def detectBetweenness(G, numClusters, sites, bipartite):
Gnew = copy.deepcopy(G)
numComponents = nx.number_connected_components(G)
betweenness = nx.edge_betweenness_centrality(Gnew, weight='capacity')
pickle.dump(betweenness, open("betweennessUnipartite.p", "wb"))
#betweenness = pickle.load("betweenessUnipartite.p", "rb")
while (numComponents < numClusters):
print "num components is now ", numComponents ### REMEMBER TO DELETE THIS ###
# calculate betweenness of each edge
betweenness = nx.edge_betweenness_centrality(Gnew, weight='capacity')
## identify and remove the edge with highest betweenness
max_ = max(betweenness.values())
for k, v in betweenness.iteritems():
if float(v) == max_:
G.remove_edge(k[0], k[1])
numComponents = nx.number_connected_components(G)
clusters = {}
i=0
j = 0
for component in list(nx.connected_components(Gnew)):
for node in component:
if node in sites:
clusters[node] = i
j +=1
print j, "Nodes in cluster ", i
j = 0
i += 1
return clusters
def find_groups_girvan_newman(self, num_groups):
if (num_groups==1):
return set([self.G])
elif (num_groups in self.groupCache):
#return a copy of the stored set
return self.groupCache[num_groups].copy()
elif (num_groups > len(self.G.nodes())):
return self.find_groups(len(self.G.nodes))
#returns set of subgraphs
previous_partition = self.find_groups(num_groups-1)
#map subgraph to betweenness dict (a dict mapping edges to betweenness)
betweenness_map = {subgraph:nx.edge_betweenness_centrality(subgraph) for subgraph in previous_partition}
#Map subgraph to the (edge, betweenness) pair of the max betweenness in that subgraph
betweenness_max_map = {e[0]:max(e[1].items(), key=lambda(x):x[1]) for e in betweenness_map.items() if len(e[0].nodes()) > 1}
#Track removed edges to add them again at end of algorithm
removed_edges = []
#Loop until a subgraph is split
while True:
print "Removing edge"
#Identify the subgraph and edge with max betweenness
target_subgraph_edge=max(betweenness_max_map.items(), key=lambda(x):x[1][1])
target_subgraph = target_subgraph_edge[0]
target_edge= target_subgraph_edge[1][0]
max_betweenness = -1
#Remove the edge (temporarily)
target_subgraph.remove_edge(target_edge[0], target_edge[1])
removed_edges.append(target_edge)
connected_components = nx.connected_components(target_subgraph)
if len(connected_components) > 1:
#Removing one edge from a connected component will result in max 2 connected components
new_subgraph_1 = target_subgraph.subgraph(connected_components[0])
new_subgraph_2 = target_subgraph.subgraph(connected_components[1])
#Repair removed edges in target_subgraph
target_subgraph.add_edges_from(removed_edges)
#Remove target subgraph
previous_partition.discard(target_subgraph)
#Add new subgraphs
previous_partition.add(new_subgraph_1)
previous_partition.add(new_subgraph_2)
#Store result
self.groupCache[num_groups] = previous_partition
return previous_partition.copy()
else:
#Recalculate betweenness, max betweenness for target subgraph
target_betweenness = nx.edge_betweenness_centrality(target_subgraph)
betweenness_map[target_subgraph] = target_betweenness
betweenness_max_map[target_subgraph] = max(target_betweenness.items(), key=lambda(x):x[1])
#Repeat loop
continue
def run_n(self, n):
# Until there is no edge in the graph
while len(self.G.edges()) != 0:
# Find the most betweenness edge
edge = max(nx.edge_betweenness_centrality(self.G).items(),
key=lambda item: item[1])[0]
# Remove the most betweenness edge
self.G.remove_edge(edge[0], edge[1])
# Get the the connected nodes
components = [
list(c) for c in list(nx.connected_components(self.G))
]
# Divide the graph into n parts.
if len(components) <= n:
# Compute Q
currentQ = self.calculateQ(components, self.G_copy)
if currentQ not in self.all_Q:
self.all_Q.append(currentQ)
if currentQ > self.max_Q:
self.max_Q = currentQ
self.partition = components
print('The number of communities:', len(self.partition))
print('Max_Q:', self.max_Q)
print(self.partition)
return self.partition, self.all_Q, self.max_Q
def plot_edge_btwn(G, bins=20):
"""
Plot the edge-betweenness distributions.
Args:
G: networkx graph object
Returns:
figure handle & axes array.
