality(self.G) self.katz = nx.katz_centrality(self.G)
def katz_centrality(G, dim):
katz_cent_matrix = np.zeros((dim, 1))
katz_cent_dict = nx.katz_centrality(G)
z = 0
for i in hosts_list:
katz_cent_matrix[z] = katz_cent_dict.get(i)
z += 1
return katz_cent_matrix
def readGraph(self):
self.readingUsersFile()
self.graph = networkx.read_graphml(self.graphFile)
(self.followees, self.followers) = self.getFolloweesAndFollowers(self.graph)
self.pageRanks = networkx.pagerank(self.graph)
self.katz = networkx.katz_centrality(self.graph)
self.paths = networkx.shortest_path(self.graph)
return self.graph
def test_beta_as_dict(self):
alpha = 0.1
beta = {0: 1.0, 1: 1.0, 2: 1.0}
b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449, 2: 0.5598852584152162}
G = nx.path_graph(3)
b = nx.katz_centrality(G, alpha, beta)
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
def competitive_part(links_dataset, number):
# Edge Filtering
# k = number of edges we remove per iteration
k = 1000
G = nx.from_pandas_edgelist(links_dataset.init_graph,
'target',
'source',
edge_attr=True,
create_using=nx.Graph())
removed_edges = list()
for i in range(number // k):
print("iter = ", i)
# bridges = list(nx.bridges(G))
ranking = nx.katz_centrality(G, max_iter=100, weight='weight')
mean_katz_centrality = np.mean(list(ranking.values()))
weight_dict = dict()
# reweight edges
for edge in G.edges():
print(edge)
WG = G.copy()
WG.remove_edge(edge[0], edge[1])
_katz = nx.katz_centrality(G,
max_iter=20,
weight='weight',
tol=10e-4)
_mean_katz_centrality = np.mean(list(ranking.values()))
weight_dict[edge] = mean_katz_centrality - _mean_katz_centrality
# sort descending
weight_dict = sorted(weight_dict.items(),
key=lambda x: x[1],
reverse=True)
i = 0
# remove bridges with maximal weighted span
for edge in dict(weight_dict).keys():
if i == k:
break
removed_edges.append(edge)
G.remove_edge(edge[0], edge[1])
i += 1
return removed_edges
def katz(self):
"""Compute the Katz centrality for the nodes of the graph G.
Returns
-------
nodes : dictionary
Dictionary of nodes with Katz centrality as the value.
"""
return nx.katz_centrality(self._graph, weight=self._weight_field)
def test_maxiter(self):
alpha = 0.1
G = nx.path_graph(3)
max_iter = 0
try:
b = nx.katz_centrality(G, alpha, max_iter=max_iter)
except nx.NetworkXError as e:
assert str(max_iter) in e.args[0], "max_iter value not in error msg"
raise # So that the decorater sees the exception.
def kaltzCentrality(graph, numberOfPoints):
"""Compute the largest kalz centralities coefficients of a graph.
You can specify the number of points to output.
"""
c_eigenvector = nx.katz_centrality(graph)
c_eigenvector = heapq.nlargest(numberOfPoints,
list(c_eigenvector.values()))
return c_eigenvector
def test_beta_as_dict(self):
alpha = 0.1
beta = {0: 1.0, 1: 1.0, 2: 1.0}
b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449,
2: 0.5598852584152162}
G = networkx.path_graph(3)
b = networkx.katz_centrality(G, alpha, beta)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n], places=4)
def test_P3(self):
"""Katz centrality: P3"""
alpha = 0.1
G = nx.path_graph(3)
b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449,
2: 0.5598852584152162}
b = nx.katz_centrality(G, alpha)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n], places=4)
def test_P3(self):
"""Katz centrality: P3"""
alpha = 0.1
G = networkx.path_graph(3)
b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449,
2: 0.5598852584152162}
b = networkx.katz_centrality(G, alpha)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n], places=4)
def calculate_scores(self):
"""Computes the Kats centrality indexes for a given graph and with the tunable alpha parameter.
Returns:
:returns: kc. Returns the Kats centrality indexes.
