def augmentNodes(g):
r1 = nx.eigenvector_centrality_numpy(g)
r2 = nx.degree_centrality(g) # DP MY
r3 = nx.betweenness_centrality(g)
r5 = nx.load_centrality(g,weight='weight') # DY, WY-writename # Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001).
r6 = nx.pagerank(g, alpha=0.85, personalization=None, max_iter=100, tol=1e-08, nstart=None, weight='weight')
if nx.is_directed(g) == True:
r8 = nx.in_degree_centrality(g)
r9 = nx.out_degree_centrality(g)
# r10 = nx.hits(g, max_iter=100, tol=1e-08, nstart=None)
else:
r4 = nx.communicability_centrality(g)
r7 = nx.clustering(g, weight='weight')
for x in g.nodes():
g.node[x]['eigenvector_centrality_numpy'] = r1[x]
g.node[x]['degree_centrality'] = r2[x]
g.node[x]['betweenness_centrality'] = r3[x]
g.node[x]['load_centrality'] = r5[x]
g.node[x]['pagerank'] = r6[x]
if nx.is_directed(g) == True:
g.node[x]['in_degree_centrality'] = r8[x]
g.node[x]['out_degree_centrality'] = r9[x]
# g.node[x]['hits'] = r10[x]
else:
g.node[x]['communicability_centrality'] = r4[x]
g.node[x]['clustering'] = r7[x]
return g
def eval_proximity_importance(network,graph_xml):
'''returns the proximity of page rank scores distributions between synthetic network(test) and real network (goal)'''
#we need to reverse the network to get a score such that the importance of a node is related to the importance of nodes that point towards it.
if network.is_directed() :
importance_test = nx.eigenvector_centrality_numpy(network.reverse()).values()
else :
importance_test = nx.eigenvector_centrality_numpy(network).values()
importance_goal = eval(graph_xml.find('importance').get('value'))
proximity = proximity_distributions_different_size(importance_goal,importance_test)
return proximity
def calculate_eigenvector(self):
eigen_attack = []
G = nx.Graph()
G.add_nodes_from(range(self.node_num))
G.add_weighted_edges_from(self.aggregated_list)
eigen = nx.eigenvector_centrality_numpy(G)
eigen_sort = sorted(eigen, key=eigen.__getitem__, reverse=True)
eigen_attack.append(eigen_sort[0])
for num_of_deletion in range (0,self.node_num/2-1):
G.remove_node(eigen_sort[0])
eigen = nx.eigenvector_centrality_numpy(G)
eigen_sort = sorted(eigen, key=eigen.__getitem__, reverse=True)
eigen_attack.append(eigen_sort[0])
return eigen_attack
def test_eigenvector_v_katz_random(self):
G = nx.gnp_random_graph(10,0.5, seed=1234)
l = float(max(eigvals(nx.adjacency_matrix(G).todense())))
e = nx.eigenvector_centrality_numpy(G)
k = nx.katz_centrality_numpy(G, 1.0/l)
for n in G:
assert_almost_equal(e[n], k[n])
def randomEigenvectorSampling(G_, keptNodes):
sumEigen = 0.0
eigenvector = nx.eigenvector_centrality_numpy(G_)
for node in G_.nodes():
sumEigen = sumEigen+eigenvector[node]
probs = []
picked = []
for node in G_.nodes():
probs.append(eigenvector[node]/sumEigen)
cumEigenProbs = cumulative_sum(probs)
cumEigenProbs[len(cumEigenProbs)-1] = 1.0
num = 0
while num < keptNodes:
random.seed(time.clock())
number = random.random()
for node in range(0, len(G_.nodes())):
if (number <= cumEigenProbs[node]):
if(G_.nodes()[node] not in picked):
print "Adding node "+ str(G_.nodes()[node])
picked.append(G_.nodes()[node])
num = num+1
break
else:
#print "Collision"
break
return picked
def concepts(self, terms):
paths = self._synset_paths(terms)
root = _path_root(paths).split('.')[0]
self.graph = _create_subgraph(paths, root)
return sorted(nx.eigenvector_centrality_numpy(self.graph, weight='w').items(),
key=lambda x: x[1], reverse=True)
def centrality(net):
values ={}
close = nx.closeness_centrality(net, normalized= True)
eigen = nx.eigenvector_centrality_numpy(net)
page = nx.pagerank(net)
bet = nx.betweenness_centrality(net,normalized= True)
flow_c = nx.current_flow_closeness_centrality(net,normalized= True)
flow_b = nx.current_flow_betweenness_centrality(net,normalized= True)
load = nx.load_centrality(net, normalized = True)
com_c = nx.communicability_centrality(net)
com_b = nx.communicability_betweenness_centrality(net, normalized= True)
degree = net.degree()
file3 = open("bl.csv",'w')
for xt in [bet,load,degree,page,flow_b,com_c,com_b,eigen,close,flow_c]:#[impo,bet,flow_b,load,com_c,com_b] :
for yt in [bet,load,degree,page,flow_b,com_c,com_b,eigen,close,flow_c]:#[impo,bet,flow_b,load,com_c,com_b] :
corr(xt.values(),yt.values(),file3)
print
file3.write("\n")
file3.close()
#plt.plot(x,y, 'o')
#plt.plot(x, m*x + c, 'r', label='Fitted line')
#plt.show()
#for key,item in close.iteritems() :
#values[key] = [impo.get(key),bet.get(key),flow_b.get(key), load.get(key),com_c.get(key),com_b.get(key)]
return values
def analyze_graph(G):
#centralities and node metrics
out_degrees = G.out_degree()
in_degrees = G.in_degree()
betweenness = nx.betweenness_centrality(G)
eigenvector = nx.eigenvector_centrality_numpy(G)
closeness = nx.closeness_centrality(G)
pagerank = nx.pagerank(G)
avg_neighbour_degree = nx.average_neighbor_degree(G)
redundancy = bipartite.node_redundancy(G)
load = nx.load_centrality(G)
hits = nx.hits(G)
vitality = nx.closeness_vitality(G)
for name in G.nodes():
G.node[name]['out_degree'] = out_degrees[name]
G.node[name]['in_degree'] = in_degrees[name]
G.node[name]['betweenness'] = betweenness[name]
G.node[name]['eigenvector'] = eigenvector[name]
G.node[name]['closeness'] = closeness[name]
G.node[name]['pagerank'] = pagerank[name]
G.node[name]['avg-neigh-degree'] = avg_neighbour_degree[name]
G.node[name]['redundancy'] = redundancy[name]
G.node[name]['load'] = load[name]
G.node[name]['hits'] = hits[name]
G.node[name]['vitality'] = vitality[name]
#communities
partitions = community.best_partition(G)
for member, c in partitions.items():
G.node[member]['community'] = c
return G
def Centrality(Au):
"""docstring for Centrality"""
b = nx.betweenness_centrality(Au)
e = nx.eigenvector_centrality_numpy(Au)
c = nx.closeness_centrality(Au)
d = nx.degree_centrality(Au)
return b, e, c, d
def test_P3_unweighted(self):
