def degree_fracture(infile, outfile, fraction, recalculate = False):
"""
Removes given fraction of nodes from infile network in reverse order of
degree centrality (with or without recalculation of centrality values
after each node removal) and saves the network in outfile.
"""
g = networkx.read_gml(infile)
m = networkx.degree_centrality(g)
l = sorted(m.items(), key = operator.itemgetter(1), reverse = True)
largest_component = max(networkx.connected_components(g), key = len)
n = len(g.nodes())
for i in range(1, n - 1):
g.remove_node(l.pop(0)[0])
if recalculate:
m = networkx.degree_centrality(g)
l = sorted(m.items(), key = operator.itemgetter(1),
reverse = True)
largest_component = max(networkx.connected_components(g), key = len)
if i * 1. / n >= fraction:
break
components = networkx.connected_components(g)
component_id = 1
for component in components:
for node in component:
g.node[node]["component"] = component_id
component_id += 1
networkx.write_gml(g, outfile)
def degree(infile, recalculate = False):
"""
Performs robustness analysis based on degree centrality,
on the network specified by infile using sequential (recalculate = True)
or simultaneous (recalculate = False) approach. Returns a list
with fraction of nodes removed, a list with the corresponding sizes of
the largest component of the network, and the overall vulnerability
of the network.
"""
g = networkx.read_gml(infile)
m = networkx.degree_centrality(g)
l = sorted(m.items(), key = operator.itemgetter(1), reverse = True)
x = []
y = []
largest_component = max(networkx.connected_components(g), key = len)
n = len(g.nodes())
x.append(0)
y.append(len(largest_component) * 1. / n)
R = 0.0
for i in range(1, n - 1):
g.remove_node(l.pop(0)[0])
if recalculate:
m = networkx.degree_centrality(g)
l = sorted(m.items(), key = operator.itemgetter(1),
reverse = True)
largest_component = max(networkx.connected_components(g), key = len)
x.append(i * 1. / n)
R += len(largest_component) * 1. / n
y.append(len(largest_component) * 1. / n)
return x, y, 0.5 - R / n
def degree_component(seed_num, graph=None, graph_json_filename=None, graph_json_str=None):
if graph_json_filename is None and graph_json_str is None and graph is None:
return []
G = None
if graph is not None:
G = graph
elif graph_json_str is None:
G = util.load_graph(graph_json_filename=graph_json_filename)
else:
G = util.load_graph(graph_json_str=graph_json_str)
components = list(nx.connected_components(G))
components = filter(lambda x: len(x) > 0.1 * len(G), components)
total_size = sum(map(lambda x: len(x), components))
total_nodes = 0
rtn = []
for comp in components[1:]:
num_nodes = int(float(len(comp)) / total_size * seed_num)
component = G.subgraph(list(comp))
clse_cent = nx.degree_centrality(component)
collector = collections.Counter(clse_cent)
clse_cent = collector.most_common(num_nodes)
rtn += map(lambda (x, y): x, clse_cent)
total_nodes += num_nodes
num_nodes = seed_num - total_nodes
component = G.subgraph(list(components[0]))
clse_cent = nx.degree_centrality(component)
collector = collections.Counter(clse_cent)
clse_cent = collector.most_common(num_nodes)
rtn += map(lambda (x, y): x, clse_cent)
return rtn
def degree_removal(g, recalculate=False):
"""
Performs robustness analysis based on degree centrality,
on the network specified by infile using sequential (recalculate = True)
or simultaneous (recalculate = False) approach. Returns a list
with fraction of nodes removed, a list with the corresponding sizes of
the largest component of the network, and the overall vulnerability
of the network.
"""
m = nx.degree_centrality(g)
l = sorted(m.items(), key=operator.itemgetter(1), reverse=True)
x = []
y = []
dimension = fd.fractal_dimension(g, iterations=100, debug=False)
n = len(g.nodes())
x.append(0)
y.append(dimension)
for i in range(1, n-1):
g.remove_node(l.pop(0)[0])
if recalculate:
m = nx.degree_centrality(g)
l = sorted(m.items(), key=operator.itemgetter(1),
reverse=True)
dimension = fd.fractal_dimension(g, iterations=100, debug=False)
x.append(i * 1. / n)
y.append(dimension)
return x, y
def sna_calculations(g, play_file):
"""
:param g: a NetworkX graph object
:type g: object
:param play_file: the location of a play in .txt format
:type play_file: string
:return: returns a dictionary containing various network related figures
:rtype: dict
:note: also writes into results/file_name-snaCalculations.csv and results/allCharacters.csv
"""
file_name = os.path.splitext(os.path.basename(play_file))[0]
sna_calculations_list = dict()
sna_calculations_list['playType'] = file_name[0]
sna_calculations_list['avDegreeCentrality'] = numpy.mean(numpy.fromiter(iter(nx.degree_centrality(g).values()),
dtype=float))
sna_calculations_list['avDegreeCentralityStd'] = numpy.std(
numpy.fromiter(iter(nx.degree_centrality(g).values()), dtype=float))
sna_calculations_list['avInDegreeCentrality'] = numpy.mean(
numpy.fromiter(iter(nx.in_degree_centrality(g).values()), dtype=float))
sna_calculations_list['avOutDegreeCentrality'] = numpy.mean(
numpy.fromiter(iter(nx.out_degree_centrality(g).values()), dtype=float))
try:
sna_calculations_list['avShortestPathLength'] = nx.average_shortest_path_length(g)
except:
sna_calculations_list['avShortestPathLength'] = 'not connected'
sna_calculations_list['density'] = nx.density(g)
sna_calculations_list['avEigenvectorCentrality'] = numpy.mean(
numpy.fromiter(iter(nx.eigenvector_centrality(g).values()), dtype=float))
sna_calculations_list['avBetweennessCentrality'] = numpy.mean(
numpy.fromiter(iter(nx.betweenness_centrality(g).values()), dtype=float))
sna_calculations_list['DegreeCentrality'] = nx.degree_centrality(g)
sna_calculations_list['EigenvectorCentrality'] = nx.eigenvector_centrality(g)
sna_calculations_list['BetweennessCentrality'] = nx.betweenness_centrality(g)
# sna_calculations.txt file
sna_calc_file = csv.writer(open('results/' + file_name + '-snaCalculations.csv', 'wb'), quoting=csv.QUOTE_ALL,
delimiter=';')
for key, value in sna_calculations_list.items():
sna_calc_file.writerow([key, value])
# all_characters.csv file
if not os.path.isfile('results/allCharacters.csv'):
with open('results/allCharacters.csv', 'w') as f:
f.write(
'Name;PlayType;play_file;DegreeCentrality;EigenvectorCentrality;BetweennessCentrality;speech_amount;AverageUtteranceLength\n')
all_characters = open('results/allCharacters.csv', 'a')
character_speech_amount = speech_amount(play_file)
for character in sna_calculations_list['DegreeCentrality']:
all_characters.write(character + ';' + str(sna_calculations_list['playType']) + ';' + file_name + ';' + str(
sna_calculations_list['DegreeCentrality'][character]) + ';' + str(
sna_calculations_list['EigenvectorCentrality'][character]) + ';' + str(
sna_calculations_list['BetweennessCentrality'][character]) + ';' + str(
character_speech_amount[0][character]) + ';' + str(character_speech_amount[1][character]) + '\n')
all_characters.close()
return sna_calculations
def __init__(self, time, voteomat):
self.foldername = voteomat.network_func_name + voteomat.distribution_func_name
self.foldertime = time
self.path = "Statistics//"+self.foldername+"//"
self.path += g_candidates_affecting_nodes + "=" + str(voteomat.candidates_affecting) + "_"
self.path += g_candidates_affected_by_median + "=" + str(voteomat.candidates_affected) + "_"
self.path += g_neighbours_affecting_each_other + "=" + str(voteomat.affecting_neighbours) + "_"
self.path += g_counterforce_affecting_candidates + "=" + str(voteomat.counter_force_affecting) + "_"
self.path += "counterforce_left="+str(voteomat.counter_force_left)+"_"+"counterforce_right="+str(voteomat.counter_force_right)+ "_" + time
self.make_sure_path_exists(self.path)
self.file = open(self.path + "//statistic.csv", 'w')
self.statistic = {}
self.statistic["networkfunc"] = voteomat.network_func_name
self.statistic["distributionfunc"] = voteomat.distribution_func_name
self.statistic["acceptance"] = voteomat.acceptance
median, avg, std = voteomat.get_statistic()
self.statistic["median"] = []
self.statistic["median"].append(median)
self.statistic["avg"] = []
self.statistic["avg"].append(avg)
self.statistic["std"] = []
self.statistic["std"].append(std)
self.statistic["node_with_highest_degree_centrality"] = []
self.max_degree_node = max( nx.degree_centrality(voteomat.get_network()).items(),key = lambda x: x[1])[0]
self.statistic["node_with_highest_degree_centrality"].append(voteomat.get_network().nodes(data = True)[self.max_degree_node][1]["orientation"])
self.statistic["node_with_minimum_degree_centrality"] = []
self.min_degree_node = min(nx.degree_centrality(voteomat.get_network()).items(), key = lambda x: x[1])[0]
self.statistic["node_with_minimum_degree_centrality"].append(voteomat.get_network().nodes(data = True)[self.min_degree_node][1]["orientation"])
self.statistic["node_with_highest_closeness_centrality"] = []
self.max_closeness_node = max( nx.closeness_centrality(voteomat.get_network()).items(),key = lambda x: x[1])[0]
self.statistic["node_with_highest_closeness_centrality"].append(voteomat.get_network().nodes(data = True)[self.max_closeness_node][1]["orientation"])
self.statistic["node_with_highest_betweenness_centrality"] = []
self.max_betweenness_node = max(nx.betweenness_centrality(voteomat.get_network()).items() ,key = lambda x: x[1])[0]
self.statistic["node_with_highest_betweenness_centrality"].append(voteomat.get_network().nodes(data = True)[self.max_betweenness_node][1]["orientation"])
try:
self.statistic["node_with_highest_eigenvector_centrality"] = []
self.max_eigenvector_node = max( nx.eigenvector_centrality(voteomat.get_network(), max_iter = 1000).items(),key = lambda x: x[1])[0]
self.statistic["node_with_highest_eigenvector_centrality"].append(voteomat.get_network().nodes(data = True)[self.max_eigenvector_node][1]["orientation"])
except nx.NetworkXError:
print "Eigenvector centrality not possible."