"""
# Get edge-betweenness dictionary
edge_btwn_dict = nx.edge_betweenness_centrality(G)
# Sort edge-betweenness dictionary by edge-betweenness values
edge_btwn_labels_sorted, edge_btwn_vec_sorted = \
network_compute.get_ranked(edge_btwn_dict)
# Open figure & axes
fig, axs = plt.subplots(2, 1)
# Plot histogram
axs[0].hist(edge_btwn_vec_sorted, bins)
axs[0].set_ylabel('Occurrences')
axs[0].set_xlabel('Edge-betweenness')
# Plot sorted node between values
axs[1].scatter(np.arange(len(edge_btwn_vec_sorted)),
edge_btwn_vec_sorted, s=20, c='r')
axs[1].set_xlabel('Area')
axs[1].set_ylabel('Edge-betweenness')
return fig, axs
def f28(self):
start = 0
c_vals = nx.edge_betweenness_centrality(self.G).values()
res = sum(c_vals)
stop = 0
# self.feature_time.append(stop - start)
return res
def test_C4(self):
"""Edge betweenness centrality: C4"""
G=nx.cycle_graph(4)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer={(0, 1):2,(0, 3):2, (1, 2):2, (2, 3): 2}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n]/6.0)
def run(self):
while len(self.G.edges()) != 0:
edges = {}
edges_betweenness_centrality = nx.edge_betweenness_centrality(
self.G)
#for e, ebc in edges_betweenness_centrality.items():
#print(print(self.G.get_edge_data(e[0],e[1])))
for e, ebc in edges_betweenness_centrality.items():
#print(self.G.get_edge_data(e[0],e[1]))
edge_weight = ebc / self.G.get_edge_data(e[0], e[1])['weight']
edges[e] = edge_weight
edge = max(edges.items(), key=lambda item: item[1])[0]
self.G.remove_edge(edge[0], edge[1])
components = [
list(c) for c in list(nx.connected_components(self.G))
]
if len(components) != len(self.partition):
#compute the Q
cur_Q = self.cal_Q(components, self.G_copy)
if cur_Q not in self.all_Q:
self.all_Q.append(cur_Q)
if cur_Q > self.max_Q:
self.max_Q = cur_Q
self.partition = components
print('-----------the divided communities and the Max Q------------')
print('The number of Communites:', len(self.partition))
print('Max_Q:', self.max_Q)
print(self.partition)
return self.partition, self.all_Q, self.max_Q
def divisive_approach(graph):
"""
a modularity-based algorithm, by deleting the weakest links in graph;
edge betweenness is the negatively relevant strength score for a link
:param graph: a nx.Graph
:return: labels of each node
"""
time_start = time.time()
print("Calculating communities with DA...")
g = clone_graph(graph)
partitions = [[n for n in g.nodes()]]
labels = list(g.nodes())
max_q = 0.0
while len(g.edges()) > 0:
edge = max(nx.edge_betweenness_centrality(g).items(),
key=lambda item: item[1])[0]
g.remove_edge(edge[0], edge[1])
components = [list(c) for c in list(nx.connected_components(g))]
if len(components) != len(partitions):
q = cal_Q(components, graph)
if q > max_q:
max_q = q
partitions = components
for i in range(len(partitions)):
for node in partitions[i]:
labels[node] = i
time_end = time.time()
print("Calculation time:", time_end - time_start, "seconds")
return labels
def run(self):
#Until there is no edge in the graph
while len(self.G.edges()) != 0:
#Find the most betweenness edge
edge = max(nx.edge_betweenness_centrality(self.G).items(),
key=lambda item: item[1])[0]
#Remove the most betweenness edge
self.G.remove_edge(edge[0], edge[1])
#List the the connected nodes
components = [
list(c) for c in list(nx.connected_components(self.G))
]
if len(components) != len(self.partition):
#compute the Q
cur_Q = self.cal_Q(components, self.G_copy)
if cur_Q not in self.all_Q:
self.all_Q.append(cur_Q)
if cur_Q > self.max_Q:
self.max_Q = cur_Q
self.partition = components
print('-----------the Max Q and divided communities-----------')
print('The number of Communites:', len(self.partition))
print("Communites:", self.partition)
print('Max_Q:', self.max_Q)
return self.partition, self.all_Q, self.max_Q
def test_K5(self):
"""Edge betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer=dict.fromkeys(G.edges(),1)
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def cluster_edge_betweenness(iterations, G):
for i in range(iterations):
print('Iteration ', i + 1, ' of ', iterations)
eb = nx.edge_betweenness_centrality(G, 10)
max_eb = max(eb, key=eb.get)
G.remove_edge(max_eb[0], max_eb[1])
return G
def run(self):
while len(self.G.edges()) != 0:
# nx.edge_betweenness_centrality 返回的是类似于 {('C', 'F'): 0.4} 这种结构
# 计算每天边界数，寻找边届数最大的边
edge = max(nx.edge_betweenness_centrality(self.G).items(),
key=lambda item: item[1])[0]
# 移除边界数最大的边
self.G.remove_edge(edge[0], edge[1])
# List the the connected nodes
components = [
list(c) for c in list(nx.connected_components(self.G))
]
if len(components) != len(self.partition):
# compute the Q
# nx.algorithms.community.modularity(self.G_copy, components) 可以直接调用networkx的库函数 等价于 call_Q()
cur_Q = self.cal_Q(components, self.G_copy)
if cur_Q not in self.all_Q:
self.all_Q.append(cur_Q)
# 还可以在这一步做一个map换成call_Q与components的关系
if cur_Q > self.max_Q:
self.max_Q = cur_Q
self.partition = components
print('-----------the Max Q and divided communities-----------')
print('The number of Communites:', len(self.partition))
print("Communites:", self.partition)
print('Max_Q:', self.max_Q)
return self.partition, self.all_Q, self.max_Q
def test_P4(self):
"""Edge betweenness centrality: P4"""