:rtype: set
"""
kc = nx.katz_centrality(self.graph, self.alpha, beta=0).items()
return kc
def get_katz_centrality(Graph):
dictionary = nx.katz_centrality(Graph, max_iter=2000)
D = []
for name in dictionary:
D.append((name, dictionary[name]))
D.sort(key=lambda x: x[1])
D.reverse()
return D
def comparisons(G):
evec = nx.eigenvector_centrality(G)
print "EVEC:",evec
pagerank = nx.pagerank(G)
print "PAGERANK: ", pagerank
katz = nx.katz_centrality(G)
print "KATZ: ", katz
def test_beta_as_dict(self):
alpha = 0.1
beta = {0: 1.0, 1: 1.0, 2: 1.0}
b_answer = {0: 0.5598852584152165, 1: 0.6107839182711449,
2: 0.5598852584152162}
G = nx.path_graph(3)
b = nx.katz_centrality(G, alpha, beta)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n], places=4)
def test_maxiter(self):
alpha = 0.1
G = nx.path_graph(3)
max_iter = 0
try:
b = nx.katz_centrality(G, alpha, max_iter=max_iter)
except nx.NetworkXError as e:
assert str(
max_iter) in e.args[0], "max_iter value not in error msg"
raise # So that the decorater sees the exception.
def katz(g):
eigv = eig(nx.adjacency_matrix(g, weight='diff').todense())
max_eigv = max(eigv[0])
max_eigv_reciprocal = 1./max_eigv
alpha = max_eigv_reciprocal
alpha = 0.9 * alpha
beta = 1 - alpha
katz_centrality = nx.katz_centrality(g, alpha=alpha, beta=beta,
weight='diff')
return katz_centrality
def katz_cent(G):
A = nx.to_numpy_matrix(G)
e = np.linalg.eigvals(A)
maxe = np.max(np.real(e))
alpha = 1 / (2 * maxe)
return nx.katz_centrality(G, alpha=alpha)
def compute_mean_katz_cent(self):
"""Computes the mean Katz centrality of a network of neurons.
The centrality of a node measures how many of the shortest paths
between all other nodes pairs in the network pass through it. A node
with high centrality is thus crucial to efficient communication.
(Bullmore et. al. 2009)
https://en.wikipedia.org/wiki/Katz_centrality
"""
graph_centrality = nx.katz_centrality(self.network, weight="weight")
return np.mean(list(graph_centrality.values()))
def node_katz_centrality(nx_graph, dict=False):
"""
Calculate the katz centrality for the nodes
on the graph.
"""
katz_cent = nx.katz_centrality(nx_graph, max_iter=2000, tol=1e-03)
if not dict:
katz_cent = [(node, katz_cent[node])
for node in sorted(katz_cent, key=lambda v: katz_cent[v])]
return katz_cent
def test_K5_unweighted(self):
"""Katz centrality: K5"""
G = nx.complete_graph(5)
alpha = 0.1
b = nx.katz_centrality(G, alpha, weight=None)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n])
nstart = dict([(n, 1) for n in G])
b = nx.eigenvector_centrality_numpy(G)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[n], places=3)
def centralityMeasures(G): # Betweenness # betw = nx.betweenness_centrality(G, normalized=True, weight='weight') # print sorted([(k,v) for k,v in betw.iteritems()], key= lambda x:(-x[1],x[0])) # clsn = nx.closeness_centrality(G, normalized=True) # print sorted([(k,v) for k,v in clsn.iteritems()], key= lambda x:(-x[1],x[0])) # evec = nx.eigenvector_centrality(G, weight='weight') # print sorted([(k,v) for k,v in evec.iteritems()], key= lambda x:(-x[1],x[0])) katz = nx.katz_centrality(G, normalized=True, weight='weight', alpha=0.005) print sorted([(k,v) for k,v in katz.iteritems()], key= lambda x:(-x[1],x[0]))