"""Eigenvector centrality: P3"""
G=nx.path_graph(3)
b_answer={0: 0.5, 1: 0.7071, 2: 0.5}
b=nx.eigenvector_centrality_numpy(G, weight=None)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=4)
def get_sna(path):
sna_data = {}
print 'Building relations graph'
G = nx.read_gexf(path)
print 'Nodes:', len(G.nodes())
print 'Edges:', len(G.edges())
print 'Calculating centralities:'
print ' -degrees'
degrees = G.degree()
for c in degrees:
sna_data[c] = { 'degree':degrees[c],
'betweenness':0,
'closeness':0,
'eigenvector':0}
print ' -betweenness'
betweenness = nx.betweenness_centrality(G)
for c in betweenness:
sna_data[c]['betweenness'] = betweenness[c]
print ' -closeness'
closeness = nx.closeness_centrality(G)
for c in closeness:
sna_data[c]['closeness'] = closeness[c]
print ' -eigenvector'
eigenvector = nx.eigenvector_centrality_numpy(G)
for c in eigenvector:
sna_data[c]['eigenvector'] = eigenvector[c]
return sna_data
def centrality_scores(vote_matrix, season_graph):
deg = nx.degree(season_graph)
deg = {k: round(v,1) for k,v in deg.iteritems()}
close = nx.closeness_centrality(season_graph)
close = {k: round(v,3) for k,v in close.iteritems()}
btw = nx.betweenness_centrality(season_graph)
btw = {k: round(v,3) for k,v in btw.iteritems()}
eig = nx.eigenvector_centrality_numpy(season_graph)
eig = {k: round(v,3) for k,v in eig.iteritems()}
page = nx.pagerank(season_graph)
page = {k: round(v,3) for k,v in page.iteritems()}
# Add contestant placement (rank)
order = list(vote_matrix.index)
place_num = list(range(len(order)))
place = {order[i]:i+1 for i in place_num}
names = season_graph.nodes()
# Build a table with centralities
table=[[name, deg[name], close[name], btw[name], eig[name], page[name], place[name]] for name in names]
# Convert table to pandas df
headers = ['name', 'deg', 'close', 'btw', 'eig', 'page', 'place']
df = pd.DataFrame(table, columns=headers)
df = df.sort_values(['page', 'eig', 'deg'], ascending=False)
return df
def set_evaluation_datas(graph,graph_xml,**kwargs) :
'''if no precise evaluation method is given, we compute every possible measure (wrong !!)'''
evaluation_method = kwargs.get('evaluation_method','')
def add_sub(name,value):
sub = xml.SubElement(graph_xml,name)
sub.attrib['value'] = str(value)
#First relevant infos are number of nodes and number of edges,
#should be dependant on the method used to develop the network,
#but until now they are necessary and always stored
add_sub('number_of_nodes',nx.number_of_nodes(graph))
add_sub('number_of_edges',nx.number_of_edges(graph))
#number of nodes
nodes = nx.number_of_nodes(graph)
#should be replaced by getattr(graph, variable) loop
if graph.is_directed() :
if 'vertices' in evaluation_method :
add_sub('vertices',nx.number_of_edges(graph)/(nodes*(nodes-1)))
if 'degrees' in evaluation_method :
add_sub('degree_in',graph.in_degree().values())
add_sub('degree_out', graph.out_degree().values())
if 'importance' in evaluation_method :
add_sub('importance',nx.eigenvector_centrality_numpy(graph.reverse()).values())
if 'clustering' in evaluation_method or 'heterogeneity' in evaluation_method :
add_sub('clustering',nx.clustering(graph.to_undirected()).values())
if 'community_structure' in evaluation_method :
add_sub('degree',graph.degree().values())
else :
if 'vertices' in evaluation_method :
add_sub('vertices',2*nx.number_of_edges(graph)/(nodes*(nodes-1)))
if 'communities' in evaluation_method :
add_sub('communities',get_communities(graph))
if 'degrees' in evaluation_method or 'community_structure' in evaluation_method :
add_sub('degrees',graph.degree().values())
if 'clustering' in evaluation_method or 'heterogeneity' in evaluation_method :
add_sub('clustering',nx.clustering(graph).values())
if 'importance' in evaluation_method :
add_sub('importance',nx.eigenvector_centrality_numpy(graph).values())
if 'distances' in evaluation_method :
add_sub('distances',list(it.chain.from_iterable([ dict_of_length.values() for dict_of_length in nx.shortest_path_length(graph).values()])))
def betweenness_centrality(graph):
#centrality = nx.betweenness_centrality(graph, normalized=True)
#centrality = nx.closeness_centrality(graph)
centrality = nx.eigenvector_centrality_numpy(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
print "%i. %s: %0.3f" % item
def analyze_graph(G):
betweenness = nx.betweenness_centrality(G)
eigenvector = nx.eigenvector_centrality_numpy(G)
closeness = nx.closeness_centrality(G)
pagerank = nx.pagerank(G)
degrees = G.degree()
for name in G.nodes():
G.node[name]['betweenness'] = betweenness[name]
G.node[name]['eigenvector'] = eigenvector[name]
G.node[name]['closeness'] = closeness[name]
G.node[name]['pagerank'] = pagerank[name]
G.node[name]['degree'] = degrees[name]
components = nx.connected_component_subgraphs(G)
i = 0
for cc in components:
#Set the connected component for each group
for node in cc:
G.node[node]['component'] = i
i += 1
cent_betweenness = nx.betweenness_centrality(cc)
cent_eigenvector = nx.eigenvector_centrality_numpy(cc)
cent_closeness = nx.closeness_centrality(cc)
for name in cc.nodes():
G.node[name]['cc-betweenness'] = cent_betweenness[name]
G.node[name]['cc-eigenvector'] = cent_eigenvector[name]
G.node[name]['cc-closeness'] = cent_closeness[name]
#Assign each person to his bigger clique
cliques = list(nx.find_cliques(G))
j = 0
for clique in cliques:
clique_size = len(clique)
for member in clique:
if G.node[member]['clique-size'] < clique_size:
G.node[member]['clique-size'] = clique_size
G.node[member]['clique'] = j
j +=1
return G
def perform_GA(Graphs, commGraphs, gtoidict, itogdict, genedict):
'''
Perform the GA algorithm here, Graphs has the original graphs with all
Nodes in both top and bottom networks, commGraphs contains only the
specific communities needed for the third part of the equation
'''
EVCTop = NX.eigenvector_centrality_numpy(Graphs['Top'])