freeman = self.freeman_centrality([x[1] for x in nx.degree_centrality(voteomat.get_network()).items()], max( nx.degree_centrality(voteomat.get_network()).items(),key = lambda x: x[1])[1])
self.statistic["freeman_centrality"] = round(freeman,2)
self.statistic["affecting_neighbours"] = voteomat.affecting_neighbours
self.statistic["affecting_candidates"] = voteomat.candidates_affecting
self.statistic["affected_canddiates"] = voteomat.candidates_affected
self.statistic["affecting_counter_force"] = voteomat.counter_force_affecting
self.statistic["affecting_counter_force_left"] = voteomat.counter_force_left
self.statistic["affecting_counter_force_right"] = voteomat.counter_force_right
self.statistic["candidates"] = []
for candidate in voteomat.candidates:
self.statistic["candidates"].append(candidate.to_save())
self.statistic["network"] = voteomat.get_network().nodes(data=True);
def degree_apl(g, recalculate=False):
"""
Performs robustness analysis based on degree centrality,
on the network specified by infile using sequential (recalculate = True)
or simultaneous (recalculate = False) approach. Returns a list
with fraction of nodes removed, a list with the corresponding sizes of
the largest component of the network, and the overall vulnerability
of the network.
"""
m = networkx.degree_centrality(g)
l = sorted(m.items(), key=operator.itemgetter(1), reverse=True)
x = []
y = []
average_path_length = 0.0
number_of_components = 0
n = len(g.nodes())
for sg in networkx.connected_component_subgraphs(g):
average_path_length += networkx.average_shortest_path_length(sg)
number_of_components += 1
average_path_length = average_path_length / number_of_components
initial_apl = average_path_length
x.append(0)
y.append(average_path_length * 1. / initial_apl)
r = 0.0
for i in range(1, n - 2):
g.remove_node(l.pop(0)[0])
if recalculate:
m = networkx.degree_centrality(g)
l = sorted(m.items(), key=operator.itemgetter(1),
reverse=True)
average_path_length = 0.0
number_of_components = 0
for sg in networkx.connected_component_subgraphs(g):
if len(sg.nodes()) > 1:
average_path_length += networkx.average_shortest_path_length(sg)
number_of_components += 1
average_path_length = average_path_length / number_of_components
x.append(i * 1. / initial_apl)
r += average_path_length * 1. / initial_apl
y.append(average_path_length * 1. / initial_apl)
return x, y, r / initial_apl
def labels(G, threshhold = 95):
'''return labels(dictionary) for nodes with high centrality for a given percentile'''
labels = {}
# create cutoff based on the given percentile
cen_cutoff = np.percentile(list(nx.degree_centrality(G).values()), threshhold)
# put nodes label in the dictionary if the centrality passes the threshold
for key,value in nx.degree_centrality(G).items():
if value >= cen_cutoff:
labels[key] = key
return labels
def __init__(self) :
self.g = nx.barabasi_albert_graph(random.randint(100,1000),random.randint(2,7))
self.degree_centrality = nx.degree_centrality(self.g)
self.deg = nx.degree_centrality(self.g)
self.sorted_deg = sorted(self.deg.items(), key=operator.itemgetter(1))
self.nodes = len(self.g.nodes())
self.edges = len(self.g.edges())
self.degree_rank()
self.degree_dict = self.g.degree()
self.avg_deg = sum(self.g.degree().values())/float(len(self.g.nodes()))
#print self.rank
#print self.degree_dict
self.form_dataset()
def degree_centrality(self, withme=True, node=None, average=False):
if node==None:
if withme:
my_dict = nx.degree_centrality(self.mynet)
new = {}
new2={}
for i in my_dict:
new[self.id_to_name(i)] = my_dict[i]
new2[i] = my_dict[i]
if average:
print "The average is " + str(round(sum(new.values())/float(len(new.values())),4))
else:
for i,j in new.items():
print i, round(j,4)
return new2
else:
my_dict = nx.degree_centrality(self.no_ego_net)
new = {}
new2={}
for i in my_dict:
new[self.id_to_name(i)] = my_dict[i]
new2[i] = my_dict[i]
if average:
print "The average is " + str(round(sum(new.values())/float(len(new.values())),4))
else:
for i,j in new.items():
print i, round(j,4)
return new2
else:
if withme:
my_dict = nx.degree_centrality(self.mynet)
try:
print "The coefficient for node "+str(node)+ "is "+ str(round(my_dict[node],4))
except:
try:
return my_dict [self.name_to_id(node)]
except:
print "Invalid node name"
else:
my_dict = nx.degree_centrality(self.no_ego_net)
try:
print "The coefficient for node "+str(node)+ "is "+ str(round(my_dict[node],4))
except:
try:
print "The coefficient for node "+str(node)+ "is "+ str(round(my_dict[[self.name_to_id(node)]],4))
except:
print "Invalid node name"
def set_capacities_degree_gravity(topology, capacities, capacity_unit='Mbps'):
"""
Set link capacities proportionally to the product of the degrees of the
two end-points of the link
Parameters
----------
topology : Topology
The topology to which link capacities will be set
capacities : list
A list of all possible capacity values
capacity_unit : str, optional
The unit in which capacity value is expressed (e.g. Mbps, Gbps etc..)
"""
if topology.is_directed():
in_degree = nx.in_degree_centrality(topology)
out_degree = nx.out_degree_centrality(topology)
gravity = {(u, v): out_degree[u] * in_degree[v]
for (u, v) in topology.edges()}
else:
degree = nx.degree_centrality(topology)
gravity = {(u, v): degree[u] * degree[v]
for (u, v) in topology.edges()}
_set_capacities_proportionally(topology, capacities, gravity,
capacity_unit=capacity_unit)
def high_degrees_fast(seed_num, graph=None, graph_json_filename=None, graph_json_str=None):
"""
Find the high-degree nodes of the given graph by sorting on the adjacency
list lengths and slicing.
Parameters:
seed_num: Number of nodes to choose.
graph_json_filename: Filename where the adjacency list lives as JSON.
graph_json_str: Graph as an adjacency list string in JSON.
Return: List of 'seed_num' highest degree nodes.
"""
if graph_json_filename is None and graph_json_str is None and graph is None:
return []
G = None
if graph is not None:
G = graph
elif graph_json_str is None:
G = util.load_graph(graph_json_filename=graph_json_filename)
else:
G = util.load_graph(graph_json_str=graph_json_str)
clse_cent = nx.get_node_attributes(G, "centrality")
if len(clse_cent) == 0:
clse_cent = nx.degree_centrality(G)
nx.set_node_attributes(G, "centrality", clse_cent)
print "hi high-degree"
collector = collections.Counter(clse_cent)
clse_cent = collector.most_common(seed_num)
return map(lambda (x, y): x, clse_cent)
def centrality_month_airports(data):
df = data.copy()
df['DateOfDeparture'] = pd.to_datetime(df['DateOfDeparture'])
df['month'] = df['DateOfDeparture'].dt.week.astype(str)
df['year'] = df['DateOfDeparture'].dt.year.astype(str)
df['year_month'] = df[['month','year']].apply(lambda x: '-'.join(x),axis=1)
df['year_month_dep'] = df[['Departure','month','year']].apply(lambda x: '-'.join(x),axis=1)
df['year_month_arr'] = df[['Arrival','month','year']].apply(lambda x: '-'.join(x),axis=1)
year_month = pd.unique(df['year_month'])
G = nx.Graph()
centrality = {}
for i, item in enumerate(year_month):
sub_df = df[df['year_month'] == item][['Departure','Arrival']]
list_dep_arr = zip(sub_df['Departure'], sub_df['Arrival'])
G.add_edges_from(list_dep_arr)
#G.number_of_nodes()
#G.number_of_edges()
centrality_month = nx.degree_centrality(G)
centrality_month = pd.DataFrame(centrality_month.items())
centrality_month['year_month'] = [item] * centrality_month.shape[0]
centrality_month['airport_year_month'] = centrality_month[centrality_month.columns[[0,2]]].apply(lambda x: '-'.join(x),axis=1)
centrality_month =dict(zip(centrality_month['airport_year_month'], centrality_month[1]))
z = centrality.copy()
z.update(centrality_month)
centrality = z
df['centrality_month_dep'] = df['year_month_dep'].map(centrality)
df['centrality_month_arr'] = df['year_month_arr'].map(centrality)
return df
def degree_centrality(graph, records):
""" Reports on the most central individuals in the graph """
dc = nx.degree_centrality(graph)
nodes = sorted(dc.items(), key=operator.itemgetter(1), reverse=True)[:records]
print("Degree Centrality - top {} individuals".format(records))
for n in nodes:
print(" {:30}:\t{}".format(n[0], n[1]))
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 fast_approximate_solution_two(graph):
"""
Given a graph, construct a solution greedily using approximation methods.