G=nx.path_graph(4)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer={(0, 1):3,(1, 2):4, (2, 3):3}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def CalculateBetweeness(graph):
BetweenValue = nx.edge_betweenness_centrality(graph, normalized=True, k=None, weight=None, seed=None)
graph.remove_edges_from([k for k, v in BetweenValue.iteritems() if v == max(BetweenValue.values())])
return graph
def test_normalized_P4(self):
"""Edge betweenness centrality: P4"""
G = nx.path_graph(4)
b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer = {(0, 1): 3, (1, 2): 4, (2, 3): 3}
for n in sorted(G.edges()):
assert_almost_equal(b[n], b_answer[n] / 6.0)
def file_to_dot(infile):
interactions = defaultdict(lambda: 0)
es = list(edges(infile))
for a, b, users in es:
interactions[a, b] = users
keys, ratio = compute_ratios(interactions,
lambda k: interactions[k, k] > 5)
G = nx.Graph()
for a, b, users in es:
if a > b and a in keys and b in keys and users > 0 and ratio[a, b] > 0:
rat = (ratio[a, b] + ratio[b, a]) / 2
G.add_edge(a, b, {
'ratio': rat,
'users': users,
'connection': rat**-1
})
btwn = nx.edge_betweenness_centrality(G, weight='connection')
GG = nx.Graph()
GG.add_edges_from([(a, b, {
'weight': val
}) for (a, b), val in btwn.items()])
# GG.add_edges_from([(a, b, merge({'betweenness':btwn[a,b]}, G[a][b]))
# for a,b in G.edges_iter()])
for node in GG.nodes_iter():
GG.node[node]['height'] = GG.node[node]['width'] = size(G, node)
GG.node[node]['color'] = color(G, node)
Gtree = nx.minimum_spanning_tree(GG)
Gtree_dot = nx.to_pydot(Gtree)
return Gtree_dot.to_string()
def list_edge_betweenness(G):
edge={}
edges_list=list(G.edges())
edge_betweenness=nx.edge_betweenness_centrality(G, normalized=True, weight='weight')
for i in edge_betweenness.keys():
edge[i]=edge_betweenness[i]
return edge
def _calc_bc_subset(G, Gnx, normalized, weight, k, seed, result_dtype):
# NOTE: Networkx API does not allow passing a list of vertices
# And the sampling is operated on Gnx.nodes() directly
# We first mimic acquisition of the nodes to compare with same sources
random.seed(seed) # It will be called again in nx's call
sources = random.sample(Gnx.nodes(), k)
# NOTE: Since we sampled the Networkx graph, the sources are already
# external ids, so we don't need to translate to external ids for
# cugraph
df = cugraph.edge_betweenness_centrality(
G,
k=sources,
normalized=normalized,
weight=weight,
result_dtype=result_dtype,
)
nx_bc_dict = nx.edge_betweenness_centrality(
Gnx, k=k, normalized=normalized, weight=weight, seed=seed
)
nx_df = generate_nx_result(nx_bc_dict, type(Gnx) is nx.DiGraph).rename(
columns={"betweenness_centrality": "ref_bc"}, copy=False
)
merged_df = df.merge(nx_df, on=['src', 'dst']).rename(
columns={"betweenness_centrality": "cu_bc"}, copy=False
).reset_index(drop=True)
return merged_df
def get_communities(graph):
betweenness = nx.edge_betweenness_centrality(graph)
sorted_betweeness = [x[0] for x in sorted(betweenness.items(), key = lambda x : x[1], reverse = True)]
best_partitions = []
max_modularity = -1.0
graph_copy = graph.copy()
while sorted_betweeness:
communities = [list(x) for x in nx.connected_components(graph_copy)]
partitions = {}
for i in range(len(communities)):
for node in communities[i]:
partitions[node] = i
modularity = community.modularity(partitions, graph_copy)
if modularity > max_modularity:
best_partitions = communities
max_modularity = modularity
elif modularity <= max_modularity:
break;
graph_copy.remove_edge(*sorted_betweeness[0])
del sorted_betweeness[0]
for partition in best_partitions:
print sorted(partition)
val_map = {}
for partition in best_partitions:
value = random.random()
while value in val_map.values():
value = random.random()
for node in partition:
val_map[node] = value
values = [val_map.get(node) for node in graph.nodes()]
nx.draw_spring(graph, node_color = values, node_size = 500, with_labels = True)
plt.savefig(sys.argv[2])
def _calc_bc_full(G, Gnx, normalized, weight, k, seed, result_dtype):
df = cugraph.edge_betweenness_centrality(
G,
k=k,
normalized=normalized,
weight=weight,
seed=seed,
result_dtype=result_dtype,
)
assert (
df["betweenness_centrality"].dtype == result_dtype
), "'betweenness_centrality' column has not the expected type"
nx_bc_dict = nx.edge_betweenness_centrality(
Gnx, k=k, normalized=normalized, seed=seed, weight=weight
)
nx_df = generate_nx_result(nx_bc_dict, type(Gnx) is nx.DiGraph).rename(
columns={"betweenness_centrality": "ref_bc"}, copy=False
)
merged_df = df.merge(nx_df, on=['src', 'dst']).rename(
columns={"betweenness_centrality": "cu_bc"}, copy=False
).reset_index(drop=True)
return merged_df
def girvan_newman_algorithm(G, weight):
""" G는 원래 네트워크 g는 Edge를 한개씩 끊어나갈 네트워크 """
g = G.copy()
""" initial """
step = 0 # step
log_step = [] # step 기록
log_modularity = [] # modularity 기록
old_max_m = 0 # 이전 최대 modularity 기억
k = sorted(nx.connected_components(G), key=len,
reverse=True) # k 는 모두 연결되어있는 Community를 노드로 나타낸 값
m = community.modularity(G, communities=k, weight=weight) # modularity
max_step = 0 # max_step은 modularity가 최대일 때 step값 기록용
""" Girvan-Newman algorithm """
while len(g.edges()) > 0:
k = sorted(nx.connected_components(g), key=len,