EVCBot = NX.eigenvector_centrality_numpy(Graphs['Bot'])
randPop = produce_population(genedict)
communities = split_graph_into_communities(commGraphs['Top'],
C.best_partition(commGraphs['Top']))
while (phi > 0):
geneList = calc_fitness_x(randPop, EVCTop, EVCBot, gtoidict, itogdict,
commGraphs['Top'], communities)
filterList = filter_genes(geneList.values())
break
def centrailtyM(A,num=5):
G=nx.DiGraph(A)
ranks=np.zeros((num,8))
ranks[:,0]=np.argsort(nx.in_degree_centrality(G).values())[::-1][:num]
ranks[:,1]=np.argsort(nx.closeness_centrality(G).values())[::-1][:num]
ranks[:,2]=np.argsort(nx.betweenness_centrality(G).values())[::-1][:num]
ranks[:,3]=np.argsort(nx.eigenvector_centrality_numpy(G).values())[::-1][:num]
ranks[:,4]=np.argsort(nx.katz_centrality_numpy(G,weight=None).values())[::-1][:num]
ranks[:,5]=np.argsort(nx.pagerank_numpy(G,weight=None).values())[::-1][:num]
return ranks
def forUndirected(G):
myList = [nx.eigenvector_centrality_numpy(G),
nx.degree_centrality(G),
nx.betweenness_centrality(G),
nx.communicability_centrality(G),
nx.load_centrality(G),
nx.pagerank(G, alpha=0.85, personalization=None, max_iter=100, tol=1e-08, nstart=None, weight='weight'),
nx.clustering(G, weight='weight')]
return myList
def calculateEigenCentrality_numpy(userConnectedGraph, counter):
"""
calculates the eigenVector Centrality for given graph and writes the output to file
parameters:
userConnectedGraph - graph
counter - int value for maintaining unique file names
"""
eigenCentrality = nx.eigenvector_centrality_numpy(userConnectedGraph)
writeCentralityOutput(eigenCentrality, path + 'eigenCentrality' + str(counter))
plotgraph(conn, path, 'eigenCentrality' + str(counter))
def test_K5(self):
"""Eigenvector centrality: K5"""
G=networkx.complete_graph(5)
b=networkx.eigenvector_centrality(G)
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])
b=networkx.eigenvector_centrality_numpy(G)
for n in sorted(G):
assert_almost_equal(b[n],b_answer[n],places=3)
def run_metric(metric_name, G, domain, topic, metric_weight, use_norm, fileout, top_x):
print '\n>> ' + 'Calculating ' + metric_name + ' for ' + domain + " - " + topic
start_time = datetime.now()
if metric_name == 'Degree':
graph_metric = G.degree(nbunch=None, weight=metric_weight)
normalize_metric(G, graph_metric, metric_weight)
elif metric_name == 'In Degree':
graph_metric = G.in_degree(nbunch=None, weight=metric_weight)
normalize_metric(G, graph_metric, metric_weight)
elif metric_name == 'Out Degree':
graph_metric = G.out_degree(nbunch=None, weight=metric_weight)
normalize_metric(G, graph_metric, metric_weight)
elif metric_name == 'Closeness Centrality':
graph_metric = nx.closeness_centrality(G, distance=None, normalized=use_norm)
# use distance as weight? to increase importance as weight increase distance = 1/weight
elif metric_name == 'Betweenness Centrality':
graph_metric = nx.betweenness_centrality(G, normalized=use_norm, weight=metric_weight)
elif metric_name == 'Eigenvector Centrality':
try:
graph_metric = nx.eigenvector_centrality(G, max_iter=1000)
normalize_metric(G, graph_metric, metric_weight)
except nx.exception.NetworkXError:
# use numpy eigenvector if fail to converge
print "power method for calculating eigenvector did not converge, using numpy"
graph_metric = nx.eigenvector_centrality_numpy(G)
normalize_metric(G, graph_metric, metric_weight)
elif metric_name == 'Pagerank':
try:
graph_metric = nx.pagerank(G, weight=metric_weight)
normalize_metric(G, graph_metric, metric_weight)
except:
# use numpy if fails to converge
print "power method for calculating pagerank did not converge, using numpy"
graph_metric = nx.pagerank_numpy(G, weight=metric_weight)
normalize_metric(G, graph_metric, metric_weight)
end_time = datetime.now()
print "Calculation completed in: " + str(end_time - start_time)
# append the entire list to the output file
append_to_file(graph_metric, fileout, domain, topic, metric_name)
'''
### output to screen the top x results
# convert to a list of tuples
graph_metric = graph_metric.items()
# sort
graph_metric.sort(key=lambda tup: -tup[1])
# get and print the top X
# print metric_results(graph_metric)
top_list = take(top_x, graph_metric)
for item in top_list:
print ((item[0]) + "," + str(item[1]))
'''
return graph_metric
def eigen_vector_centrality(self):
#Compute the eigen vector centrality of the graph
logging.info("Inside eigne vector centrality module")
eigenvector_centrality_dict = nx.eigenvector_centrality_numpy(self.G)
logging.info("Eigen vector centrality dict count is %s " % (len(eigenvector_centrality_dict.keys())))
eigen_vector_sorted_list = sorted(eigenvector_centrality_dict.items(), key=lambda x:x[1], reverse=True)[:3]
for a,b in eigen_vector_sorted_list:
logging.info("Eigen vector cent for %s is %s" % (a,b))
eigenvector_centrality_dict = {}
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 output_eigenvector_centrality_info (graph, path, nodes_dict):
"""Output Eigenvector centrality information about the graph.
graph : (networkx.Graph)
path: (String) contains the path to the output file
nodes_dict: (dictionary) maps node id to node name
"""
eigen_dict = nx.eigenvector_centrality_numpy(graph, weight='weight')
eigen_dict = dict((nodes_dict[key], eigen_dict[key]) for key in nodes_dict if key in eigen_dict)
eigen_list = dict_to_sorted_list(eigen_dict)
with open(path, 'w') as out:
out.write('***Eigenvector Centrality***\n')
out.write('Node\tLayer\tEigenvector centrality\n')
for element in eigen_list:
out.write('%d\t%d\t%f\n' % (element[0][0], element[0][1], element[1]))
def network_value_distribution(orig_g_M, otherModel_M, name):
eig_cents = [nx.eigenvector_centrality_numpy(g) for g in orig_g_M] # nodes with eigencentrality
net_vals = []
for cntr in eig_cents:
net_vals.append(sorted(cntr.values(), reverse=True))
df = pd.DataFrame(net_vals)
df = pd.DataFrame.from_dict(eig_cents[0].items())