Performs bad.
"""
new_graph = nx.Graph()
degrees = nx.degree_centrality(graph)
largest = argmax(degrees)
new_graph.add_node(largest)
while new_graph.number_of_edges() < graph.number_of_nodes() - 1:
degrees = {n: count_uncovered_degree(graph, new_graph, n) for n in nx.nodes(graph)}
neighbor_list = [nx.neighbors(graph, n) for n in new_graph.nodes()]
neighbors = set()
for lst in neighbor_list:
neighbors = neighbors.union(lst)
if not neighbors:
break
next_largest = argmax_in(degrees, neighbors, exceptions = new_graph.nodes())
possible_edge_ends = [n for n in nx.neighbors(graph, next_largest)
if graph.has_edge(n, next_largest)
and n in new_graph.nodes()]
new_graph.add_node(next_largest)
edge_end = argmax_in(degrees, possible_edge_ends)
new_graph.add_edge(edge_end, next_largest)
return new_graph
def modularity(self):
"""
Compute the modularity.
Returns:
Numerical value of the modularity of the graph.
"""
g = self.gr
A = nx.adj_matrix(g)
degDict = nx.degree_centrality(g)
adjDict = {}
n = A.shape[0]
B = A.sum(axis=1)
for i in range(n):
adjDict[g.nodes()[i]] = B[i,0]
m = len(g.edges())
connComponents = nx.connected_components(g)
mod = 0
for c in connComponents:
edgesWithinCommunity = 0
randomEdges = 0
for u in c:
edgesWithinCommunity += adjDict[u]
randomEdges += degDict[u]
mod += (float(edgesWithinCommunity) - float(randomEdges * randomEdges)/float(2 * m))
mod = mod/float(2 * m)
return mod
def run_main(file):
NumberOfStations=465
print file
adjmatrix = np.loadtxt(file,delimiter=' ',dtype=np.dtype('int32'))
# for i in range (0,NumberOfStations):
# if(adjmatrix[i,i]==1):
# print "posicion: ["+str(i)+","+str(i)+"]"
g = nx.from_numpy_matrix(adjmatrix, create_using = nx.MultiGraph())
degree = g.degree()
density = nx.density(g)
degree_centrality = nx.degree_centrality(g)
clossness_centrality = nx.closeness_centrality(g)
betweenless_centrality = nx.betweenness_centrality(g)
print degree
print density
print degree_centrality
print clossness_centrality
print betweenless_centrality
#nx.draw(g)
# np.savetxt(OutputFile, Matrix, delimiter=' ',newline='\n',fmt='%i')
def draw_graph(label_flag=True, remove_isolated=True, different_size=True, iso_level=10, node_size=40):
G=build_graph(fb.get_friends_network())
betweenness=nx.betweenness_centrality(G)
degree=nx.degree_centrality(G)
degree_num=[ degree[v] for v in G]
maxdegree=max(degree_num);mindegree=min(degree_num);
print maxdegree,mindegree
clustering=nx.clustering(G)
print nx.transitivity(G)
# Judge whether remove the isolated point from graph
if remove_isolated is True:
H = nx.empty_graph()
for SG in nx.connected_component_subgraphs(G):
if SG.number_of_nodes() > iso_level:
H = nx.union(SG, H)
G = H
# Ajust graph for better presentation
if different_size is True:
L = nx.degree(G)
G.dot_size = {}
for k, v in L.items():
G.dot_size[k] = v
#node_size = [betweenness[v] *1000 for v in G]
node_size = [G.dot_size[v] * 10 for v in G]
node_color= [((degree[v]-mindegree))/(maxdegree-mindegree) for v in G]
#edge_width = [getcommonfriends(u,v) for u,v in G.edges()]
pos = nx.spring_layout(G, iterations=15)
nx.draw_networkx_edges(G, pos, alpha=0.05)
nx.draw_networkx_nodes(G, pos, node_size=node_size, node_color=node_color, vmin=0.0,vmax=1.0, alpha=0.3)
# Judge whether shows label
if label_flag is True:
nx.draw_networkx_labels(G, pos, font_size=6,alpha=0.1)
#nx.draw_graphviz(G)
plt.show()
return G
def mean_degree_centrality(pg, normalize=0):
"""
mean_degree_centrality(pg) calculates mean in- and out-degree
centralities for directed graphs and simple degree-centralities
for undirected graphs. If the normalize flag is set, each node's
centralities are weighted by the number of edges in the (di)graph.
"""
centrality = {}
try:
if networkx.is_directed_acyclic_graph(pg):
cent_sum_in, cent_sum_out = 0, 0
for n in pg.nodes():
n_cent_in = pg.in_degree(n)
n_cent_out = pg.out_degree(n)
if normalize:
n_cent_in = float(n_cent_in) / float(pg.size()-1)
n_cent_out = float(n_cent_out) / float(pg.size()-1)
cent_sum_in = cent_sum_in + n_cent_in
cent_sum_out = cent_sum_out + n_cent_out
centrality['in'] = cent_sum_in / float(pg.order())
centrality['out'] = cent_sum_out / float(pg.order())
else:
cent_sum = 0
for n in pg.nodes():
if not normalize:
n_cent = pg.degree(n)
else:
n_cent = networkx.degree_centrality(pg,n)
cent_sum = cent_sum + n_cent
centrality['all'] = cent_sum / float(pg.order())
except:
logging.error('pyp_network.mean_degree_centrality() failed!')
return centrality
def plotGraph(G, figsize=(8, 8), filename=None):
"""
Plots an individual graph, node size by degree centrality,
edge size by edge weight.