def test_multiple_alpha(self):
alpha_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]
for alpha in alpha_list:
b_answer = {0.1: {0: 0.5598852584152165, 1: 0.6107839182711449,
2: 0.5598852584152162},
0.2: {0: 0.5454545454545454, 1: 0.6363636363636365,
2: 0.5454545454545454},
0.3: {0: 0.5333964609104419, 1: 0.6564879518897746,
2: 0.5333964609104419},
0.4: {0: 0.5232045649263551, 1: 0.6726915834767423,
2: 0.5232045649263551},
0.5: {0: 0.5144957746691622, 1: 0.6859943117075809,
2: 0.5144957746691622},
0.6: {0: 0.5069794004195823, 1: 0.6970966755769258,
2: 0.5069794004195823}}
G = nx.path_graph(3)
b = nx.katz_centrality(G, alpha)
for n in sorted(G):
assert_almost_equal(b[n], b_answer[alpha][n], places=4)
def calculate_center(tcgaSubgraph):
"""
DESCRIPTION: Calculate centrality measures
INPUT: Graph object
OUTPUT: Dictionary of dictionaries, each being a different centrality
measure
"""
# calculate maximum eigenvalue of graph
denseMat = nx.adjacency_matrix(tcgaSubgraph).todense() # make adj mat
eigs = numpy.linalg.eig(denseMat)[0] # calculate eigenvalues
maxEig = max(eigs)
alpha = 1 / maxEig.real
# calculate centrality measures
centers = {}
centers["eigen"] = nx.eigenvector_centrality(tcgaSubgraph)
centers["degree"] = nx.degree_centrality(tcgaSubgraph)
centers["katz"] = nx.katz_centrality(tcgaSubgraph, alpha=alpha - 0.01, beta=1.0)
centers["pagerank"] = nx.pagerank(tcgaSubgraph)
return centers
def centrality_calculation_by_networkx(G):
'''
使用 networkx 计算 Centrality
'''
d_c = nx.degree_centrality(G)
k_z = nx.katz_centrality(
G=G,
alpha=0.3,
beta=0.3,
max_iter=1000,
tol=1.0e-6,
nstart=None,
normalized=True)
# 归一化，每个元素除以集合中最大元素
d_c = [round(1.0 * item / max(d_c), 4) for item in d_c]
k_z = [round(1.0 * item / max(k_z), 4) for item in k_z]
nx_list = [{'Degree': d_c}, {'Katz': k_z}]
return nx_list
def test(G):
d_c = nx.degree_centrality(G)
e_v = nx.eigenvector_centrality(G=G, max_iter=1000, tol=1.0e-6)
k_z = nx.katz_centrality(
G=G,
alpha=0.3,
beta=0.3,
max_iter=1000,
tol=1.0e-6,
nstart=None,
normalized=True)
p_k = nx.pagerank(G=G, alpha=0.3, personalization=None, max_iter=100,
tol=1.0e-6, nstart=None, weight='weight', dangling=None)
b_c = nx.betweenness_centrality(G=G, k=None, normalized=True,
weight=None, endpoints=False, seed=None)
c_c = nx.closeness_centrality(G=G, u=None, distance=None, normalized=True)
d_c = [round(1.0 * item / max(d_c), 4) for item in d_c]
k_z = [round(1.0 * item / max(k_z), 4) for item in k_z]
e_v = [round(1.0 * item / max(e_v), 4) for item in e_v]
b_c = [round(1.0 * item / max(b_c), 4) for item in b_c]
c_c = [round(1.0 * item / max(c_c), 4) for item in c_c]
p_k = [round(1.0 * item / max(p_k), 4) for item in p_k]
return [{'Eigenvector': e_v},
{'Betweenness': b_c},
{'Closeness': c_c},
{'PageRank': p_k},
{'Degree': d_c},
{'Katz': k_z}]
dep_count = tz.pipe(edges, c.pluck(1), tz.frequencies)
dep_count['skimage']
import networkx as nx
deps = nx.DiGraph()
'scikit-image' in packages
'scikit-learn' in packages
for u, v in edges:
u = u.replace('scikit-', 'sk')
v = v.replace('scikit-', 'sk')
deps.add_edge(u, v)
deps.number_of_edges()
deps.number_of_nodes()
deps.node['skimage']
deps.in_edges('skimage')
nodes = nx.katz_centrality(deps)
central = sorted(deps.nodes(), key=nodes.__getitem__, reverse=True)