# Compute the eigenvector centrality for the graph G.
# Dictionary of nodes with eigenvector centrality as the value.
df.columns=['v','eig'] # eig: eigenvector centrality
df['eig'].to_csv('Results/{}NetValue.tsv'.format(name), sep='\t', header=True, \
#float_format='%4.18f ',
encoding='utf-8', index=True)
print "orig"
l = list(df.mean())
zz = float(len(l))
if not zz == 0:
sa = int(math.ceil(zz/75))
for i in range(0, len(l), sa):
print "(" + str(i) + "," + str(l[i]) + ")"
eig_cents = [nx.eigenvector_centrality_numpy(g) for g in otherModel_M] # nodes with eigencentrality
net_vals = []
for cntr in eig_cents:
net_vals.append(sorted(cntr.values(), reverse=True))
df = pd.DataFrame(net_vals)
print "other model"
l = list(df.mean())
zz = float(len(l))
if not zz == 0:
sa = int(math.ceil(zz/75))
for i in range(0, len(l), sa):
print "(" + str(i) + "," + str(l[i]) + ")"
def detectCenters(self):
for community in self.communities:
if len(self.Labels[community]) < 1:
self.centers1.append(-1)
self.centers2.append(-1)
self.centers3.append(-1)
self.centers4.append(-1)
self.centers5.append(-1)
self.centers6.append(-1)
else:
self.G1 = nx.MultiGraph()
self.G1.add_nodes_from(self.Labels[community])
for agent in self.Labels[community]:
r = np.where(self.trusts[agent, :] > 0)[0]
self.G1.add_edges_from(zip(r, [agent] * len(r)))
r = np.where(self.trusts[:, agent] > 0)[0]
self.G1.add_edges_from(zip(r, [agent] * len(r)))
eigen = nx.eigenvector_centrality_numpy(self.G1)
betweenness = nx.betweenness_centrality(self.G1)
center1 = center2 = center3 = center4 = center5 = center6 = self.Labels[community][0]
max_betweenness = betweenness[center1]
max_degree = self.agents[center2].deg
max_trustee = self.agents[center3].trustee
max_trustor = self.agents[center4].trustor
max_eigen = eigen[center6]
for agent in self.Labels[community]:
if betweenness[agent] >= max_betweenness:
center1 = agent
max_betweenness = betweenness[agent]
if self.agents[agent].deg >= max_degree:
center2 = agent
max_degree = self.agents[agent].deg
if self.agents[agent].trustee >= max_trustee:
center3 = agent
max_trustee = self.agents[agent].trustee
if self.agents[agent].trustor >= max_trustor:
center4 = agent
max_trustor = self.agents[agent].trustor
if eigen[agent] >= max_eigen:
center6 = agent
max_eigen = eigen[agent]
center5 = random.choice(self.Labels[community])
self.centers1.append(center1)
self.centers2.append(center2)
self.centers3.append(center3)
self.centers4.append(center4)
self.centers5.append(center5)
self.centers6.append(center6)
def getHugeStats(g):
if nx.is_directed(g) == True:
P1 = pd.DataFrame({'load_centrality': nx.load_centrality(g, weight='weight'),
'betweenness_centrality': nx.betweenness_centrality(g, weight='weight'),
'pagerank': pd.Series(nx.pagerank(g, alpha=0.85, personalization=None, max_iter=100, tol=1e-08, nstart=None, weight='weight')),
'eigenvector_centrality': nx.eigenvector_centrality_numpy(g),
'degree_centrality': pd.Series(nx.degree_centrality(g)),
'in_degree_centrality': pd.Series(nx.in_degree_centrality(g)),
'out_degree_centrality': pd.Series(nx.out_degree_centrality(g))})
else:
P1 = pd.Panel({'spl': pd.DataFrame(nx.shortest_path_length(g)),
'apdp': pd.DataFrame(nx.all_pairs_dijkstra_path(g)),
'apdl': pd.DataFrame(nx.all_pairs_dijkstra_path_length(g)),
'c_exp': pd.DataFrame(nx.communicability_exp(g))})
return P1
def testRandomCentralNode():
df = readEdgeList('testEdgeList.csv')
g = pandasToNetworkX(df)
# make sure randomCentralNode is actually a node in the graph
assert randomCentralNode(g) in g.nodes()
# the following few lines sample 500 random nodes, getting
# the most- and least-frequently chosen ones.
# if the random sampling is being done right, then the
# eigenvector centrality of the most-frequent node should be
# larger than that of the least-frequent node (with high probability)
smpl = Counter([randomCentralNode(g) for i in xrange(500)])
top,topCount = smpl.most_common()[0]
btm,btmCount = smpl.most_common()[-1]
evc = nx.eigenvector_centrality_numpy(g)
# this could fail by chance every once in a while
# but it should be very rare
assert evc[top] > evc[btm]
def karate_rule(base, new):
"""
The original karate club has two densly connected clusters, with a few critical bridges. This rule attempts
to simulate a growth function from this by first bringing together all components, then with a simple
preferential attachment model to those actors with relatively high Eigenvector centrality. The original
Zachary data forms two tightly clustered communities with a select few bridges. This growth rule is meant to
re-constrcut this in reverse, by first forming the bridges, then the polar hubs.
"""
# If the base graph has multiple components, first attempt to unify them into a single component
if nx.components.number_connected_components(base)>1:
comps=nx.connected_components(base)
# Select two random components and form bridge with new structure
rand_comps=random_integers(low=0,high=len(comps)-1,size=2)
# Select random node from each component
rand0=comps[rand_comps[0]][random_integers(low=0,high=len(comps[rand_comps[0]])-1)]
rand1=comps[rand_comps[1]][random_integers(low=0,high=len(comps[rand_comps[1]])-1)]
while rand0==rand1:
rand1=comps[rand_comps[1]][random_integers(low=0,high=len(comps[rand_comps[1]])-1)]
outer_bound=[rand0,rand1]
outer_bound.extend(range(base.number_of_nodes(),base.number_of_nodes()+((new.number_of_nodes())-1)))
mapping=dict(zip(new.nodes(),outer_bound))
new=nx.relabel_nodes(new,mapping)
else:
# Use Eigenvector centrality as pref attachment attribute
cent=nx.eigenvector_centrality_numpy(base).items()
# Normalize values to sum to 1.0
norm_const=sum([(b) for (a,b) in cent])
pref_prob=[(b/norm_const) for (a,b) in cent]
# Step through probability mass to find a node to attach to. Same method used in
# gmm.algorithms.draw_structure to select a probability weighted motif from the set.
draw=uniform()
node_index=0
mass_sum=pref_prob[node_index]
while draw>mass_sum:
node_index+=1
mass_sum+=pref_prob[node_index]
rand0=cent[node_index][0] # Return the appropriate node ID
outer_bound=[rand0]
outer_bound.extend(range(base.number_of_nodes(),base.number_of_nodes()+((new.number_of_nodes())-1)))
mapping=dict(zip(new.nodes(),outer_bound))
new=nx.relabel_nodes(new,mapping)
return nx.compose(base,new)
def get_network_average(coords, knn):
# create all nodes
print '\tCreating graph'
g = nx.DiGraph()
n_frames = coords.shape[0]
g.add_nodes_from(range(n_frames))
# get distances
print '\tCalculating distance matrix'
distances = get_dist_matrix(coords)
# add edges
print '\tAdding edges'
for i in range(n_frames):
# find knn + 1 nearest neighbors
neighbors = numpy.argsort(distances[i, :])[:knn+1]
for j in neighbors:
if not i == j:
g.add_edge(i, j)
# turn the graph into a directed graph
g = g.to_undirected(reciprocal=True)
# find the largest connected component
connected_components = nx.connected_component_subgraphs(g)
largest_connected_component = connected_components[0]
print '\t{} connected components.'.format( len(connected_components) )
print '\tLargest connected component contains {} nodes.'.format( len(largest_connected_component) )
# find most central point
print '\tFinding most central point'
centrality = nx.eigenvector_centrality_numpy(largest_connected_component)
index_of_max = max( centrality.iteritems(), key=operator.itemgetter(1) )[0]
# calculate the average of central point and all it's neighbors
neighbors = largest_connected_component.neighbors(index_of_max)
neighbors.append(index_of_max)
average = numpy.mean( coords[neighbors,:], axis=0 )
# return it
return average
# %%%%%%%%%%%%%%%
print('Nodes:', len(social_network.nodes()))
print('Edges:', len(social_network.edges()))
# %%%%%%%%%%%%%%%
L = max(nx.connected_component_subgraphs(social_network), key=len)
print("Nodes in largest sub component:", len(L.nodes()))
print("Edges in largest sub component:", len(L.edges()))
avg_cluster_index = nx.average_clustering(social_network)
print(avg_cluster_index)
# %%%%%%%%%%%%%%%
##### EIGEN VECTOR CENTRALITY #####
eigen_value = nx.eigenvector_centrality_numpy(social_network)
eigen_elite_user_avg = np.mean(
[eigen_value[node] for node in eigen_value if node.Type == elites])
eigen_regular_avg = np.mean(
[eigen_value[node] for node in eigen_value if node.Type == user_reg])
eigen_all_avg = np.mean([
eigen_value[node] for node in eigen_value
if node.Type == user_reg or node.Type == elites
])
print(eigen_elite_user_avg, eigen_regular_avg, eigen_all_avg)
# %%%%%%%%%%%%%%%
deg_central = nx.degree_centrality(social_network)
degree_elite_avg = np.mean(
[deg_central[node] for node in deg_central if node.Type == elites])
curVillage = int(filename[37:-4])
mat = pd.read_csv(os.path.join(directory, filename), header=None)
show_graph_with_labels(mat.values, curVillage)
FG = nx.from_numpy_matrix(mat.values)
try:
eigveccentNWX = pd.DataFrame.from_dict(
nx.algorithms.eigenvector_centrality(FG), orient='index'
).squeeze(
) #convert dictionary to pandas dataframe, maybe .squeeze() into a Series?