"""
labels = {n:n for n in G.nodes()}
d = nx.degree_centrality(G)
layout=nx.spring_layout
pos=layout(G)
plt.figure(figsize=figsize)
plt.subplots_adjust(left=0,right=1,bottom=0,top=0.95,wspace=0.01,hspace=0.01)
# nodes
nx.draw_networkx_nodes(G,pos,
nodelist=G.nodes(),
node_color="steelblue",
node_size=[v * 250 for v in d.values()],
alpha=0.8)
try:
weights = [G[u][v]['weight'] for u,v in G.edges()]
except:
weights = [1 for u,v in G.edges()]
nx.draw_networkx_edges(G,pos,
with_labels=False,
edge_color="grey",
width=weights
)
if G.order() < 1000:
nx.draw_networkx_labels(G,pos, labels)
plt.savefig(filename)
plt.close("all")
def compute_static_graph_statistics(G,start_time,end_time):
verts = G.vertices
n = len(verts)
m = float(end_time - start_time)
agg_statistics = [dict.fromkeys(verts,0),dict.fromkeys(verts,0),dict.fromkeys(verts,0)]*3
avg_statistics = [dict.fromkeys(verts,0),dict.fromkeys(verts,0),dict.fromkeys(verts,0)]*3
aggregated_graph = nx.Graph()
aggregated_graph.add_nodes_from(verts)
start_time = max(1,start_time)
for t in xrange(start_time,end_time+1):
aggregated_graph.add_edges_from(G.snapshots[t].edges_iter())
dc = G.snapshots[t].degree()
cc = nx.closeness_centrality(G.snapshots[t])
bc = nx.betweenness_centrality(G.snapshots[t])
for v in verts:
avg_statistics[0][v] += dc[v]/(n-1.0)
avg_statistics[1][v] += cc[v]
avg_statistics[2][v] += bc[v]
for v in verts:
avg_statistics[0][v] = avg_statistics[0][v]/m
avg_statistics[1][v] = avg_statistics[1][v]/m
avg_statistics[2][v] = avg_statistics[2][v]/m
dc = nx.degree_centrality(aggregated_graph)
cc = nx.closeness_centrality(aggregated_graph)
bc = nx.betweenness_centrality(aggregated_graph)
for v in verts:
agg_statistics[0][v] = dc[v]
agg_statistics[1][v] = cc[v]
agg_statistics[2][v] = bc[v]
return (agg_statistics, avg_statistics)
def degree_centrality(graph, outfile, records=10):
""" Perform a degree centrality analysis on graph """
ranking = nx.degree_centrality(graph)
ordering = sorted(ranking.items(), key=operator.itemgetter(1), reverse=True)[:records]
print("Employee,Degree Centrality", file=outfile)
for employee, rank in ordering:
print("{},{}".format(employee, rank), file=outfile)
def degree_centrality_report(graph, n):
""" Reports on the top n most central individuals on the graph """
pr = nx.degree_centrality(graph)
nodes = sorted(pr.items(), key=operator.itemgetter(1), reverse=True)[:n]
print("Degree Centrality - top {} individuals".format(n))
for n in nodes:
print(" {:30}:\t{}".format(n[0], n[1]))
def degree_centrality(graph):
centrality = nx.degree_centrality(graph)
nx.set_node_attributes(graph, 'centrality', centrality)
degrees = sorted(centrality.items(), key=itemgetter(1), reverse=True)
for idx, item in enumerate(degrees[0:10]):
item = (idx+1,) + item + (graph.degree(item[0]),)
print "%i. %s: %0.3f (%i)" % item
def print_info(G):
#info prints name, type, number of nodes and edges, and average degree already
print(nx.info(G))
print "Density: ", nx.density(G)
print "Number of connected components: ", nx.number_connected_components(G)
all_degree_cent = nx.degree_centrality(G)
all_bet_cent = nx.betweenness_centrality(G)
all_close_cent = nx.closeness_centrality(G)
oldest = []
agerank = 0
names = []
print ("Node, Degree Centrality, Betweenness Centrality, Closeness Centrality:")
for x in range(G.number_of_nodes()):
names.append(G.nodes(data=True)[x][1]['label'])
if G.nodes(data=True)[x][1]['agerank'] >= agerank:
if G.nodes(data=True)[x][1]['agerank'] != agerank:
oldest = []
agerank = G.nodes(data=True)[x][1]['agerank']
oldest.append(G.nodes(data=True)[x][1])
print G.nodes(data=True)[x][1]['label'],' %.2f' % all_degree_cent.get(x),\
' %.2f' % all_bet_cent.get(x),\
' %.2f' % all_close_cent.get(x)
print "Oldest facebook(s): ", ', '.join([x['label'] for x in oldest])
return names
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 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 allocate(G_phy, G_bgp):
log.info("Allocating route reflectors")
graph_phy = G_phy._graph
for asn, devices in G_phy.groupby("asn").items():
routers = [d for d in devices if d.is_router]
router_ids = ank_utils.unwrap_nodes(routers)
subgraph_phy = graph_phy.subgraph(router_ids)
if len(subgraph_phy) == 1:
continue # single node in graph, no ibgp
betw_cen = nx.degree_centrality(subgraph_phy)
ordered = sorted(subgraph_phy.nodes(), key = lambda x: betw_cen[x], reverse = True)
rr_count = len(subgraph_phy)/5 # Take top 20% to be route reflectors
route_reflectors = ordered[:rr_count] # most connected 20%
rr_clients = ordered[rr_count:] # the other routers
route_reflectors = list(ank_utils.wrap_nodes(G_bgp, route_reflectors))
rr_clients = list(ank_utils.wrap_nodes(G_bgp, rr_clients))
G_bgp.update(route_reflectors, route_reflector = True) # mark as route reflector
# rr <-> rr
over_links = [(rr1, rr2) for rr1 in route_reflectors for rr2 in route_reflectors if rr1 != rr2]
G_bgp.add_edges_from(over_links, type = 'ibgp', direction = 'over')
# client -> rr
up_links = [(client, rr) for (client, rr) in itertools.product(rr_clients, route_reflectors)]
G_bgp.add_edges_from(up_links, type = 'ibgp', direction = 'up')
# rr -> client
down_links = [(rr, client) for (client, rr) in up_links] # opposite of up
G_bgp.add_edges_from(down_links, type = 'ibgp', direction = 'down')
log.debug("iBGP done")
def plotGraph(graph, color="r", figsize=(12, 8)):
labels = {n:n for n in graph.nodes()}
d = nx.degree_centrality(graph)
layout=nx.spring_layout
pos=layout(graph)
plt.figure(figsize=figsize)
plt.subplots_adjust(left=0,right=1,bottom=0,top=0.95,wspace=0.01,hspace=0.01)
# nodes
nx.draw_networkx_nodes(graph,pos,
nodelist=graph.nodes(),
node_color=color,
node_size=[v * 250 for v in d.values()],
alpha=0.8)
nx.draw_networkx_edges(graph,pos,
with_labels=False,
edge_color=color,
width=0.50
)
if graph.order() < 1000:
nx.draw_networkx_labels(graph,pos, labels)
return plt
def centrality(G2):
print("Running Centrality Module")
# Check the type of centrality, and calculate for each node
if myargs.centrality == "degree":
cent = nx.degree_centrality(G2)
cent_size = numpy.fromiter(cent.values(), float)
print(cent)
if myargs.centrality == "eigen":
cent = nx.eigenvector_centrality(G2)
cent_size = numpy.fromiter(cent.values(), float)
print(cent)
if myargs.centrality == "betweenness":
cent = nx.betweenness_centrality(G2)
cent_size = numpy.fromiter(cent.values(), float)
print(cent)
if myargs.centrality == "closeness":
cent = nx.closeness_centrality(G2)
cent_size = numpy.fromiter(cent.values(), float)
print(cent)
# This gives a degree frequency index (useful to compare to Power Law)
degree_G2 = nx.degree(G2)
degree_df = pd.DataFrame(degree_G2, columns=["Node", "Degree"])
degree_list = degree_df["Degree"].to_numpy()
degree_freq_G2 = nx.degree_histogram(G2)
degree_freq_df = pd.DataFrame(degree_freq_G2, columns=["Frequency"])
degree_freq_df["Degree"] = degree_freq_df.index
degree_freq_df = degree_freq_df[["Degree", "Frequency"]]
degree_df.to_csv(f"{edge_file}_Freq.txt", sep="\t")
# This allows us to compare centrality between two different
Cents1 = []
Cents0 = []
for v in G2.nodes:
if v in group:
G2.nodes[v]["subgroup"] = 1
G2.nodes[v]["centrality"] = cent[v]
Cents1.append(cent[v])
else:
G2.nodes[v]["subgroup"] = 0
G2.nodes[v]["centrality"] = cent[v]
Cents0.append(cent[v])
node_color = [get_color(G2.nodes[v]["subgroup"]) for v in G2.nodes]
# print(G2.nodes)
# print(Cents1)
# print(Cents0)
# Output1: Graph, Highlight High Centrality & Groups.
plt.figure()
nx.draw(
G2,
pos=None,
with_labels=True,
node_color=node_color,
node_size=cent_size * 2000,
width=1,
) # ,ax=fig.subplot(111))
plt.savefig(f"{myargs.centrality}_{myargs.thresh}_{edge_file}_Network.png")
# plt.show()
# Output2: Degree Histogram
fig = plt.figure("Degree of Graph", figsize=(8, 8))
# Create a gridspec for adding subplots of different sizes
# axgrid = fig.add_gridspec(5, 4)
# ax2 = fig.add_subplot(axgrid[:, :])
# ax2.bar(*numpy.unique(degree_sequence, return_counts=True))
# ax2.set_title("Degree histogram")
# ax2.set_xlabel("Degree")
# ax2.set_ylabel("# of Nodes")
histoimage = plt.hist(cent.values(), range=[0, 0.15], color="skyblue")
fig.tight_layout()