reverse=True) # 커뮤니티 추출
m = community.modularity(G, communities=k,
weight=weight) # 추출된 커뮤니티의 modularity 계산
if m > old_max_m: # 이전 최대 modularity보다 현재 modularity가 높을 경우 기록
max_step = step
old_max_m = m
log_step = log_step + [step] # 로깅용
log_modularity = log_modularity + [m] # 로깅용
print("step: ", step, " modularity: ", m)
""" remove edge """
step = step + 1
betweenness = nx.edge_betweenness_centrality(
g, weight=weight) # betweennes centrality 계산
max_edge = max(
betweenness,
key=betweenness.get) # betweeness centrality가 가장 큰 Edge 선택
g.remove_edge(max_edge[0], max_edge[1]) # Edge 추출
return log_step, log_modularity, max_step
def test_edge_betweenness_centrality_nx(
graph_file,
directed,
edgevals
):
Gnx = utils.generate_nx_graph_from_file(graph_file, directed, edgevals)
assert nx.is_directed(Gnx) == directed
nx_bc = nx.edge_betweenness_centrality(Gnx)
cu_bc = cugraph.edge_betweenness_centrality(Gnx)
# Calculating mismatch
networkx_bc = sorted(nx_bc.items(), key=lambda x: x[0])
cugraph_bc = sorted(cu_bc.items(), key=lambda x: x[0])
err = 0
assert len(networkx_bc) == len(cugraph_bc)
for i in range(len(cugraph_bc)):
if (
abs(cugraph_bc[i][1] - networkx_bc[i][1]) > 0.01
and cugraph_bc[i][0] == networkx_bc[i][0]
):
err = err + 1
print(f"{cugraph_bc[i][1]} and {cugraph_bc[i][1]}")
print("Mismatches:", err)
assert err < (0.01 * len(cugraph_bc))
def test_K5(self):
"""Edge betweenness centrality: K5"""
G=nx.complete_graph(5)
b=nx.edge_betweenness_centrality(G, weight=None, normalized=False)
b_answer=dict.fromkeys(G.edges(),1)
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def EBGirvanNewman(G):
print("Inside EBGirvanNewman")
initcomp = nx.number_connected_components(G)
ncomp = initcomp
print("Initial ncomp, ", ncomp)
while ncomp <= initcomp:
bw = nx.edge_betweenness_centrality(G, weight='weight')
#print(bw)
#find the edge with max centrality
max_ = max(bw.values())
print(".....................", max_)
#find the edge with the highest centrality and remove all of them-more than one
#for k, v in bw.iteritems():
for k, v in bw.items():
if float(v) == max_:
G.remove_edge(k[0], k[1])
global k1
k1 = k[1]
global k0
k0 = k[0]
#recalculate the no of components
ncomp = nx.number_connected_components(G)
print("No. of components", ncomp)
print("Over............")
def gRa(g, w):
'''w为图中的边数，表示经过减边p扰动后仍然留在数据中的边数'''
tg = g.copy()
Rq = nx.to_scipy_sparse_matrix(g)
Rq = Rq.toarray()
bw = nx.edge_betweenness_centrality(g, normalized=False)
norm = sum(bw.values())
e_num = len(g.edges())
n = len(g)
N = (n * (n - 1)) / 2
for k, v in bw.items():
g.add_edge(*k, weight=v)
# print g.edges(data=True)
R = nx.to_scipy_sparse_matrix(g, weight='weight')
Rp = R.toarray()
Rp = w * Rp * 2.0 / Rp.sum()
q = float(e_num - w) / (N - e_num)
for i, each in enumerate(Rq):
for j, e in enumerate(each):
if e == 0:
Rp[i, j] = q # 超级绕采用特别方式在Rp中加入Rq
for i in range(n):
Rp[i,i]=0 #去除对角线上的q
return Rp
def run(self):
# Until there is no edge in the graph
while len(self.G.edges()) != 0:
# Find the most betweenness edge
edge = max(nx.edge_betweenness_centrality(self.G).items(),
key=lambda item: item[1])[0]
# Remove the most betweenness edge
self.G.remove_edge(edge[0], edge[1])
# Get the the connected nodes
components = [
list(c) for c in list(nx.connected_components(self.G))
]
# When the dividing is needed, this is for finding the maxQ and record it while trying.
if len(components) != len(self.partition):
# Compute Q
currentQ = self.calculateQ(components, self.G_copy)
if currentQ not in self.all_Q:
self.all_Q.append(currentQ)
if currentQ > self.max_Q:
self.max_Q = currentQ
self.partition = components
print('The number of communities:', len(self.partition))
print('Max_Q:', self.max_Q)
print(self.partition)
def find_disjoint_graphs(my_graph):
#Dictionary of edges with the calculated value of betweenness centrality
edgeList = nx.edge_betweenness_centrality(my_graph)
maxEdgeBetweenness = 0
edgeNodes = ()
# Loop over items and unpack each item, find maxEdgeBetweenness among all items.
for node_id, edgeBetweennessVal in edgeList.items():
#print("EdgeBetweenness = %f " % edgeBetweennessVal)
#print("EdgeNodes = %s" % (node_id,))
if edgeBetweennessVal > maxEdgeBetweenness:
maxEdgeBetweenness = edgeBetweennessVal
edgeNodes = node_id
print("Highest betweenness is %f - for the edge %s" % (maxEdgeBetweenness, edgeNodes,))
#Remove the edge with highest betweenness
my_graph.remove_edge(edgeNodes[0], edgeNodes[1])
print("Removed edge %s" % (edgeNodes,))
#Add the removed edge to the edges_removed list
edges_removed.append(edgeNodes)
num_of_connected_components = nx.number_connected_components(my_graph)
print("Number of connected components(sub-graphs/communities) after removing edge %s = %d" % (edgeNodes,num_of_connected_components))
G = my_graph
# Draw and show the graph, with labels
nx.draw_networkx(my_graph, pos=None, with_labels=True)
plt.show()
def EBC_weights(g):
w = nx.edge_betweenness_centrality(g)
edges = [(u, v, w[(u, v)]) for u, v in w]
_g = g.copy()
_g.add_weighted_edges_from(edges)
return nx.to_numpy_array(_g)
def girvan_newman_step(graph):
'''
INPUT: Graph G
OUTPUT: None
Run one step of the Girvan-Newman community detection algorithm.