except:
print(
"Could not converge with power iteration for the Eigenvector Centrality for village: "
+ str(curVillage))
eigveccentNWX = pd.DataFrame.from_dict(
nx.eigenvector_centrality_numpy(FG), orient='index'
).squeeze(
) #https://stackoverflow.com/questions/43208737/using-networkx-to-calculate-eigenvector-centrality
degcentNWX = pd.DataFrame.from_dict(
nx.algorithms.degree_centrality(FG), orient='index'
).squeeze(
) #convert dictionary to pandas dataframe, maybe .squeeze() into a Series?
closecentNWX = pd.DataFrame.from_dict(
nx.algorithms.closeness_centrality(FG), orient='index'
).squeeze(
) #convert dictionary to pandas dataframe, maybe .squeeze() into a Series?
betcentNWX = pd.DataFrame.from_dict(
nx.algorithms.betweenness_centrality(FG), orient='index'
).squeeze(
) #convert dictionary to pandas dataframe, maybe .squeeze() into a Series?
def test_eigenvector_centrality_unweighted_numpy(self):
G = self.H
p = nx.eigenvector_centrality_numpy(G)
for (a, b) in zip(list(p.values()), self.G.evc):
assert a == pytest.approx(b, abs=1e-7)
def test_empty_numpy(self):
with pytest.raises(nx.NetworkXException):
e = nx.eigenvector_centrality_numpy(nx.Graph())
def principal_eigenvector(c: np.Array) -> List[float]:
graph = nx.from_numpy_matrix(c.T, create_using=nx.DiGraph)
return np.array([v for v in nx.eigenvector_centrality_numpy(graph, weight='weight').values()])
def __init__(self, contacts, modes, block_prob=0.1):
self.contacts = contacts
self.modes = modes
self.people = np.unique(self.contacts[['p1', 'p2']])
self.n = len(self.people)
self.block_prob = {}
p2id = {}
for i, p in enumerate(self.people):
p2id[p] = i
self.contacts['id1'] = self.contacts['p1'].apply(lambda row: p2id[row])
self.contacts['id2'] = self.contacts['p2'].apply(lambda row: p2id[row])
# aggregate the contacts
self.backbones = np.zeros([self.n, self.n])
for i, c in self.contacts.iterrows():
t, p1, p2 = c[['time', 'id1', 'id2']]
self.backbones[p1, p2] += 1
self.backbones[p2, p1] += 1
self.agg_graph = nx.from_numpy_array(self.backbones)
for mode in self.modes:
if mode == 'degree product':
adj = (self.backbones > 0)
degree = np.sum(adj, axis=0)
feature = np.outer(degree, degree)
elif mode == 'r degree product':
adj = (self.backbones > 0)
degree = np.sum(adj, axis=0)
feature = 1 / np.outer(degree, degree)
elif mode == 'strength product':
strength = np.sum(self.backbones, axis=0)
feature = np.outer(strength, strength)
elif mode == 'r strength product':
strength = np.sum(self.backbones, axis=0)
feature = 1 / np.outer(strength, strength)
elif mode == 'betweeness':
feature = np.zeros([self.n, self.n])
bet = nx.algorithms.edge_betweenness_centrality(self.agg_graph)
for k, v in bet.items():
feature[k] = v
feature += feature.T
elif mode == 'r betweeness':
feature = np.zeros([self.n, self.n])
bet = nx.algorithms.edge_betweenness_centrality(self.agg_graph)
for k, v in bet.items():
if v > 0:
feature[k] = 1 / v
feature += feature.T
elif mode == 'link weight':
feature = np.copy(self.backbones)
elif mode == 'r link weight':
feature = np.zeros([self.n, self.n])
feature[self.backbones !=
0] = 1 / self.backbones[self.backbones != 0]
elif mode == 'weighted eigen':
eigen = nx.eigenvector_centrality_numpy(self.agg_graph,
weight='weight')
feature = np.zeros([self.n, self.n])
for i in range(self.n):
for j in range(self.n):
feature[i, j] = (eigen[i]) * (eigen[j])
elif mode == 'r weighted eigen':
eigen = nx.eigenvector_centrality_numpy(self.agg_graph,
weight='weight')
feature = np.zeros([self.n, self.n])
for i in range(self.n):
for j in range(self.n):
feature[i, j] = 1 / (eigen[i] * eigen[j])
elif mode == 'unweighted eigen':
eigen = nx.eigenvector_centrality_numpy(self.agg_graph)
feature = np.zeros([self.n, self.n])
for i in range(self.n):
for j in range(self.n):
feature[i, j] = eigen[i] * eigen[j]
elif mode == 'r unweighted eigen':
eigen = nx.eigenvector_centrality_numpy(self.agg_graph)
feature = np.zeros([self.n, self.n])
for i in range(self.n):
for j in range(self.n):
feature[i, j] = 1 / (eigen[i] * eigen[j])
elif mode == 'random':
feature = np.ones([self.n, self.n])
else:
print('unspported mode')
block = feature * np.sum(self.backbones) / np.sum(
feature * self.backbones) * block_prob
while True:
block[block > 1] = 1
new = np.sum(self.backbones) * block_prob - np.sum(
self.backbones[block == 1])
old = np.sum((block * self.backbones)[block < 1])
block[block < 1] = block[block < 1] * new / old
block[block > 1] = 1
if abs(
np.sum(self.backbones * block) -
np.sum(self.backbones) * block_prob) < 0.01:
break
self.block_prob[mode] = block
def test_multigraph_numpy(self):
e = nx.eigenvector_centrality_numpy(nx.MultiGraph())
def Eigen_Centrality(G):
Eigen_Centrality = nx.eigenvector_centrality_numpy(G)
#Eigen_Centrality = nx.eigenvector_centrality(G)
#nx.eigenvector_centrality_numpy
#print "Eigen_Centrality:", sorted(Eigen_Centrality.iteritems(), key=lambda d:d[1], reverse = True)
return Eigen_Centrality
def get_network_analytics(data_reduced):
#calculate average breach and average beds occupied:
average_breach_perc = data_reduced['breach_percentage'].mean()
average_bed_occupancy = data_reduced['Total Occupied'].mean()
# weighted edges first
# count the number of times a specific transfer appears to get edge weight
transfer_counts = data_reduced.groupby(['from', 'to']).count()