fig.savefig(f"{myargs.centrality}_{myargs.thresh}_{edge_file}_Histo.png")
def central_characters(graph, n=10):
res = Counter(nx.degree_centrality(graph)).most_common(n)
return res
import pickle
import networkx as nx
import matplotlib.pyplot as plt
from nxviz import MatrixPlot, CircosPlot
from nxviz.plots import ArcPlot
from itertools import combinations
from collections import defaultdict
graph = pickle.load(open('github_users.p', 'rb'))
print("no. of users: " + str(len(graph.nodes())))
print("no. of user-collaborations(p2p) : " + str(len(graph.edges())))
plt.hist(list(nx.degree_centrality(graph).values()))
plt.show()
# Calculate the largest connected component subgraph
largest_ccs = sorted(nx.connected_component_subgraphs(graph),
key=lambda x: len(x))[-1]
h = MatrixPlot(largest_ccs)
h.draw()
plt.show()
for n, d in graph.nodes(data=True):
graph.node[n]['degree'] = nx.degree(graph, n)
# a = ArcPlot(graph=graph, node_order='degree')
# a.draw()
def getSCV(v, g):
return nx.degree_centrality(g)[v]
G = nx.DiGraph()
df = pd.read_csv(path, sep="\t")
nodes = df.iloc[:, 1].unique().tolist()
edges = [(f[0], f[1]) for f in df.as_matrix()]
G.add_nodes_from(nodes)
G.add_edges_from(edges)
return G
# 2
# A
hits = nx.hits_scipy(g)
pagerank = nx.pagerank_scipy(g) # default .85
eigen = nx.eigenvector_centrality(g)
degree = nx.degree_centrality(g)
get_top_hubs = lambda hits: get_top_nodes(hits[0])
get_top_auths = lambda hits: get_top_nodes(hits[1])
def get_top_nodes(d, n=20):
return map(lambda x: x[0], sorted(d.items(), key=lambda x: x[1]))[0:n]
get_top_nodes(degree)
get_top_nodes(eigen)
get_top_nodes(pagerank)
get_top_hubs(hits)
get_top_auths(hits)
nodes.set_norm(mcolors.SymLogNorm(linthresh=0.01, linscale=1))
# labels = nx.draw_networkx_labels(G, pos)
edges = nx.draw_networkx_edges(G, pos)
plt.title(measure_name)
plt.colorbar(nodes)
plt.axis('off')
plt.show()
pos = nx.spring_layout(G)
my_graph = nx.DiGraph()
my_graph.add_edges_from(G.edges())
d = nx.degree_centrality(G)
print(d)
#draw(my_graph, pos=none, nx.degree_centrality(my_graph), 'Degree of Centrality')
d = nx.in_degree_centrality(my_graph)
print(d)
draw(my_graph, pos, d, 'Degree of Incentrality')
d = nx.out_degree_centrality(my_graph)
print(d)
draw(my_graph, pos, d, 'Degree of Outcentrality')
"""### Eigen Vector Centrality
indegree and outdegree ka different
"""
e = nx.eigenvector_centrality(G)
def main():
qid = sys.argv[1]
for cdo in CDO.objects.values('doc', 'citation').distinct()[:5]:
print(cdo)
#CDO.objects.filter(pk__in=CDO.objects.filter(doc=).values_list('id', flat=True)[1:]).delete()
sys.exit()
#time.sleep(14400)
q = Query.objects.get(pk=qid)
mdocs = Doc.objects.filter(query=q, wosarticle__cr__isnull=False)
cdos = CDO.objects.filter(doc__query=q)
# cdos = CDO.objects.filter(
# doc__in=mdocs.values_list('UT',flat=True)
# )
m = mdocs.count()
m_dict = dict(zip(list(mdocs.values_list('UT', flat=True)),
list(range(m))))
rev_m_dict = dict(
zip(list(range(m)), list(mdocs.values_list('UT', flat=True))))
del mdocs
n = Citation.objects.count()
n_dict = dict(
zip(list(Citation.objects.all().values_list('id', flat=True)),
list(range(n))))
print("ROWIDS")
row_ids = list(cdos.values_list('doc__UT', flat=True))
rows = np.array([m_dict[x] for x in row_ids])
print("colids")
col_ids = list(cdos.values_list('citation__id', flat=True))
cols = np.array([n_dict[x] for x in col_ids])
print("data")
data = np.array([1] * cdos.count())
print("matrix")
Scoo = coo_matrix((data, (rows, cols)), shape=(m, n))
del cdos
del row_ids
del rows
del col_ids
del cols
del data
del n_dict
gc.collect()
S = Scoo.tocsr()
del Scoo
gc.collect()
print("transpose")
St = S.transpose()
print("multiply")
Cmat = S * St
del S
del St
gc.collect()
ltri = tril(Cmat, k=-1)
G = nx.from_scipy_sparse_matrix(ltri)
cnode = m_dict[Doc.objects.get(UT='WOS:000297683800015').UT]
paths = nx.single_source_shortest_path(G, cnode)
deg = nx.degree_centrality(G)
ecent = nx.eigenvector_centrality(G)
x = nx.core_number(G)
for i in range(G.number_of_nodes()):
d = Doc.objects.get(pk=rev_m_dict[i])
d.k = x[i]
d.degree = deg[i]
d.eigen_cent = ecent[i]
try:
d.distance = len(paths[i])
except:
pass
d.save()
del x
del G
del deg
del ecent
gc.collect()
bcmatrix = find(tril(Cmat, k=-1))
N = len(bcmatrix[0])
bcrange = list(range(N))
print(N)
chunk_size = 5000
BibCouple.objects.all().delete()
for i in range(N // chunk_size + 1):
f = i * chunk_size
print(f)
l = (i + 1) * chunk_size - 1
if l > N:
l = N - 1
bcs = []
chunk = bcrange[f:l]
pool = Pool(processes=5)
bcs.append(
pool.map(
partial(bib_couple, bc_matrix=bcmatrix, rev_m_dict=rev_m_dict),
chunk))
pool.terminate()
gc.collect()
django.db.connections.close_all()
bcs = flatten(bcs)
BibCouple.objects.bulk_create(bcs)
def diminish_community(sbm_graph, community_id, nodes_to_purturb, criteria,
criteria_r):
"""Function to diminsh the SBM community
Attributes:
sbm_graph (Object): Networkx Graph Object
community_id (int): Community to diminish
criteria (str): Criteria used to diminish the community
criteria_r (bool): Used to sort the nodes in reverse once order based on criteria
nodes_to_purturb (int): Number of nodes to perturb
"""
n = sbm_graph._node_num
community_nodes = [
i for i in range(n) if sbm_graph._node_community[i] == community_id
]
nodes_to_purturb = min(len(community_nodes), nodes_to_purturb)
labels = {}
try:
function = function_mapping[criteria]
if criteria == 'katz':
G_cen = function(sbm_graph._graph, alpha=0.01)
else:
G_cen = function(sbm_graph._graph)
except KeyError:
print(criteria,
'is an invalid input! Using degree_centrality instead.')
G_cen = nx.degree_centrality(sbm_graph._graph)
pass
G_cen = sorted(G_cen.items(),
key=operator.itemgetter(1),
reverse=criteria_r)
perturb_nodes = []
count = 0
i = 0
while count < nodes_to_purturb:
if sbm_graph._node_community[G_cen[i][0]] == community_id:
perturb_nodes.append(G_cen[i][0])
count += 1
i += 1
node_plot = []
count = 0
i = 0
while count < 20:
if sbm_graph._node_community[G_cen[i][0]] == community_id:
node_plot.append(G_cen[i][0])
count += 1
i += 1
node_plot_reverse = []
count = 0
i = len(G_cen) - 1
while count < 20:
if sbm_graph._node_community[G_cen[i][0]] == community_id:
node_plot_reverse.append(G_cen[i][0])
count += 1
i -= 1
for i, nid in enumerate(perturb_nodes):
labels[nid] = str("{0:.2f}".format(G_cen[i][1]))
del G_cen
# perturb_nodes = random.sample(community_nodes, nodes_to_purturb)
left_communitis = [
i for i in range(sbm_graph._community_num) if i != community_id
]
for node_id in perturb_nodes:
new_community = random.sample(left_communitis, 1)[0]
print('Node %d change from community %d to %d' %
(node_id, sbm_graph._node_community[node_id], new_community))
sbm_graph._node_community[node_id] = new_community
for node_id in perturb_nodes:
_resample_egde_for_node(sbm_graph, node_id)
return perturb_nodes, labels, node_plot, node_plot_reverse
if nx.is_connected(G_mentions):
print("graph is connected")
else:
print("graph is not connected")
print(
f"Number of connected components: {nx.number_connected_components(G_mentions)}"
)
print(
f"Average clustering coefficient: {nx.average_clustering(G_mentions):.5f}")
print(f"Transitivity: {nx.transitivity(G_mentions):.5f}")
# Takes 7 minutes
start = time.time()
graph_centrality = nx.degree_centrality(G_mentions)
max_de = max(graph_centrality.items(), key=itemgetter(1))
sorted_centrality = sorted(graph_centrality.items(),
key=itemgetter(1),
reverse=True)
graph_closeness = nx.closeness_centrality(G_mentions)
sorted_closeness = sorted(graph_closeness.items(),
key=itemgetter(1),
reverse=True)
max_clo = max(graph_closeness.items(), key=itemgetter(1))
graph_betweenness = nx.betweenness_centrality(G_mentions,
normalized=True,
endpoints=False)
sorted_betweeness = sorted(graph_betweenness.items(),
key=itemgetter(1),
reverse=True)
def graph_json():
if len(request.args)==0:
return jsonify(json_graph)
graph_={'nodes':[],'links':[]}
nodes_=set()
graph_nodes=[]
min_nodes=5
exp_arts=False
court_cases=False
if request.args.get('min'):
min_nodes=int(request.args.get('min'))
if request.args.get('exp_arts'):
if request.args.get('exp_arts')=="true":
exp_arts=True