central[:10]
central[:20]
central[:40]
central[40:80]
central.index('skimage')
central.index('scipy')
import pickle
stdlib = pickle.load(open('/Users/jni/projects/depsy/data/python_standard_libs.pickle', 'rb'))
central_nonstd = list(tz.filter(lambda x: x not in stdlib, central))
len(central_nonstd)
central_nonstd.index('scipy')
len(central)
central[:5]
nx.is_connected(deps.to_undirected())
def test_maxiter(self):
alpha = 0.1
G = networkx.path_graph(3)
b = networkx.katz_centrality(G, alpha, max_iter=0)
def test_empty(self):
e = networkx.katz_centrality(networkx.Graph(), 0.1)
def make_net(centrality_name, in_path, out_path):
#sample code
#import _2_time_based_data_network_feature
#make_net_in_path = "../3.time_based_data/1.cite_relation_devide/"
#make_net_out_path = "../3.time_based_data/2.centrality_data/"
#_2_time_based_data.make_net( "in_degree", make_net_in_path, make_net_out_path)
#네트워크를 만들고 Centurality를 계산하고 저장할 것이다.
import networkx as nx
global Dump
Dump = {}
make_net_initialize(in_path)
start_time = time.time()
temp_start_time = time.time()
print "============= make_net start:" + centrality_name + " =============="
print "============= from 1951 to 2015 =============="
for year in range(1951, 2016):
print year
f_in = open(in_path + str(year) + "_cite.csv","r")
lines = f_in.readlines()
f_in.close()
edge_list = []
for line in lines:
data = line.split(",")
data_tuple = (data[0].strip(), data[1].strip())
edge_list.append(data_tuple)
Net = nx.DiGraph(edge_list)
Cen_in = {}
if (centrality_name == "in_degree"):
Cen_in = nx.in_degree_centrality(Net)
elif (centrality_name == "degree"):
Cen_in = nx.degree_centrality(Net)
elif (centrality_name == "eigenvector"):
Cen_in = nx.eigenvector_centrality_numpy(Net)
elif (centrality_name == "katz"):
Cen_in = nx.katz_centrality(Net)
elif (centrality_name == "pagerank"):
Cen_in = nx.pagerank(Net)
elif (centrality_name == "communicability"):
Net = nx.Graph(edge_list)
Cen_in = nx.communicability_centrality(Net)
elif (centrality_name == "load"):
Cen_in = nx.load_centrality(Net)
for j in Cen_in:
key = j
val = Cen_in[j]
Dump[key][year] = val
#저장하는 코드
f_out = open(out_path + centrality_name +"_centrality.csv", "w")
for key in Dump:
line = str(key)
for year in range(1951, 2016):
data = Dump[key].get(year, 0)
line = line + ","+ str(data)
line = line + "\n"
f_out.write(line)
f_out.close()
print "============= make_net end =============="
print(centrality_name + "takes %s seconds" % (time.time() - temp_start_time))
temp_start_time = time.time()
def add_katz_node(graf):
print "Adding katz to nodes"
k_dict = nx.katz_centrality(graf)
nx.set_node_attributes(graf, 'kat', k_dict)
for r in results:
edge_list.append((r[0],r[1]))
cur.close()
connection.close()
print edge_list
#set up a blank graph
G=nx.Graph()
#add edges from edge list to graph G
G.add_edges_from(edge_list)
#calculate degree and katz centrality in graph G
deg1 = nx.degree_centrality(G)
katz1 = nx.katz_centrality(G)
#print the nodes and edges from graph G
print 'Graph G has the following nodes: ',(G.nodes())
print 'Graph G has the following edges: ',(G.edges())
print 'Graph has degree centrality: ',deg1
print 'Graph has katz centrality: ', katz1
#
#edge_list_2 = []