# add the old index as a column - int he above the count became the index.
transfer_counts = transfer_counts.reset_index()
transfer_counts = transfer_counts[transfer_counts['ptid'] > 1]
# Get a list of tuples that contain the values from the rows.
edge_weight_data = transfer_counts[['from', 'to', 'ptid']]
edge_weight_data.rename(index=str,
columns={'ptid': 'weight'},
inplace=True)
sum_of_all_transfers = edge_weight_data['weight'].sum()
#print(sum_of_all_transfers)
#edge_weight_data['ptid'] = edge_weight_data['ptid']/sum_of_all_transfers
#edge_weight_data.to_csv('edge_wdadult%s.csv' % str(i), header=True, index=False)
weighted_edges = list(
itertools.starmap(lambda f, t, w: (f, t, int(w)),
edge_weight_data.itertuples(index=False, name=None)))
G = nx.DiGraph()
# print(weighted_edges)
G.add_weighted_edges_from(weighted_edges)
en = G.number_of_edges()
nn = G.number_of_nodes()
# calculate the degree
degrees = nx.classes.function.degree(G)
degrees_list = [[n, d] for n, d in degrees]
if b == 1000:
print(degrees_list)
degrees_data = pd.DataFrame(degrees_list, columns=['node', 'degree'])
#degrees_data_degree = degrees_data['degree']
degrees_data.to_csv('degrees_weadult%s.csv' % str(i),
header=True,
index=False)
#look at degrees of the emergency department, need to change it to a dictionary to be able to look up the degree value for this node
degrees_data.set_index('node', inplace=True)
degrees_dict = degrees_data.to_dict()['degree']
#check if there is data in this specific subset eg there may not be data in a weekend stress set in summer...
if 'AE' in degrees_dict:
emergency_degrees = degrees_dict['AE']
#print('in dict')
no_data = False
else:
#print('not in dict')
no_data = True
emergency_degrees = 0
#degrees_list.append(list(degrees.values))
#degrees_list.to_csv('degrees%s.csv' % str(i), header=True, index=False)
#number of transfers from medical wards to theatre
acute_to_theatre = G.get_edge_data('acute medical ward',
'theatre',
default={}).get('weight', 0)
gen_to_theatre = G.get_edge_data('general medical ward',
'theatre',
default={}).get('weight', 0)
card_to_theatre = G.get_edge_data('cardiology ward', 'theatre',
default={}).get('weight', 0)
rehab_to_theatre = G.get_edge_data('rehab', 'theatre',
default={}).get('weight', 0)
total_medical_to_theatre = acute_to_theatre + gen_to_theatre + card_to_theatre + rehab_to_theatre
#number of circular or unnecessary ward transfers
med_to_med_acute = G.get_edge_data('acute medical ward',
'acute medical ward',
default={}).get('weight', 0)
med_to_med_acgen = G.get_edge_data('acute medical ward',
'general medical ward',
default={}).get('weight', 0)
med_to_med_genac = G.get_edge_data('general medical ward',
'acute medical ward',
default={}).get('weight', 0)
med_to_med_general = G.get_edge_data('general medical ward',
'general medical ward',
default={}).get('weight', 0)
med_to_surg = G.get_edge_data('general medical ward',
'general surgical ward',
default={}).get('weight', 0)
med_to_ortho = G.get_edge_data('general medical ward',
' orthopaedic ward',
default={}).get('weight', 0)
med_to_surg_acute = G.get_edge_data('acute medical ward',
'general surgical ward',
default={}).get('weight', 0)
med_to_orth_acute = G.get_edge_data('acute medical ward',
' orthopaedic ward',
default={}).get('weight', 0)
acmed_to_ns = G.get_edge_data('acute medical ward', 'ns ward',
default={}).get('weight', 0)
genmed_to_ns = G.get_edge_data('general medical ward',
'ns ward',
default={}).get('weight', 0)
acmed_to_atc = G.get_edge_data('acute medical ward',
'ATC surgical ward',
default={}).get('weight', 0)
genmed_to_atc = G.get_edge_data('general medical ward',
'ATC surgical ward',
default={}).get('weight', 0)
total_medical_ward_transfers = med_to_med_acute + med_to_med_general + med_to_med_acgen + med_to_med_genac + med_to_ortho + med_to_surg + med_to_surg_acute + med_to_orth_acute + acmed_to_ns + genmed_to_ns + acmed_to_atc + genmed_to_atc
# print (total_medical_ward_transfers)
ae_surg = G.get_edge_data('AE', 'general surgical ward', default={}).get(
'weight',
0) + G.get_edge_data('AE', 'orthopaedic ward', default={}).get(
'weight',
0) + G.get_edge_data('AE', 'ATC surgical ward', default={}).get(
'weight',
0) + G.get_edge_data('AE', 'gynae ward', default={}).get(
'weight', 0) + G.get_edge_data(
'AE', 'ns ward', default={}).get('weight', 0)
print(ae_surg)
ae_med = G.get_edge_data('AE', 'acute medical ward', default={}).get(
'weight',
0) + G.get_edge_data('AE', 'general medical ward', default={}).get(
'weight',
0) + G.get_edge_data('AE', 'cardiology ward', default={}).get(
'weight', 0) + G.get_edge_data('AE', 'rehab', default={}).get(
'weight', 0) + G.get_edge_data(
'AE', 'cdu', default={}).get('weight', 0)
if ae_surg == 0:
ratio_wards_surg_med = 0
else:
ratio_wards_surg_med = ae_med / ae_surg
# calculate the centrality of each node - fraction of nodes the incoming/outgoing edges are connected to
incentrality = nx.algorithms.centrality.in_degree_centrality(G)
# check if the theatre node exists in this data subset
if 'theatre' in incentrality:
in_theatre_centrality = incentrality['theatre']
else:
in_theatre_centrality = 0
outcentrality = nx.algorithms.centrality.out_degree_centrality(G)
if 'theatre' in outcentrality:
out_theatre_centrality = outcentrality['theatre']
else:
out_theatre_centrality = 0
if 'AE' in outcentrality:
out_ed_centrality = outcentrality['AE']
else:
out_ed_centrality = 0
# flow hiearchy - finds strongly connected components
if nn == 0:
flow_hierarchy = 0
else:
flow_hierarchy = nx.algorithms.hierarchy.flow_hierarchy(G)
bet_centr = nx.algorithms.centrality.betweenness_centrality(G)
if 'theatre' in bet_centr:
theatres_bet_centrality = bet_centr['theatre']
else:
theatres_bet_centrality = 0
if en == 0:
theatres_eigen_centr = 0
ed_eigen_centr = 0
assortativity_net_inout = 0
else:
eigen_centr = nx.eigenvector_centrality_numpy(G)
assortativity_net_inout = nx.degree_assortativity_coefficient(
G, x='out', y='in', weight='weights')
if 'theatre' in eigen_centr:
theatres_eigen_centr = eigen_centr['theatre']
else:
theatres_eigen_centr = 0
if 'AE' in eigen_centr:
ed_eigen_centr = eigen_centr['AE']
else:
ed_eigen_centr = 0
density_net = nx.density(G)
transitivity_net = nx.transitivity(G)
data_list.append({
'month': i,
'number of transfers': len(data_reduced['transfer_day']),
'number nodes': nn,
'number edges': en,
'flow hierarchy': flow_hierarchy,
'emergency degrees': emergency_degrees,
'outcentrality ed': out_ed_centrality,