Afterwards, the graph will have one more connected component.
'''
size = nx.number_connected_components(graph)
edges = graph.number_of_edges()
biggroup = len(max(nx.connected_components(graph), key=len))
cur = 0
while cur <= size:
most_connected = Counter(
nx.edge_betweenness_centrality(graph,
weight='sim')).most_common(1)[0][0]
node1 = most_connected[0]
node2 = most_connected[1]
outitems = (node1, node2, size, edges, biggroup, time())
outs = '%d, %d, %d, %d, %d, %f\n' % outitems
print outs
sys.stdout.flush()
#print most_connected; sys.stdout.flush()
graph.remove_edge(*most_connected)
cur = nx.number_connected_components(graph)
def whole_graph_metrics(graph, weighted=False):
graph_metrics = {}
# Shortest average path length
graph_metrics['avg_shortest_path'] = \
nx.average_shortest_path_length(graph, weight=weighted)
# Average eccentricity
ecc_dict = nx.eccentricity(graph)
graph_metrics['avg_eccentricity'] = np.mean(np.array(ecc_dict.values()))
# Average clustering coefficient
# NOTE: Option to include or exclude zeros
graph_metrics['avg_ccoeff'] = \
nx.average_clustering(graph, weight=weighted, count_zeros=True)
# Average node betweeness
avg_node_btwn_dict = nx.betweenness_centrality(graph, normalized=True)
graph_metrics['avg_node_btwn'] = \
np.mean(np.array(avg_node_btwn_dict.values()))
# Average edge betweeness
avg_edge_btwn_dict = nx.edge_betweenness_centrality(graph, normalized=True)
graph_metrics['avg_edge_btwn'] = \
np.mean(np.array(avg_edge_btwn_dict.values()))
# Number of isolates
graph_metrics['isolates'] = len(nx.isolates(graph))
return graph_metrics
def test_balanced_tree(self):
"""Edge betweenness centrality: balanced tree"""
G = nx.balanced_tree(r=2, h=2)
b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
b_answer = {(0, 1): 12, (0, 2): 12, (1, 3): 6, (1, 4): 6, (2, 5): 6, (2, 6): 6}
for n in sorted(G.edges()):
assert_almost_equal(b[n], b_answer[n])
def communitySplits(self, graph): """ Compute the splits for the formation of communities. Arguments: graph - A networkx graph of digraph. Returns: The graph with weak edges removed. """ nConnComp = nx.number_connected_components(graph) nComm = nConnComp while (nComm <= nConnComp): betweenness = nx.edge_betweenness_centrality(graph) if (len(betweenness.values()) != 0 ): max_betweenness = max(betweenness.values()) else: break for u,v in betweenness.iteritems(): if float(v) == max_betweenness: graph.remove_edge(u[0], u[1]) nComm = nx.number_connected_components(graph) return graph
def edge_betweeness_centrality(X):
"""
based on networkx function: edge_betweenness_centrality
"""
XX = np.zeros(X.shape)
for i, value in enumerate(X):
adj_mat = value.reshape((np.sqrt(len(value)),-1))
adj_mat = (adj_mat - np.min(adj_mat)) / (np.max(adj_mat) - np.min(adj_mat))
adj_mat = 1 - adj_mat
# th = np.mean(adj_mat) + 0.1
# adj_mat = np.where(adj_mat < th, adj_mat, 0.)
percent, th, adj_mat, triu = percentage_removed(adj_mat, 0.43) # 43 #63 #73
print("percent = {0}, threshold position = {1}, threshold = {2}\n".format(percent, th, triu[th]))
g = nx.from_numpy_matrix(adj_mat)
print "Graph Nodes = {0}, Graph Edges = {1} ".format(g.number_of_nodes(), g.number_of_edges())
print "\nEdge kept ratio, {0}".format(float(g.number_of_edges())/((g.number_of_nodes()*(g.number_of_nodes()-1))/2))
bet_cent = nx.edge_betweenness_centrality(g, weight = 'weight', normalized = True)
edge_cent = np.zeros(adj_mat.shape)
for k in bet_cent:
edge_cent[k[0],k[1]] = bet_cent[k]
XX[i] = edge_cent.reshape(-1)
print "graph {0} => mean {1}, min {2}, max {3}".format(i, np.mean(XX[i]), np.min(XX[i]), np.max(XX[i]))
return XX
def test_C4(self):
"""Edge betweenness centrality: C4"""
G = nx.cycle_graph(4)
b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer = {(0, 1): 2, (0, 3): 2, (1, 2): 2, (2, 3): 2}
for n in sorted(G.edges()):
assert_almost_equal(b[n], b_answer[n] / 6)
def most_valuable_edge(G):
"""Returns the edge with the highest betweenness centrality
in the graph `G`.