if request.args.get('court_cases'):
if request.args.get('court_cases')=="true":
court_cases=True
if request.args.get('include'):
re_include=re.compile(request.args.get('include'))
if request.args.get('include_doc'):
re_include_doc=re.compile(request.args.get('include_doc'))
for node in json_graph['nodes']:
if node['type']==1:
if request.args.get('include'):
if re_include.search(node['name'].lower()):
if not node['id'] in nodes_:
nodes_.add(node['id'])
graph_nodes.append(node)
else:
if not node['id'] in nodes_:
graph_nodes.append(node)
nodes_.add(node['id'])
elif not court_cases and not exp_arts and node['type']==2:
if request.args.get('include_doc'):
if re_include_doc.search(node['name'].lower()):
if not node['id'] in nodes_:
graph_nodes.append(node)
nodes_.add(node['id'])
else:
if not node['id'] in nodes_:
graph_nodes.append(node)
nodes_.add(node['id'])
elif not court_cases and exp_arts and node['type']==3:
if request.args.get('include_doc'):
if re_include_doc.search(node['name'].lower()):
if not node['id'] in nodes_:
graph_nodes.append(node)
nodes_.add(node['id'])
else:
if not node['id'] in nodes_:
graph_nodes.append(node)
nodes_.add(node['id'])
graph_nodes_=[]
nodes_=set()
if request.args.get('exclude'):
re_exclude=re.compile(request.args.get('exclude'))
if request.args.get('exclude_doc'):
re_exclude_doc=re.compile(request.args.get('exclude_doc'))
for node in graph_nodes:
if node['type']==1:
if request.args.get('exclude'):
if not re_exclude.search(node['name'].lower()):
if not node['id'] in nodes_:
graph_nodes_.append(node)
nodes_.add(node['id'])
else:
if not node['id'] in nodes_:
graph_nodes_.append(node)
nodes_.add(node['id'])
elif not court_cases and not exp_arts and node['type']==2:
if request.args.get('exclude_doc'):
if not re_exclude_doc.search(node['name'].lower()):
if not node['id'] in nodes_:
graph_nodes_.append(node)
nodes_.add(node['id'])
else:
if not node['id'] in nodes_:
graph_nodes_.append(node)
nodes_.add(node['id'])
elif not court_cases and exp_arts and node['type']==3:
if request.args.get('exclude_doc'):
if not re_exclude_doc.search(node['name'].lower()):
if not node['id'] in nodes_:
graph_nodes_.append(node)
nodes_.add(node['id'])
else:
if not node['id'] in nodes_:
graph_nodes_.append(node)
nodes_.add(node['id'])
targets_=set()
sources_=set()
for edge in json_graph['links']:
if edge['source'] in nodes_ and edge['target'] in nodes_:
if int(edge['ori_val'])>= min_nodes:
graph_['links'].append(edge)
targets_.add(edge['target'])
sources_.add(edge['source'])
for node in graph_nodes_:
if node['type']==1:
if node['id'] in sources_ or node['id'] in targets_:
graph_['nodes'].append(node)
if node['type']>1:
if node['id'] in targets_:
graph_['nodes'].append(node)
G = nx.DiGraph()
G.add_nodes_from([ n['id'] for n in graph_['nodes']])
G.add_weighted_edges_from([ (e['source'],e['target'],e['ori_val']) for e in graph_['links']])
graph_['stats']={}
graph_['stats']['Density']=nx.density(G)
dc=nx.degree_centrality(G)
m,nm=get_max(dc)
if m>0.0:
graph_['stats']['avg Degree Centrality']=sum([v for v in dc.values()])/len(dc)
graph_['stats']['max Degree Centrality']=m
graph_['stats']['Node Degree Centrality']=nm
for i,node in enumerate(graph_['nodes']):
graph_['nodes'][i]['dc']=dc[node['id']]
return jsonify(graph_)
def Degree_Centrality(G):
Degree_Centrality = nx.degree_centrality(G)
#print "Degree_Centrality:", sorted(Degree_Centrality.iteritems(), key=lambda d:d[1], reverse = True)
return Degree_Centrality
def extended_stats(G,
connectivity=False,
anc=False,
ecc=False,
bc=False,
cc=False):
"""
Calculate extended topological stats and metrics for a graph.
Many of these algorithms have an inherently high time complexity. Global
topological analysis of large complex networks is extremely time consuming
and may exhaust computer memory. Consider using function arguments to not
run metrics that require computation of a full matrix of paths if they
will not be needed.
Parameters
----------
G : networkx.MultiDiGraph
input graph
connectivity : bool
if True, calculate node and edge connectivity
anc : bool
if True, calculate average node connectivity
ecc : bool
if True, calculate shortest paths, eccentricity, and topological metrics
that use eccentricity
bc : bool
if True, calculate node betweenness centrality
cc : bool
if True, calculate node closeness centrality
Returns
-------
stats : dict
dictionary of network measures containing the following elements (some
only calculated/returned optionally, based on passed parameters):
- avg_neighbor_degree
- avg_neighbor_degree_avg
- avg_weighted_neighbor_degree
- avg_weighted_neighbor_degree_avg
- degree_centrality
- degree_centrality_avg
- clustering_coefficient
- clustering_coefficient_avg
- clustering_coefficient_weighted
- clustering_coefficient_weighted_avg
- pagerank
- pagerank_max_node
- pagerank_max
- pagerank_min_node
- pagerank_min
- node_connectivity
- node_connectivity_avg
- edge_connectivity
- eccentricity
- diameter
- radius
- center
- periphery
- closeness_centrality
- closeness_centrality_avg
- betweenness_centrality
- betweenness_centrality_avg
"""
stats = {}
# create a DiGraph from the MultiDiGraph, for those metrics that require it
G_dir = nx.DiGraph(G)
# create an undirected Graph from the MultiDiGraph, for those metrics that
# require it
G_undir = nx.Graph(G)
# get the largest strongly connected component, for those metrics that
# require strongly connected graphs
G_strong = utils_graph.get_largest_component(G, strongly=True)
# average degree of the neighborhood of each node, and average for the graph
avg_neighbor_degree = nx.average_neighbor_degree(G)
stats["avg_neighbor_degree"] = avg_neighbor_degree
stats["avg_neighbor_degree_avg"] = sum(
avg_neighbor_degree.values()) / len(avg_neighbor_degree)
# average weighted degree of the neighborhood of each node, and average for
# the graph
avg_wtd_nbr_deg = nx.average_neighbor_degree(G, weight="length")
stats["avg_weighted_neighbor_degree"] = avg_wtd_nbr_deg
stats["avg_weighted_neighbor_degree_avg"] = sum(
avg_wtd_nbr_deg.values()) / len(avg_wtd_nbr_deg)
# degree centrality for a node is the fraction of nodes it is connected to
degree_centrality = nx.degree_centrality(G)
stats["degree_centrality"] = degree_centrality
stats["degree_centrality_avg"] = sum(
degree_centrality.values()) / len(degree_centrality)
# calculate clustering coefficient for the nodes
stats["clustering_coefficient"] = nx.clustering(G_undir)
# average clustering coefficient for the graph
stats["clustering_coefficient_avg"] = nx.average_clustering(G_undir)
# calculate weighted clustering coefficient for the nodes
stats["clustering_coefficient_weighted"] = nx.clustering(G_undir,
weight="length")
# average clustering coefficient (weighted) for the graph
stats["clustering_coefficient_weighted_avg"] = nx.average_clustering(
G_undir, weight="length")
# pagerank: a ranking of the nodes in the graph based on the structure of
# the incoming links
pagerank = nx.pagerank(G_dir, weight="length")
stats["pagerank"] = pagerank
# node with the highest page rank, and its value
pagerank_max_node = max(pagerank, key=lambda x: pagerank[x])
stats["pagerank_max_node"] = pagerank_max_node
stats["pagerank_max"] = pagerank[pagerank_max_node]
# node with the lowest page rank, and its value
pagerank_min_node = min(pagerank, key=lambda x: pagerank[x])
stats["pagerank_min_node"] = pagerank_min_node
stats["pagerank_min"] = pagerank[pagerank_min_node]
# if True, calculate node and edge connectivity
if connectivity:
# node connectivity is the minimum number of nodes that must be removed
# to disconnect G or render it trivial
stats["node_connectivity"] = nx.node_connectivity(G_strong)
# edge connectivity is equal to the minimum number of edges that must be
# removed to disconnect G or render it trivial
stats["edge_connectivity"] = nx.edge_connectivity(G_strong)
utils.log("Calculated node and edge connectivity")
# if True, calculate average node connectivity
if anc:
# mean number of internally node-disjoint paths between each pair of
# nodes in G, i.e., the expected number of nodes that must be removed to
# disconnect a randomly selected pair of non-adjacent nodes
stats["node_connectivity_avg"] = nx.average_node_connectivity(G)