'incentrality theatres': in_theatre_centrality,
'outcentrality theatres': out_theatre_centrality,
'bet centrality theatres': theatres_bet_centrality,
'medical to theatre': total_medical_to_theatre,
'medical ward transfers': total_medical_ward_transfers,
'med surg ratio': ratio_wards_surg_med,
'eigen_centr_theatre': theatres_eigen_centr,
'eigen_centr_ed': ed_eigen_centr,
'density': density_net,
'transitivity': transitivity_net,
'average_breach_percentage': average_breach_perc,
'average bed occupancy': average_bed_occupancy
})
return data_list
print("Exportação do arquivo GraphML com a rede:")
nx.write_graphml(DG, '/home/akina/Dropbox/TCC/Resultados/Graphml/rede_financiamento.graphml')
################################################
print("-----------------------------------------------------")
print("Exportação dos resultados dos cálculos de centralidade:")
################################################
print("1 - Cálculo da centralidade de autovetor")
#eigenvector_centrality_numpy(G, weight=None, max_iter=50, tol=0)
eigenvector_centrality = nx.eigenvector_centrality_numpy(DG, "weight", len(DG), 0)
#print(['{}, {:0.20f}'.format(node, eigenvector_centrality[node]) for node in eigenvector_centrality], file=open('/home/akina/Dropbox/TCC/Dados/teste_eigenvector_centrality.csv', "w"))
csv_file_eigenvector = '/home/akina/Dropbox/TCC/Resultados/Centralidades_Geral_Todos/eigenvector_centrality.csv'
with open(csv_file_eigenvector, "w") as output_eigenvector:
writer = csv.writer(output_eigenvector)
for node in sorted(eigenvector_centrality, key=lambda x: eigenvector_centrality[x], reverse=True):
writer.writerow(
["{}".format(DG.node[node]["nome_rotulo_vertice"]), "{:0.20f}".format(eigenvector_centrality[node])])
csv_file_eigenvector_votos = '/home/akina/Dropbox/TCC/Resultados/Centralidades_Candidatos_Votos/votos_eigenvector_centrality.csv'
with open(csv_file_eigenvector_votos, "w") as output_eigenvector_votos:
writer = csv.writer(output_eigenvector_votos)
for node in sorted(eigenvector_centrality, key=lambda x: eigenvector_centrality[x], reverse=True):
print("1")
measure_unsorted[0][j] = measure[0][j]
measure[0][j] = sorted(measure[0][j].items(),
key=operator.itemgetter(1),
reverse=True) ## descending
for j in range(no_of_graphs):
measure[1][j] = nx.closeness_centrality(graph_list[j])
print("2")
measure_unsorted[1][j] = measure[1][j]
measure[1][j] = sorted(measure[1][j].items(),
key=operator.itemgetter(1),
reverse=True) ## descending
for j in range(no_of_graphs):
measure[2][j] = nx.eigenvector_centrality_numpy(graph_list[j])
print("3")
measure_unsorted[2][j] = measure[2][j]
measure[2][j] = sorted(measure[2][j].items(),
key=operator.itemgetter(1),
reverse=True) ## descending
with open(
"/home/sukanya/Desktop/jadavpur_internship/CODES/Result_corr_coeff.odt",
"a+") as sn:
sn.write("\n")
sn.write(" FOR GRAPH 6 :----")
sn.write("\n\n")
##### correlation coefficient between degree and closeness centrality
a, b = zip(*sorted(measure_unsorted[0][i].items()))
x = b
def test_eigenvector_centrality_unweighted_numpy(self):
G = self.H
p = nx.eigenvector_centrality_numpy(G)
for (a, b) in zip(list(p.values()), self.G.evc):
assert_almost_equal(a, b)
def centrality(cname, directed=False):
C = np.genfromtxt('dat/' + cname + '.dat')
if ((directed == True) & (np.max(C) == 2)):
C = C.T / 2.0
# print np.max(C)
if directed == True:
G = nx.from_numpy_matrix(C, create_using=nx.DiGraph())
BC = np.asarray(nx.betweenness_centrality(G).values())
IC = np.asarray(nx.in_degree_centrality(G).values())
OC = np.asarray(nx.out_degree_centrality(G).values())
EC = np.asarray((nx.eigenvector_centrality_numpy(G)).values())
KC = np.asarray((nx.katz_centrality(G)).values())
CC = np.asarray((nx.closeness_centrality(G)).values())
LC = np.asarray((nx.load_centrality(G)).values())
i_BC = BC.argsort()[::-1]
i_IC = IC.argsort()[::-1]
i_OC = OC.argsort()[::-1]
i_EC = EC.argsort()[::-1]
i_KC = KC.argsort()[::-1]
i_CC = CC.argsort()[::-1]
i_LC = LC.argsort()[::-1]
np.savetxt('dat/BC-' + cname + '.txt',
zip(i_BC,
np.sort(BC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/IC-' + cname + '.txt',
zip(i_IC,
np.sort(IC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/OC-' + cname + '.txt',
zip(i_OC,
np.sort(OC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/EC-' + cname + '.txt',
zip(i_EC,
np.sort(EC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/KC-' + cname + '.txt',
zip(i_KC,
np.sort(KC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/CC-' + cname + '.txt',
zip(i_CC,
np.sort(CC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/LC-' + cname + '.txt',
zip(i_LC,
np.sort(LC)[::-1]),
fmt='%10d %15.9f')
if directed == False:
G = nx.from_numpy_matrix(C)
BC = np.asarray(nx.betweenness_centrality(G).values())
DC = np.asarray(nx.degree_centrality(G).values())
LC = np.asarray((nx.load_centrality(G)).values())
CC = np.asarray((nx.closeness_centrality(G)).values())
EC = np.asarray((nx.eigenvector_centrality_numpy(G)).values())
i_BC = BC.argsort()[::-1]
i_DC = DC.argsort()[::-1]
i_LC = LC.argsort()[::-1]
i_CC = CC.argsort()[::-1]
i_EC = EC.argsort()[::-1]
np.savetxt('dat/BC-' + cname + '.txt',
zip(i_BC,
np.sort(BC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/DC-' + cname + '.txt',
zip(i_DC,
np.sort(DC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/LC-' + cname + '.txt',
zip(i_LC,
np.sort(LC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/CC-' + cname + '.txt',
zip(i_CC,
np.sort(CC)[::-1]),
fmt='%10d %15.9f')
np.savetxt('dat/EC-' + cname + '.txt',
zip(i_EC,
np.sort(EC)[::-1]),
fmt='%10d %15.9f')
import networkx as nx
import csv
import scipy
import numpy
f = open('/Users/dukechan/Downloads/eigenvector_centrality.txt', 'w')
csv_file = "/Users/dukechan/Downloads/sms_sna_oct18_undirected-1.csv"
reader = csv.reader(file(csv_file))
G = nx.Graph()
for line in reader:
G.add_edge(line[4], line[5])
E = nx.eigenvector_centrality_numpy(G)
for item in E:
f.write("Node: %s Centrality %.10f\n" % (item, E[item]))
f.close()
def test_empty_numpy(self):
e = networkx.eigenvector_centrality_numpy(networkx.Graph())
def network_equilibrium(n, d, p, graph=False):
"""
Returns a network with the same properties as a human social network, namely high clustering, low average shortest
distance and a skewed degree distribution. This is achieved by applying an algorithm that makes new connections
using prestige and distance. The algorithm includes a birth-death process which prevents the network from reaching
completness.
