def degreeStats(g):
avg, std = vertex_average(g, "total" if not g.is_directed() else "in")
total_degrees = g.get_out_degrees(g.get_vertices())
print("Graus")
stats(total_degrees)
print("\tDesvio padrão (graphtools): ", std)
distribution = vertex_hist(g, "total" if not g.is_directed() else "in")
histogram(distribution, "Distribuição de graus", "$k_{total}$",
"$NP(k_{in})$", sys.argv[1][:-8] + ".graus")
def degree_distribution(self, g, name):
total_hist = gt.vertex_hist(g, "total", float_count=False)
self.__plot_degree(total_hist,
self.name + ' ' + name + ' ' + "totaldegdist.pdf",
"total node degree")
# in_hist = gt.vertex_hist(g, "in", float_count=False)
# self.__plot_degree(in_hist, self.name + ' ' + name + ' ' + "indegdistloglog.pdf", "in node degree")
#
# out_hist = gt.vertex_hist(g, "out", float_count=False)
# self.__plot_degree(out_hist, self.name + ' ' + name + ' ' + "outdegdistloglog.pdf", "out node degree")
[atot, stdm] = gt.vertex_average(g, "total")
stdtot = stdm * np.sqrt(g.num_vertices())
return atot, stdtot, stdm
Wuhan, China
'''
import graph_tool.all as gt
from math import *
from pylab import *
#g = gt.collection.data['cond-mat-2005']
#cond-mat-2005 updated network of coauthorships between scientists posting preprints on the Condensed Matter E-Print Archive.
#g = gt.collection.data['email-Enron']
#Enron email communication network covers all the email communication within a dataset of around half million emails.
g = gt.collection.data['pgp-strong-2009']
#Strongly connected component of the PGP web of trust circa November 2009. The full data is available at http://key-server.de/dump/.
# Let's plot its in-degree distribution
in_hist = gt.vertex_hist(g, "total")
y = in_hist[0]
err = sqrt(in_hist[0])
err[err >= y] = y[err >= y] - 1e-3
figure(figsize=(6, 4))
errorbar(in_hist[1][:-1], in_hist[0], fmt="o", yerr=err, label="all")
gca().set_yscale("log")
gca().set_xscale("log")
gca().set_ylim(1e-1, 1.1 * 1e4)
gca().set_xlim(1, 1e4)
subplots_adjust(left=0.2, bottom=0.2)
xlabel("$k_{all}$")
ylabel("$N*Pr(k_{all})$")
tight_layout()
def compute_node_degree_hist(g, direction):
return gtall.vertex_hist(g, direction, float_count=False)
'''
import graph_tool.all as gt
from math import *
from pylab import *
#g = gt.collection.data['cond-mat-2005']
#cond-mat-2005 updated network of coauthorships between scientists posting preprints on the Condensed Matter E-Print Archive.
#g = gt.collection.data['email-Enron']
#Enron email communication network covers all the email communication within a dataset of around half million emails.
g = gt.collection.data['pgp-strong-2009']
#Strongly connected component of the PGP web of trust circa November 2009. The full data is available at http://key-server.de/dump/.
# Let's plot its in-degree distribution
in_hist = gt.vertex_hist(g, "total")
y = in_hist[0]
err = sqrt(in_hist[0])
err[err >= y] = y[err >= y] - 1e-3
figure(figsize=(6,4))
errorbar(in_hist[1][:-1], in_hist[0], fmt="o", yerr=err,
label="all")
gca().set_yscale("log")
gca().set_xscale("log")
gca().set_ylim(1e-1, 1.1*1e4)
gca().set_xlim(1, 1e4)
subplots_adjust(left=0.2, bottom=0.2)
xlabel("$k_{all}$")
ylabel("$N*Pr(k_{all})$")
def statistics(G):
"""Provides general graph statistics.
Args:
G (graph_tool.Graph): The graph instance.
Returns:
An object with describing many statistical properties of the graph.
"""
if not G:
return 'No Graph Loaded'
float_formatter = lambda x: '{:.2f}'.format(x)
if G.get_vertex_filter()[0] is not None:
vfilt = G.get_vertex_filter()[0]
v_idx = np.where(vfilt.a == 1)[0]
else:
v_idx = np.arange(G.num_vertices())
deg_counts, deg_bins = gt.vertex_hist(G, 'out', float_count=False)
incl_idx = np.where(deg_counts != 0)[0]
deg_bins = list(deg_bins[incl_idx])
deg_counts = list(deg_counts[incl_idx])
comp, cc_hist = gt.label_components(G)
cc_size_counts = sorted(Counter(cc_hist).items())
cc_sizes = [csc[0] for csc in cc_size_counts]
cc_counts = [csc[1] for csc in cc_size_counts]
num_cc = len(np.unique(comp.a))
if deg_bins[0] == 0:
num_singletons = deg_counts[0]
else:
num_singletons = 0
if G.get_vertex_filter()[0] or G.get_edge_filter()[0]:
# Always correct, but much slower
peel_partition = kcore_decomposition(G)
peel_bins = sorted(peel_partition.keys())
peel_counts = [len(peel_partition[k]) for k in peel_bins]
else:
# NOTE:
# Very fast, but unstable (not always accurate) for graphs with filters
kcore = gt.kcore_decomposition(G)
C = Counter(kcore.a[v_idx])
peel_bins, peel_counts = [list(t) for t in zip(*C.items())]
vlogv = G.num_vertices() * np.log2(G.num_vertices())
return {
'num_vertices': G.num_vertices(),
'num_edges': G.num_edges(),
'num_cc': num_cc,
'num_singletons': num_singletons,
'vlogv': float_formatter(vlogv),
'deg_bins': deg_bins,
'deg_counts': deg_counts,
'cc_sizes': cc_sizes,
'cc_counts': cc_counts,
'peel_bins': peel_bins,
'peel_counts': peel_counts,
}
print("Maximum of all Degrees: ", max(degree_list_LC)) # 2025
print("Minimum of all Degrees: ", min(degree_list_LC)) # 1
print("Length of Degree List / Number of Nodes: ",
len(degree_list_LC)) # 16382
print("Avg Degree: ",
sum(degree_list_LC) / len(degree_list_LC)) # 11.444146013917715
print("Median Degree: ", np.median(degree_list_LC)) # 2.0
print("Mode Degree: ", stats.mode(degree_list_LC)[0][0]) # 1
print("\n\nDescriptives: Average Degree - done\n")
#-- Degree Distribution of Friendship Network --#
if descDDist_bool == True:
print("\n\nDesciptives: Degree Distribution - Friendship Network")
degree_hist = gt.vertex_hist(g_friend, "out")
#print("Degree Distribution Frequency: \n", degree_hist[0])
#print("Degree Distribution Values: \n", degree_hist[1])
#print(len(degree_hist[0]), len(degree_hist[1]))
y = degree_hist[0]
x = degree_hist[
1][:
-1] # gt.vertex_hist results in a 2d histogram array [[frequency][degree]]
# degree_hist that has 1 entry too much in the second
# For whatever reason, the second dimension [degree] hast one entry too much
# The last value of [degree]is excluded manually for both diemnsions being
# of same size. There is no theoretical explanation for why the last value
# should be part of the array. Confusing, but not relevant for the following analysis