"""
# We have guaranteed that the graph is non-empty, so this
# dictionary will never be empty.
betweenness = nx.edge_betweenness_centrality(G)
return max(betweenness, key=betweenness.get)
def edge_betweenness(graph):
#returns the maximum of edge_betweenness_centrality
max = 0
dict = nx.edge_betweenness_centrality(graph, True)
for v in dict.values():
if max < v:
max = v
return max
def edge_betweenness(edge_list=path+'connected-component-analysis/network-profiling-data/cid6_analysis/cid6-edge-list',
out_file=path+'connected-component-analysis/network-profiling-data/cid6_analysis/cid6-edge-betweenness-10000.json'):
G = nx.read_edgelist(edge_list, delimiter='\t')
M = nx.edge_betweenness_centrality(G, k=10000)
M_new = dict()
for k, v in M.items():
M_new[k[0]+'\t'+k[1]] = v
json.dump(M_new, open(out_file, 'w'))
def edge_betweenness_centrality(f, ft, gnx):
start = timer.start(ft, 'Edge Betweenness Centrality')
result = nx.edge_betweenness_centrality(gnx)
timer.stop(ft, start)
for k in result:
f.writelines(str(k) + ',' + str(result[k]) + '\n')
return result
def edge_remove(G):
dict1 = nx.edge_betweenness_centrality(G)
list_tup = []
for i in dict1:
k = (i, dict1[i])
list_tup.append(k)
list_tup.sort(key=lambda x:x[1], reverse=True)
return list_tup[0][0];
def split_graph(G):
initial_communities = nx.number_connected_components(G)
while initial_communities == nx.number_connected_components(G):
betweenness = nx.edge_betweenness_centrality(G)
edge_array = np.array([key for key, val in betweenness.items()])
between_array = np.array([val for key, val in betweenness.items()])
most_important_edge = edge_array[np.argmax(between_array)]
G.remove_edge(most_important_edge[0], most_important_edge[1])
def _calc_edges_betweenness(G):
# For each edge calculates the betweenness.
edge_betweenness = dict.fromkeys(G.edges, 0)
edge_betweenness_by_pair_of_nodes = nx.edge_betweenness_centrality(G)
for key in edge_betweenness:
edge_betweenness[key] = edge_betweenness_by_pair_of_nodes[key[:2]]
### G.edges[list(G.edges)[0]]['betweenness']
return edge_betweenness
def bc_filter(G):
g = G.copy()
for u, v, d in g.edges(data=True):
g[u][v]['inverse_weight'] = 1/d['weight']
for (u, v), d in nx.edge_betweenness_centrality(g, weight='inverse_weight').items():
g[u][v]['BC'] = d
return g
def Betweenness_Edge_centrality(G, fn): ''' G: Graph fn: funtion of n used to delimit the number of hotspots ''' edgeBetDict = nx.edge_betweenness_centrality(G) edgeBetCentr = SortDictionary(edgeBetDict)[:int(fn)] return edgeBetCentr
def setCapacity(G, factor): if(G.number_of_edges() > 0): bb=nx.edge_betweenness_centrality(G, normalized=True, weight='weight') for edge in G.edges(data=True): edge[2]['capacity'] = (bb[(edge[0],edge[1])]*factor) return G
def test_balanced_tree(self):
"""Edge betweenness centrality: balanced tree"""
G=nx.balanced_tree(r=2,h=2)
b=nx.edge_betweenness_centrality(G, weight='weight', normalized=False)
b_answer={(0, 1):12,(0, 2):12,
(1, 3):6,(1, 4):6,(2, 5):6,(2,6):6}
for n in sorted(G.edges()):
assert_almost_equal(b[n],b_answer[n])
def get_betweenness_dictionary(edges,costs):
## This is slow, and uses a graph library. (This is ALMOST what you're implementing for the programming assignment!)
G = nx.Graph()
G.add_edges_from(edges)
for u,v in G.edges:
G[u][v]['cost'] = costs[u][v]
centralities = nx.edge_betweenness_centrality(G, normalized=False, weight='cost')
return centralities
class Topology(object, nx.Graph):
for N in [20, 30, 40]:
for delta in [2, 4, 8]:
fmax_vector = []
for i in range(5):
nodes = range(N)
np.random.seed(5)
degree = [delta for i in xrange(N)]
G = nx.directed_havel_hakimi_graph(degree, degree)
G = nx.DiGraph(G)
bb = nx.edge_betweenness_centrality(G, normalized=False)
nx.set_edge_attributes(G, 'weight', bb)
nx.set_edge_attributes(G, 'capacity', bb)
T_matrix = np.zeros((N, N))
for s in nodes:
for d in nodes:
if s != d:
flow = np.random.uniform(0.5, 1.5)
T_matrix[s, d] = flow
if G.has_edge(s, d):
G.edge[s][d]['weight'] = flow
G.edge[s][d]['capacity'] = np.random.randint(
8, 12)
f_value = 0
(p, a) = (0, 0)
for i in range(N):
for j in range(N):
edges = nx.shortest_path(G, i, j, weight='weight')
for k in range(len(edges) - 1):
G.edge[edges[k]][edges[
k + 1]]['weight'] += T_matrix[i][j]
if i != j:
flow_value = nx.maximum_flow_value(G, i, j)
if flow_value > f_value:
f_value = flow_value
(p, a) = (i, j)
fmax = 0
(s_f, d_f) = (0, 0)
for s in G.edge:
for d in G.edge[s]:
if G.edge[s][d]['weight'] > fmax:
fmax = G.edge[s][d]['weight']
(s_f, d_f) = (s, d)
fmax_vector.append(fmax)
tot_edges = G.number_of_edges()
np.set_printoptions(precision=3)
#print T_matrix
#print tot_edges
print 'N = ' + str(N) + ' D = ' + str(delta) + 'fmax = ' + str(
np.mean(fmax_vector)) #+ ' flow = ' + str(flow_value)
def centralize_graph(graph, epb='lgth', efb='capa', ndg='capa', nec='capa', npr='capa'):
"""Compute edge centralities.