#sql = "select call_from, call_to from random_calls where c_year = '2012' and c_week_no = '2'"
#cur.execute(sql)
#results = cur.fetchall()
#for r in results:
# edge_list_2.append((r[0],r[1]))
#
#print edge_list_2
#
def test_katz_centrality_unweighted(self):
G = self.H
alpha = self.H.alpha
p = nx.katz_centrality(G, alpha)
for (a, b) in zip(list(p.values()), self.G.evc):
assert_almost_equal(a, b)
def test_bad_beta_numbe(self):
G = nx.Graph([(0,1)])
e = nx.katz_centrality(G, 0.1,beta='foo')
def test_bad_beta(self):
G = nx.Graph([(0,1)])
beta = {0:77}
e = nx.katz_centrality(G, 0.1,beta=beta)
def test_empty(self):
e = nx.katz_centrality(nx.Graph(), 0.1)
assert_equal(e, {})
def test_multigraph(self):
e = nx.katz_centrality(nx.MultiGraph(), 0.1)
def classesGraph(self,c,files_dict,scope):
edges = []
interfaces = 'select path, superClass from classes'
files_Names = [x.split(".")[-1] for x in files_dict]
pathNames = {}
for row in c.execute(interfaces):
nameClass = (row[0]).split(".")[-1]
pathNames[nameClass] = row[0]
nameSuper = (row[1]).split(".")[-1]
if (nameClass in files_Names):
sup = 'root'
if (nameSuper in files_Names):
sup = nameSuper
edges.append((sup, nameClass))
g = networkx.DiGraph()
g.add_node('root')
g.add_edges_from(edges)
paths = networkx.single_source_dijkstra_path(g, 'root')
methods={}
for x in files_Names:
methods[x]=[]
methods['root']=[]
sigsEdges=[]
interfaces='select classPath,signature,return, name from methods where scope='+scope
for row in c.execute(interfaces):
nameClass = (row[0]).split(".")[-2]
if nameClass in files_Names:
methods[nameClass].append(row[3])
retAdd=[]
if row[2] in files_Names:
retAdd=[(nameClass,row[2])]
sigsEdges.extend([ (nameClass,x) for x in self.signatureTolst(row[1]) if x in files_Names]+retAdd)
fields='select classPath, name ,type from fields where scope='+scope
fields_d={}
for x in files_Names:
fields_d[x]=[]
fields_d['root']=[]
for row in c.execute(fields):
nameClass = (row[0]).split(".")[-2]
if nameClass in files_Names:
fields_d[nameClass].append(row[1])
type_f=[]
if row[2] in files_Names:
type_f=[(nameClass,row[2])]
sigsEdges.extend(type_f)
g2=networkx.DiGraph()
g2.add_node('root')
g2.add_edges_from(sigsEdges)
counts= Counter(sigsEdges)
g3=networkx.DiGraph()
g3.add_node('root')
for e,w in counts.items():
u,v=e
g3.add_edge(u,v,weight=w)
self.addFromDict(files_dict,g2.out_degree(),pathNames)
self.addFromDict(files_dict,networkx.katz_centrality(g2),pathNames)
self.addFromDict(files_dict,networkx.core_number(g2),pathNames)
self.addFromDict(files_dict,networkx.closeness_centrality(g2),pathNames)
self.addFromDict(files_dict,networkx.degree_centrality(g2),pathNames)
self.addFromDict(files_dict,networkx.out_degree_centrality(g2),pathNames)
self.addFromDict(files_dict,g3.out_degree(),pathNames)
self.addFromDict(files_dict,networkx.core_number(g3),pathNames)
self.addFromDict(files_dict,networkx.closeness_centrality(g3),pathNames)
self.addFromDict(files_dict,networkx.degree_centrality(g3),pathNames)
self.addFromDict(files_dict,networkx.out_degree_centrality(g3),pathNames)
#gi = igraph.Graph(edges = g2.edges(),directed=True)
#gi.modularity()
#self.addFromDict(files_dict,gi.community_optimal_modularity(),pathNames)
networkx.write_graphml(g,"C:\GitHub\weka\\graph.graphml")