utils.log("Calculated average node connectivity")
# if True, calculate shortest paths, eccentricity, and topological metrics
# that use eccentricity
if ecc:
# precompute shortest paths between all nodes for eccentricity-based
# stats
sp = {
source: dict(
nx.single_source_dijkstra_path_length(G_strong,
source,
weight="length"))
for source in G_strong.nodes()
}
utils.log("Calculated shortest path lengths")
# eccentricity of a node v is the maximum distance from v to all other
# nodes in G
eccentricity = nx.eccentricity(G_strong, sp=sp)
stats["eccentricity"] = eccentricity
# diameter is the maximum eccentricity
diameter = nx.diameter(G_strong, e=eccentricity)
stats["diameter"] = diameter
# radius is the minimum eccentricity
radius = nx.radius(G_strong, e=eccentricity)
stats["radius"] = radius
# center is the set of nodes with eccentricity equal to radius
center = nx.center(G_strong, e=eccentricity)
stats["center"] = center
# periphery is the set of nodes with eccentricity equal to the diameter
periphery = nx.periphery(G_strong, e=eccentricity)
stats["periphery"] = periphery
# if True, calculate node closeness centrality
if cc:
# closeness centrality of a node is the reciprocal of the sum of the
# shortest path distances from u to all other nodes
closeness_centrality = nx.closeness_centrality(G, distance="length")
stats["closeness_centrality"] = closeness_centrality
stats["closeness_centrality_avg"] = sum(
closeness_centrality.values()) / len(closeness_centrality)
utils.log("Calculated closeness centrality")
# if True, calculate node betweenness centrality
if bc:
# betweenness centrality of a node is the sum of the fraction of
# all-pairs shortest paths that pass through node
# networkx 2.4+ implementation cannot run on Multi(Di)Graphs, so use DiGraph
betweenness_centrality = nx.betweenness_centrality(G_dir,
weight="length")
stats["betweenness_centrality"] = betweenness_centrality
stats["betweenness_centrality_avg"] = sum(
betweenness_centrality.values()) / len(betweenness_centrality)
utils.log("Calculated betweenness centrality")
utils.log("Calculated extended stats")
return stats
def plot_info(G, names):
def get_spread(dictionary):
min_val = dictionary[1]
max_val = dictionary[1]
for key in dictionary:
if min_val > dictionary[key]:
min_val = dictionary[key]
if max_val < dictionary[key]:
max_val = dictionary[key]
if min_val == 0:
dictionary['Spread'] = 'infinity'
else:
dictionary['Spread'] = max_val / min_val
return dictionary
def get_katz_alpha(matrix):
largest = max(linalg.eigvals(matrix))
return 1 / largest - 0.01
nx.draw_networkx(G, show_labels=True, labels=names)
degree_centralities = get_spread(nx.degree_centrality(G))
eigenvector_centralities = get_spread(nx.eigenvector_centrality(G))
katz_centralities = get_spread(
nx.katz_centrality(G, alpha=get_katz_alpha(nx.to_numpy_matrix(G))))
page_rank_centralities = get_spread(nx.pagerank(G, alpha=0.85))
closeness_centralities = get_spread(nx.closeness_centrality(G))
betweeness_centralities = get_spread(nx.betweenness_centrality(G))
data = []
for key in degree_centralities:
data.append([
degree_centralities[key], eigenvector_centralities[key],
katz_centralities[key], page_rank_centralities[key],
closeness_centralities[key], betweeness_centralities[key]
])
row_lables = []
for x in range(len(names)):
row_lables.append(names[x])
row_lables.append('Spread')
centralities = [
'Degree', 'Eigenvector', 'Katz', 'Page Rank', 'Closeness',
'Betweenness'
]
for row in range(len(data)):
for item in range(len(data[0])):
if type(data[row][item]) is not str:
data[row][item] = round(data[row][item], 3)
the_table = plt.table(cellText=data,
rowLabels=row_lables,
colLabels=centralities,
loc='bottom')
plt.tight_layout()
plt.subplots_adjust(left=0.29,
bottom=0.46,
right=0.75,
top=None,
wspace=None,
hspace=None)
the_table.scale(2, 2)
plt.axis('off')
the_table.auto_set_font_size(False)
the_table.set_fontsize(10)
plt.show()
def degree_centrality():
degree_centrality_saves = nx.degree_centrality(G)
order_degree_centrality_rank = sorted(degree_centrality_saves.items(), key=lambda x: x[1], reverse=True)
#cut_order_degree_centrality_rank = order_degree_centrality_rank[0:10]
#print(cut_order_degree_centrality_rank)
return order_degree_centrality_rank
nx.write_gexf(g, 'graph.gexf')
g1 = nx.read_gexf('graph.gexf')
import matplotlib.pyplot as plt
pos = nx.spring_layout(g)
nx.draw_networkx_nodes(g, pos, node_color='yellow', node_size=50)
nx.draw_networkx_edges(g, pos, edge_color='blue')
nx.draw_networkx_labels(g, pos, font_size=20)
plt.axis('off')
plt.show() #plt.savefig('graph.png')
nx.diameter(g) #самый длинный путь
g.number_of_nodes()
g.number_of_edges()
nx.density(g) #примерно отношение узлов к ребрам
nx.average_clustering(g)
deg = nx.degree_centrality(g)
# goo.gl/AQllCa - датасеты разных сетей
import re
g_dolph = nx.Graph()
f = open('out.dolphins', 'r', encoding='utf-8')
dolphins = f.readlines()
for line in dolphins:
nums = re.findall(r'[0-9]+', line)
g_dolph.add_edge(int(nums[0]), int(nums[1]))
pos_dolph = nx.spring_layout(g_dolph)
nx.draw_networkx_nodes(g_dolph, pos_dolph, node_color='blue', node_size=100)
nx.draw_networkx_edges(g_dolph, pos_dolph, edge_color='yellow')
nx.draw_networkx_labels(g_dolph, pos_dolph, font_size=20)
Density of the Graph
A good metric to begin with is network density. This is simply the ratio of
actual edges in the network to all possible edges in the network.
'''
density = nx.density(G) # calulates density of graph
print("Network density:", density)
'''
Centrality
In network analysis, measures of the importance of nodes are referred to as
centrality measures. Degree is the simplest and the most common way of
finding important nodes. A node’s degree is the sum of its edges. If a node
has three lines extending from it to other nodes, its degree is three. Five edges
'''
rsd = nx.degree_centrality(G) # calculates density of graph
rsdf = pd.DataFrame(pd.Series(rsd)) # preprocess the output
rsdf = rsdf.reset_index() # reset the index
rsdf.columns = ["addresses","Degree centrality"] # renaming columns
rsdf = rsdf.sort_values(by="Degree centrality", ascending=False) # sorting based on descending centrality value
top_5_nodes = list(rsdf.addresses[0:5]) # get top 5 nodes
print(top_5_nodes) # print top 5 nodes
'''
Finding Diameter
Diameter is the longest of all shortest paths. After calculating all shortest
paths between every possible pair of nodes in the network, diameter is the
length of the path between the two nodes that are furthest apart. The measure
is designed to give a sense of the network’s overall size, the distance from
one end of the network to another.
def degree_centrality(G):
return nx.degree_centrality(G)
weightfile=['./intermediate/enc_weightsacdm.hdf5',
'./intermediate/dec_weightsacdm.hdf5'])
sample = args.samples
if not os.path.exists('./test_data/academic/pickle'):
os.mkdir('./test_data/academic/pickle')
graphs, length = dataprep_util.get_graph_academic('./test_data/academic/adjlist')
for i in range(length):
nx.write_gpickle(graphs[i], './test_data/academic/pickle/' + str(i))
else:
length = len(os.listdir('./test_data/academic/pickle'))
graphs = []
for i in range(length):
graphs.append(nx.read_gpickle('./test_data/academic/pickle/' + str(i)))
G_cen = nx.degree_centrality(graphs[29]) # graph 29 in academia has highest number of edges
G_cen = sorted(G_cen.items(), key=operator.itemgetter(1), reverse=True)
node_l = []
i = 0
while i < sample:
node_l.append(G_cen[i][0])
i += 1
for i in range(length):
graphs[i] = graph_util.sample_graph_nodes(graphs[i], node_l)
outdir = args.resultdir
if not os.path.exists(outdir):
os.mkdir(outdir)
outdir = outdir + '/' + args.testDataType
if not os.path.exists(outdir):
def map_properties(self, sort_by=['Pagerank', 'Out_degree_wg']):
"""
Compute key properties of nodes in the aggregate map.
Returns a sorted pandas DataFrame with graph properties.
Parameters
----------
sort_by : list
List of properties to sort dataframe.
Returns
-------
pandas DataFrame
Dataframe with a set of graph metrics computed for each node in the graph.