Parameters
----------
graph : original graph
epb : edge property used for computation of edge path betweenness
efb : " flow betweenness
ndg : " degree centrality
nec : " eigenvector centrality
npr : " page rank
Returns
-------
graphCentralities : graph with computed edge centralities
"""
graphCentralities = graph.copy()
edges = graphCentralities.edges(data=True)
edgeCapacity = 1.0 * np.array([property['capa'] for node1, node2, property in edges])
edgeCapacity /= edgeCapacity.sum()
edgeLength = 1.0 / edgeCapacity
for index, (node1, node2, property) in enumerate(edges):
property['capa'] = edgeCapacity[index]
property['lgth'] = edgeLength[index]
edgeBetweenCentrality = nx.edge_betweenness_centrality(graphCentralities, weight=epb)
edgeFlowBetweennessCentrality = nx.edge_current_flow_betweenness_centrality(graphCentralities, weight=efb)
lineGraph = nx.line_graph(graphCentralities)
degree = graphCentralities.degree(weight=ndg)
for node1, node2, property in lineGraph.edges(data=True):
intersectingNodes = list(set(node1).intersection(node2))[0]
property[ndg] = degree[intersectingNodes]
eigenvectorCentrality = nx.eigenvector_centrality_numpy(lineGraph, weight=ndg)
pageRank = nx.pagerank(lineGraph, weight=ndg)
degreeCentrality = dict(lineGraph.degree(weight=ndg))
for index, (node1, node2, property) in enumerate(edges):
edge = (node1, node2)
if (edge in edgeBetweenCentrality.keys()):
property['epb'] = edgeBetweenCentrality[edge]
else:
property['epb'] = edgeBetweenCentrality[edge[::-1]]
if (edge in edgeFlowBetweennessCentrality.keys()):
property['efb'] = edgeFlowBetweennessCentrality[edge]
else:
property['efb'] = edgeFlowBetweennessCentrality[edge[::-1]]
if (edge in degreeCentrality.keys()):
property['ndg'] = degreeCentrality[edge]
else:
property['ndg'] = degreeCentrality[edge[::-1]]
if (edge in eigenvectorCentrality.keys()):
property['nec'] = eigenvectorCentrality[edge]
else:
property['nec'] = eigenvectorCentrality[edge[::-1]]
if (edge in pageRank.keys()):
property['npr'] = pageRank[edge]
else:
property['npr'] = pageRank[edge[::-1]]
return(graphCentralities)
def most_valuable_edge(G):
"""Returns the edge with the highest betweenness centrality
in the graph `G`.
"""
# We have guaranteed that the graph is non-empty, so this
# dictionary will never be empty.
betweenness = nx.edge_betweenness_centrality(G)
return max(betweenness, key=betweenness.get)
def compute_edge_betweenness(g):
mp.weight_graph(g)
ebc = nx.edge_betweenness_centrality(g,'weight')
m = 0
for v in ebc.values():
if v>m:
m = v
return ebc,m
def edge_betweenness_centrality(self, k=None):
""" Calculate the edge betweenness centrality of each pair of hyperedges
in mobile network. The algorithm uses `distance` to weight each segment.
"""
road_bw = nx.edge_betweenness_centrality(self.graph, k=k, weight='distance')
mobile_bw = {}
for (source, target), betweenness in road_bw.items():
if source in self.coordmapr and target in self.coordmapr:
mobile_bw[(self.coordmapr[source], self.coordmapr[target])] = betweenness
return mobile_bw
def find_best_edge(G0):
"""
Networkx implementation of edge_betweenness
returns a dictionary. Make this into a list,
sort it and return the edge with hoghest betweenness.