Parameters
----------
n : int
Size of network, where the network has nxn nodes
d : float
Strength of the distance decay function
p : float
Probability of a node losing most of its edges at a given iteration
graph : bool
Whether or not the a graph for the geodesics value at each round is printed
Notes
-----
The algorithm works by taking a graph and at each iteration adding an edge between nodes based on prestige
mechanics. At every iteration there is also a chance that one node gets all but its initial four edges (to its left,
right, up, and down) removed.
"""
G = nx.grid_2d_graph(n, n, True)
G = nx.convert_node_labels_to_integers(G)
initial_nbrs = {}
for node in list(G.nodes):
nbrs = [nbr for nbr in G[node]]
initial_nbrs[node] = nbrs
nodes = list(G.nodes)
num_nodes = len(nodes)
with open(r'data\{0}x{0} p={1} d={2}.csv'.format(n, p, d), 'w', newline='') as file:
fields = ['iterations', 'edges', 'geodesic', 'clustering', 'movement', 'move_avg', 'avg_degree', 'degree_skew',
'alpha', 'KS', 'p_KS', 'alpha1', 'alpha2', 'switch', 'KS_double', 'p_KS_double']
writer = csv.DictWriter(file, fieldnames=fields)
writer.writeheader()
start = {}
start['iterations'] = 0
start['edges'] = nx.number_of_edges(G)
geo = nx.average_shortest_path_length(G)
start['geodesic'] = geo
start['clustering'] = nx.average_clustering(G)
start['movement'] = 'N/A'
start['move_avg'] = 'N/A'
degrees = [G.degree(n) for n in nodes]
start['avg_degree'] = np.mean(degrees)
start['degree_skew'] = stats.skew(degrees)
alpha, ks, p_ks, alpha1, alpha2, switch, ks2, p_ks2 = ks_test(G)
start['alpha'] = alpha
start['KS'] = ks
start['p_KS'] = p_ks
start['alpha1'] = alpha1
start['alpha2'] = alpha2
start['switch'] = switch
start['KS_double'] = ks2
start['p_KS_double'] = p_ks2
writer.writerow(start)
# Necessary for graphing change in clustering and geodesic
x_vals = [0]
geos = [geo]
# Used for gathering info on behaviour of removal phase
in_a_row = 0
iterations = 0
# Used to measure whether the network is in equilibrium
prev_geo = nx.average_shortest_path_length(G)
movement = []
while in_a_row < 3:
for i in range(num_nodes):
iterations += 1
# Select random person
node = random.choice(nodes)
odds = []
centrality = nx.eigenvector_centrality_numpy(G)
nbrs = [nbr for nbr in G[node]]
nbrs.append(node)
for optn in nodes:
if optn in nbrs:
odds.append(0)
else:
dist = nx.shortest_path_length(G, node, optn)
# Set the odds of being connected to based on eigenvector centrality of the option and its
# distance from n
w = centrality[optn] * math.exp(-d*dist)
odds.append(w)
# Select at random a new connection for n from the list of options given the assigned odds
a = random.choices(nodes, weights=odds, k=1)[0]
G.add_edge(node, a)
# Removal only has a p probability of occurring
if random.random() < p:
# count_remove_n += 1
# Select node for removal
rmv = random.choice(nodes)
# List all neighbours of the node being removed
nbrs = [nbr for nbr in G[rmv]]
num_nbrs = len(nbrs)
to_add = []
for nbr in nbrs:
# The 4 initial neighbours always stay connected
if nbr in initial_nbrs[rmv]:
to_add.append(nbr)
# count_keep_e += 1
else:
# Every other connection is given a probability of maintaining their connection
mutuals = list(nx.common_neighbors(G, rmv, nbr))
odd = ((len(mutuals) + 1) / num_nbrs)
if random.random() < odd:
to_add.append(nbr)
# Update the connections
G.remove_node(rmv)
G.add_node(rmv)
for choice in to_add:
G.add_edge(rmv, choice)
end_of_round = {}
end_of_round['iterations'] = iterations
geo = nx.average_shortest_path_length(G)
end_of_round['edges'] = nx.number_of_edges(G)
end_of_round['geodesic'] = geo
end_of_round['clustering'] = nx.average_clustering(G)
move = geo - prev_geo
prev_geo = geo
end_of_round['movement'] = move
degrees = [G.degree(node) for node in nodes]
end_of_round['avg_degree'] = np.mean(degrees)
end_of_round['degree_skew'] = stats.skew(degrees)
movement.append(move)
check = np.mean(movement)
end_of_round['move_avg'] = check
alpha, ks, p_ks, alpha1, alpha2, switch, ks2, p_ks2 = ks_test(G)
end_of_round['alpha'] = alpha
end_of_round['KS'] = ks
end_of_round['p_KS'] = p_ks
end_of_round['alpha1'] = alpha1
end_of_round['alpha2'] = alpha2
end_of_round['switch'] = switch
end_of_round['KS_double'] = ks2
end_of_round['p_KS_double'] = p_ks2
writer.writerow(end_of_round)
x_vals.append(iterations)
geos.append(geo)
if abs(check) < 0.001:
in_a_row += 1
else:
in_a_row = 0
if graph:
plt.scatter(x_vals, geos, s=10)
plt.title("Geodesic Equilibrium")
plt.xlabel("# of Iterations")
plt.ylabel("Average Geodesic")
plt.axhline(3.4, c='black', lw=1)
plt.savefig(r'graphs\{0}x{0} p={1} d={2} geodesic.csv'.format(n, p, d))
plt.close()
return G