"""
metrics = {
# Node degree
'Node_degree':
dict(self.map.degree)
# Node out-degree
,
'Out_degree':
dict(self.map.out_degree)
# Node weighted out-degree
,
'Out_degree_wg':
dict(self.map.out_degree(weight='weight'))
# Node in-degree
,
'In_degree':
dict(self.map.in_degree)
# Node weighted in-degree
,
'In_degree_wg':
dict(self.map.in_degree(weight='weight'))
# Node pagerank
,
'Pagerank':
dict(nx.pagerank(self.map))
# Node eigenvector centrality
,
'Eigenvector_centrality':
dict(nx.eigenvector_centrality(self.map))
# Node degree centrality
,
'Degree_centrality':
dict(nx.degree_centrality(self.map))
# Node closeness centrality
,
'Closeness_centrality':
dict(nx.closeness_centrality(self.map))
# Node betweenness centrality
,
'Betweenness_centrality':
dict(nx.betweenness_centrality(self.map.to_undirected()))
# Node Katz centrality
#,'Katz_centrality' : dict( nx.katz_centrality( self.map.to_undirected() ) )
# Node communicability centrality
#,'Communicability centrality' : dict( nx.communicability_centrality( self.map.to_undirected() ) )
}
df_node_properties = pd.DataFrame.from_dict(metrics)
df_node_properties.set_index(np.array(self.map.nodes()), inplace=True)
df_node_properties.sort_values(sort_by, ascending=False, inplace=True)
return df_node_properties
betCent = nx.betweenness_centrality(edges, normalized=True, endpoints=True)
node_color = [20000.0 * edges.degree(v) for v in edges]
node_size = [v * 10000 for v in betCent.values()]
plt.figure(figsize=(5, 5))
nx.draw_networkx(edges,
pos=pos,
with_labels=True,
node_color=node_color,
node_size=node_size)
plt.show()
sorted(betCent, key=betCent.get, reverse=True)[:5]
#Degree Centrality
pos = nx.spring_layout(edges)
degCent = nx.degree_centrality(edges)
node_color = [20000.0 * edges.degree(v) for v in edges]
node_size = [v * 10000 for v in degCent.values()]
plt.figure(figsize=(10, 10))
nx.draw_networkx(edges,
pos=pos,
with_labels=True,
node_color=node_color,
node_size=node_size)
plt.show()
sorted(degCent, key=degCent.get, reverse=True)[:5]
#Closeness Centrality
pos = nx.spring_layout(edges)
cloCent = nx.closeness_centrality(edges)
def find_nodes_with_highest_deg_cent(G):
# Compute the degree centrality of G: deg_cent
deg_cent = nx.degree_centrality(G)
# Compute the maximum degree centrality: max_dc
max_dc = max(list(deg_cent.values()))
nodes = set()
# Iterate over the degree centrality dictionary
for k, v in deg_cent.items():
# Check if the current value has the maximum degree centrality
if v == max_dc:
# Add the current node to the set of nodes
nodes.add(k)
return nodes
# Find the node(s) that has the highest degree centrality in T: top_dc
top_dc = find_nodes_with_highest_deg_cent(T)
print(top_dc)
# Write the assertion statement
for node in top_dc:
assert nx.degree_centrality(T)[node] == max(
nx.degree_centrality(T).values())
def add_degree_centrality(network: nx.Graph):
dc = nx.degree_centrality(network)
nx.set_node_attributes(network, dc, 'Degree_Centrality')
return network
#Assortativity
print("The assortativity of the graph: " +
str(nx.degree_assortativity_coefficient(g)))
#Average Clustering
print("The average clustering coefficient: " + str(nx.average_clustering(g)))
#Density
print("The Density of our Graph: " + str(nx.density(g)))
#Number of Nodes
print("The Number of Nodes: " + str(len(g.nodes)))
#Number of Edges
print("The Number of Edges: " + str(len(g.edges)))
#MICRO ANALYSIS -------------------------------------
#degree centrality
print("The top 5 nodes by degree centrality:")
deg = pd.DataFrame(dict(nx.degree_centrality(g)).items())
print(deg.sort_values(by=[1], ascending=False).head(5))
#betweenness centrality
print("The top 5 nodes by betweenness centrality:")
bet = pd.DataFrame(dict(nx.betweenness_centrality(g)).items())
print(bet.sort_values(by=[1], ascending=False).head(5))
#boxplot
plt.boxplot(np.array(bet.sort_values(by=[1], ascending=False)[1]))
plt.title('Distribution of Betweenness')
#Bottom of each list
#degree centrality
print("The bottom 5 nodes by degree centrality:")
deg = pd.DataFrame(dict(nx.degree_centrality(g)).items())
print(deg.sort_values(by=[1], ascending=False).tail(5))
def degree_centrality(self, number=None):
"""度中心性"""
unsort_dirt = nx.degree_centrality(self.get_graph())
return sort(unsort_dirt, number)
def find_max_nodes(G):
list = nx.degree_centrality(G)
res = sorted(list.items(), key=lambda x: x[1], reverse=True)
#TOP 10% is only growth
return res[0:int(G.number_of_nodes() * 0.1)]
def centrality_compare(graph=None, nodes_string=None, value_counts=None):
measurements_dict = OrderedDict()
compare_dict = OrderedDict()
# The data from wevi
if nodes_string is None:
nodes_list = [
0.07553153757502284, 0.008804137964580436, 0.009528332679916485,
0.09411131873310066, 0.056807282025497695, 0.09709045935848355,
0.058825181534953086, 0.2655416154784191, 0.18734994882402486,
0.14641018582600146
]
else:
nodes_list = [float(x) for x in nodes_string.split(",")]
# Put the wevi data in a dictionary
node_dict = {num: val for num, val in enumerate(nodes_list)}
# Make the graph and make it simple graph instead of multi graph
if graph is None:
graph = graph_maker()
if value_counts is None:
value_counts = [14, 30, 30, 11, 15, 32, 39, 37, 45, 47]
graph = nx.Graph(graph)
measurements_dict["closeness centrality"] = nx.closeness_centrality(
graph).values()
# measurements_dict["eigenvector centrality"] = nx.eigenvector_centrality(graph).values()
measurements_dict["degree centrality"] = nx.degree_centrality(
graph).values()
measurements_dict["betweenness centrality"] = nx.betweenness_centrality(
graph).values()
# measurements_dict["katz centrality"] = nx.katz_centrality(graph).values()
measurements_dict["load centrality"] = nx.load_centrality(graph).values()
measurements_dict["nodes count"] = value_counts
# change the lists order to lexicographic
measurements_dict = {
key: [float(i) / sum(value) for i in value]
for key, value in measurements_dict.items()
}
measurements_dict["wevi"] = [i for i in node_dict.values()]
# Loop over all the cenrality measurements
for centrality_name, centrality_value in measurements_dict.items():
# Calculate correlations
pearson = pearsonr(centrality_value, nodes_list)
spearman = spearmanr(centrality_value, nodes_list)
linregres = linregress(centrality_value, nodes_list)
# add it the the compare dict
compare_dict[centrality_name] = [
pearson[0], spearman[0], linregres[2]**2, pearson[1], spearman[1],
linregres[4]
]
# Print the results nicely
print tabulate([[x] + y for x, y in compare_dict.items()],
headers=[
'Name', 'Pearson', 'Spearman', 'linregress',
'Pearson p-value', 'Spearman p-value',
'linregress p-value'
])
sorted2 = sorted(range(len(measurements_dict.values()[0])),
key=lambda k: str(k))
best_nodes_dict = {}
for measure, mes_nodes_list in measurements_dict.items():
best_nodes_dict[measure] = [
"Node " + str(x[0]) for x in sorted(
enumerate(mes_nodes_list), key=lambda x: x[1], reverse=True)
]
best_nodes_dict["wevi"] = [
"Node " + str(sorted2[x[0]])
for x in sorted(enumerate(measurements_dict["wevi"]),
key=lambda x: x[1],
reverse=True)
]
df = pd.DataFrame(measurements_dict)
# df.to_csv("C:\Users\Dvir\Desktop\NNftw\measures.csv")
print "\n\n"
print tabulate(
[[x] + y for x, y in measurements_dict.items()],
headers=[
"Node " + str(x)
for x in sorted(range(len(nodes_list)), key=lambda k: str(k))
])
print "\n\n"
print tabulate([[x] + y[:5] for x, y in best_nodes_dict.items()],
headers=[x for x in range(5)])
print "\n\n"
return compare_dict
listmincentrality = (0, 10)
listmaxcentrality = (0, 0)
for n in (nx.betweenness_centrality(G)).items():
if (listmincentrality[1] > n[1]):
listmincentrality = n
elif (listmaxcentrality[1] < n[1]):
listmaxcentrality = n
print('')
print("The node that has minimal centrality is : ", listmincentrality)
print("The node that has the maximum centrality is : ", listmaxcentrality)
# normalized
listminnormalized = (0, 10)
listmaxnormalized = (0, 0)
for n in (nx.degree_centrality(G)).items():
if (listminnormalized[1] > n[1]):
listminnormalized = n
elif (listmaxnormalized[1] < n[1]):
listmaxnormalized = n
print('')
print("The node that has the minimum (normalized) degree is : ", listminnormalized)
print("The node that has the maximal (normalized) degree is: ", listmaxnormalized)
# In[ ]:
# recherche des cliques
def centrality_distribution(G):
centrality = nx.degree_centrality(G).values()
centrality = np.asarray(centrality)
centrality /= centrality.sum()
return centrality
print("Question 2:")
print("Nodes:", len(g.nodes()))
print("Edges:", len(g.edges()))
print()
h = g.copy()
h.remove_node('Mining-the-Social-Web-2nd-Edition(repo)')
# Comment out write if file is made and uncomment read
nx.write_edgelist(h, "followers.edgelist")
# h=nx.read_edgelist("followers.edgelist")
print("Follower Only List Read or Written")
print()
dc = sorted(nx.degree_centrality(h).items(), key=itemgetter(1), reverse=True)
print("Question 3:")
print("Degree Centrality")
print(dc[:10])
print()
bc = sorted(nx.betweenness_centrality(h).items(),
key=itemgetter(1),
reverse=True)
print("Betweenness Centrality")
print(bc[:10])
print()
print("Closeness Centrality")
print(nx.minimum_node_cut(GS1)) print(nx.edge_connectivity(GS1)) print(nx.minimum_edge_cut(GS1)) # Centrality: # Indentification of Important nodes. # Degree Centrality # C_deg(V) = D_V/(|N|-1) # D_V : Degree of node V # N : Number of Nodes in the graph GK = nx.karate_club_graph() nx.draw(GK, with_labels=True) plt.show() print(nx.degree_centrality(GK)) # Degree Cenrtality: Directed Graph # Closeness Centrality nx.closeness_centrality(GK) # Page Rank Algorithm GP = nx.DiGraph() GP.add_edge(1, 2) GP.add_edge(1, 3) GP.add_edge(4, 3) GP.add_edge(3, 5) nx.draw(GP, with_labels=True) plt.show()