"""
eb = nx.edge_betweenness_centrality(G0)
eb_il = eb.items()
eb_il.sort(key=lambda x: x[1], reverse=True)
return eb_il[0][0]
def Girvannewman(G):
initialcomp = nx.number_connected_components(G)
'''totalnumcomp = initialcomp
while totalnumcomp <= initialcomp:'''
bw = nx.edge_betweenness_centrality(G)
maximum_value = max(bw.values())
for key, value in bw.iteritems():
if float(value) == maximum_value:
G.remove_edge(key[0],key[1])
totalnumcomp = nx.number_connected_components(G)
def process_data(denom=100000, round=0):
f = csv.reader(open("../applab_new_6.csv", 'rb'), delimiter=',')
db = nx.DiGraph()
full_users = set()
i = 0
uniquect = 0
for line in f:
if i % 100000 == 0 : print "processed", i, "lines"
if i == 1000: break
sender, receiver, date, time, duration, cost, location, region = map(lambda x: x.strip(), line)
if sender not in full_users:
uniquect += 1
full_users.add(sender)
if uniquect <= 2: #% denom - round == 0:
db.add_node(sender)
if db.has_node(receiver) == False:
db.add_node(receiver)
else:
if db.has_node(receiver) == False:
db.add_node(receiver)
if db.has_edge(sender, receiver):
db[sender][receiver]['weight'] += int(duration)
else:
db.add_edge(sender, receiver, weight=int(duration))
i+=1
#pickle.dump(db, open("users_networkx.p" % str(round), "wb"))
#print "degree assortativity coeff:", nx.degree_assortativity_coefficient(db)
#print "average degree connectivity:", nx.average_degree_connectivity(db)
# print "k nearest neighbors:", nx.k_nearest_neighbors(db)
print "calculating deg cent"
deg_cent = nx.degree_centrality(db) #sorted(nx.degree_centrality(db).items(), key=lambda x: x[1])
print "calculating in deg cent"
in_deg_cent = nx.in_degree_centrality(db) #sorted(nx.in_degree_centrality(db).items(), key=lambda x: x[1])
print "calculating out deg cent"
out_deg_cent = nx.out_degree_centrality(db) #sorted(nx.out_degree_centrality(db).items(), key=lambda x: x[1])
print "closeness cent"
closeness_cent = nx.closeness_centrality(db) #sorted(nx.closeness_centrality(db).items(), key=lambda x: x[1])
#print "betweenness cent"
#btwn_cent = nx.betweenness_centrality(db) #sorted(nx.betweenness_centrality(db).items(), key=lambda x: x[1])
print "done"
w = open("../output/user_network_stats.csv", 'w')
w.write("uid,deg_cent,in_deg_cent,out_deg_cent,closeness_cent,btwn_cent\n")
for user in deg_cent.keys():
try:
w.write("%s,%s,%s,%s,%s\n" % (user, deg_cent[user], in_deg_cent[user], out_deg_cent[user], closeness_cent[user]))
except: pass
w.close()
print "drawing..."
nx.draw(db)
plt.savefig("path.pdf")
print "done!"
print "edge betweenness centrality:", nx.edge_betweenness_centrality(db)
print "communicability:", nx.communicability(db)
print "communicability centrality:", nx.communicability_centrality(db)
def d3_graph(graph):
node_bc = nx.betweenness_centrality(graph, weight="weight")
node_dc = nx.degree_centrality(graph)
edge_bc = nx.edge_betweenness_centrality(graph, weight="weight")
nx.set_edge_attributes(graph, 'betweenness', edge_bc)
for node in graph.nodes():
graph.node[node]["bw"] = node_bc[node]
graph.node[node]["dc"] = node_dc[node]
# print self.new_graph.edges(data=True)
d3graph = json_graph.node_link_data(graph)
return json.dumps(d3graph)
def CmtyGirvanNewmanStep(G):
init_ncomp = nx.number_connected_components(G) #no of components
ncomp = init_ncomp
while ncomp <= init_ncomp:
bw = nx.edge_betweenness_centrality(G, weight='weight') #edge betweenness for G
#find the edge with max centrality
max_ = max(bw.values())
#find the edge with the highest centrality and remove all of them if there is more than one!
for k, v in bw.iteritems():
if float(v) == max_:
G.remove_edge(k[0],k[1]) #remove the central edge
ncomp = nx.number_connected_components(G) #recalculate the no of components
def calculte_betweenness(self, G, bonus=True):
"""
Calculate Betweenness
input:
- G: graph
- bonus: True if use my own betweenness calculator. (bonus=True by default)
"""
if bonus:
betweenness = self.my_betweenness_calculation(G)
else:
betweenness = nx.edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None)
return betweenness
def _remove_max_edge(G, weight=None):
"""
Removes edge with the highest value on betweenness centrality.
Repeat this step until more connected components than the connected
components of the original graph are detected.
"""
number_components = nx.number_connected_components(G)
while nx.number_connected_components(G) <= number_components and G.number_of_edges():
betweenness = nx.edge_betweenness_centrality(G, weight=weight)
max_value = max(betweenness.values())
# Use a list of edges because G is changed in the loop
for edge in list(G.edges()):
if betweenness[edge] == max_value:
G.remove_edge(*edge)
def disintegrate(gr):
components = list(nx.connected_components(gr))
num_comps = len(components)
num_nodes = nx.number_of_nodes(gr)
yield components
while num_comps < num_nodes:
bw = nx.edge_betweenness_centrality(gr) # betweenness dict
to_remove = max(bw.keys(), key=(lambda x: bw[x])) # edge with highest betweenness
gr.remove_edge(*to_remove) # throw it away
components = list(nx.connected_components(gr))
new_num_comps = len(components)
if new_num_comps > num_comps:
num_comps = new_num_comps
yield components
def gnewman(club,splitTo = 2):
itteration = 0
# ok so why do I check the number of connected components
# for an undirected graph it is know that a connected component of an
# an undirected graph is a subgraph in which any two vertices are connected to each other by paths
# this is useful for this application since we are splitting a graph into two subgraphs
# ie to mathematically represent the splitting of the club
while nx.number_connected_components(club) < splitTo:
# returns to us edges with the weights
between = nx.edge_betweenness_centrality(club,normalized=False)
# we want the edges with the highest edge betweenness centrality
# there might be ties so just get the max betweenness
m = max(between.values())
# unpack the tuple returned to us by between.items ((u,v), maxBetweenScore)
for (hU,hV),val in between.items():
# check to see if m(max betweenness score) is equal to val
# removes ties along the way
if val == m:
club.remove_edge(hU,hV)
print("removed edge %s--%s with betweenness score of %f"%(hU,hV,m))
itteration += 1
print("-------------------------")
# this print out can be uncommented it simply shows the same metric as described two different ways
# print(nx.number_connected_components(club),len(list(nx.connected_component_subgraphs(club))))
print("total iterations %d for splitting into %d"%(itteration,splitTo))
