def create_cits_plots(data, title_=""):
fig, ax1 = plt.subplots(1, 1, figsize=(7, 7))
fit = powerlaw.Fit(data, discrete=True)
plt.suptitle(title_, fontsize=30)
a = fit.power_law.alpha
xmin = fit.power_law.xmin
pdf = powerlaw.pdf(data)
bins = pdf[0]
widths = bins[1:] - bins[0:-1]
centers = bins[0:-1] + 0.5 * widths
xc, yc = find_pdf_at_x(xmin, pdf[0], pdf[1])
x_, y_ = fitted_pl_xy(a, xc, yc, xmin, np.max(pdf[0]))
ax1.set_xlabel("Number of word occurances", fontsize=20)
ax1.set_ylabel("Probability density function", fontsize=20)
ax1.plot(centers, pdf[1], 'o')
powerlaw.plot_pdf(data, ax=ax1, color='b', label='APS data')
ax1.plot(x_, y_, 'r--', label=r'Power law fit: $x^{-%4.3f}$' % (a))
#ax1.plot([xmin,xmin],[10**(-16),1],'--',color="grey", label=r'$\rm x_{min}=%d$' % (xmin))
ax1.legend(loc=0, fontsize=15)
fig.text(0.95,
0.05,
'(c) 2018, P.G.',
fontsize=10,
color='gray',
ha='right',
va='bottom',
alpha=0.5)
plt.show()
def plot_basics(data, data_inst, fig, units):
'''
This function is the main plotting function. Adapted from Newman's powerlaw package.
'''
import pylab
pylab.rcParams['xtick.major.pad'] = '8'
pylab.rcParams['ytick.major.pad'] = '8'
pylab.rcParams['font.sans-serif'] = 'Arial'
from matplotlib import rc
rc('font', family='sans-serif')
rc('font', size=10.0)
rc('text', usetex=False)
from matplotlib.font_manager import FontProperties
panel_label_font = FontProperties().copy()
panel_label_font.set_weight("bold")
panel_label_font.set_size(12.0)
panel_label_font.set_family("sans-serif")
n_data = 1
n_graphs = 4
from powerlaw import plot_pdf, Fit, pdf
ax1 = fig.add_subplot(n_graphs, n_data, data_inst)
x, y = pdf(data, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5, label='data')
plot_pdf(data[data > 0], ax=ax1, color='b', linewidth=2, label='PDF')
from pylab import setp
setp(ax1.get_xticklabels(), visible=False)
plt.legend(loc='bestloc')
ax2 = fig.add_subplot(n_graphs, n_data, n_data + data_inst, sharex=ax1)
plot_pdf(data[data > 0], ax=ax2, color='b', linewidth=2, label='PDF')
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g', label='w/o xmin')
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True, xmin=3)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g', label='w xmin')
from pylab import setp
setp(ax2.get_xticklabels(), visible=False)
plt.legend(loc='bestloc')
ax3 = fig.add_subplot(n_graphs, n_data,
n_data * 2 + data_inst) #, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g', label='powerlaw')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r', label='exp')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
plt.legend(loc='bestloc')
ax3.set_xlabel(units)
def plot_basics(data, data_inst, fig, units):
'''
This function is the main plotting function. Adapted from Newman's powerlaw package.
'''
import pylab
pylab.rcParams['xtick.major.pad']='8'
pylab.rcParams['ytick.major.pad']='8'
pylab.rcParams['font.sans-serif']='Arial'
from matplotlib import rc
rc('font', family='sans-serif')
rc('font', size=10.0)
rc('text', usetex=False)
from matplotlib.font_manager import FontProperties
panel_label_font = FontProperties().copy()
panel_label_font.set_weight("bold")
panel_label_font.set_size(12.0)
panel_label_font.set_family("sans-serif")
n_data = 1
n_graphs = 4
from powerlaw import plot_pdf, Fit, pdf
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5, label='data')
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2, label='PDF')
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
plt.legend(loc = 'bestloc')
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)
plot_pdf(data[data>0], ax=ax2, color='b', linewidth=2, label='PDF')
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g',label='w/o xmin')
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True,xmin=3)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g', label='w xmin')
from pylab import setp
setp(ax2.get_xticklabels(), visible=False)
plt.legend(loc = 'bestloc')
ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g',label='powerlaw')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r',label='exp')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
plt.legend(loc = 'bestloc')
ax3.set_xlabel(units)
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.4, .95)
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
if data_inst==1:
ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
from pylab import setp
setp( ax2.get_xticklabels(), visible=False)
if data_inst==1:
ax2.annotate("B", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
ax2.set_ylabel(u"p(X)")# (10^n)")
ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
if data_inst==1:
ax3.annotate("C", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
ax3.set_xlabel(units)
def plot_gamma(graphe):
#fitness = powerlaw.Fit(graphe.degree().values(),xmin =1)
#print fitness.alpha,fitness.xmin
alpha = 1 + (graphe.number_of_nodes() /
sum(np.log(graphe.degree().values())))
#powerlaw.plot_pdf(graphe.degree().values())
xdata, ydata = powerlaw.pdf(graphe.degree().values())
vala = {}
xvala = []
yvala = []
somme = 0
exceptions = []
last_exception = -1
for value in graphe.degree().values():
somme += 1
try:
vala[value] += 1
except:
vala[value] = 1
for degree in range(1, max(vala.keys()) + 1):
try:
yvala.append(float(vala[degree]) / somme)
xvala.append(degree)
except:
if len(exceptions) == 0:
last_exception = degree
#print degree
exceptions.append(degree)
#slope, intercept, r_value, p_value, std_err = stats.linregress(
#np.log(xvala[:last_exception]),np.log(yvala[:last_exception]))
#print slope
x = xvala
plt.plot(x, np.power(x, -alpha), color="orange")
#plt.plot(x,np.power(x,-2.34296138661),color ="blue")
#plfit.plfit(graphe.degree().values(),quiet = False,verbose = True,silent = False)
plt.plot(xvala, yvala, color="black")
plt.yscale('log')
plt.xscale('log')
#plt.ylim([0,0.4])
#plt.xlim([0,20])
plt.show()
def plot_gamma(graphe) :
#fitness = powerlaw.Fit(graphe.degree().values(),xmin =1)
#print fitness.alpha,fitness.xmin
alpha = 1+(graphe.number_of_nodes()/sum(np.log(graphe.degree().values())))
#powerlaw.plot_pdf(graphe.degree().values())
xdata,ydata = powerlaw.pdf(graphe.degree().values())
vala ={}
xvala=[]
yvala=[]
somme = 0
exceptions =[]
last_exception = -1
for value in graphe.degree().values() :
somme+=1
try :
vala[value]+=1
except :
vala[value] =1
for degree in range(1,max(vala.keys())+1) :
try :
yvala.append(float(vala[degree])/somme)
xvala.append(degree)
except :
if len(exceptions) ==0 :
last_exception =degree
#print degree
exceptions.append(degree)
#slope, intercept, r_value, p_value, std_err = stats.linregress(
#np.log(xvala[:last_exception]),np.log(yvala[:last_exception]))
#print slope
x = xvala
plt.plot(x,np.power(x,-alpha),color = "orange")
#plt.plot(x,np.power(x,-2.34296138661),color ="blue")
#plfit.plfit(graphe.degree().values(),quiet = False,verbose = True,silent = False)
plt.plot(xvala,yvala,color = "black")
plt.yscale('log')
plt.xscale('log')
#plt.ylim([0,0.4])
#plt.xlim([0,20])
plt.show()
#xdata,ydata=powerlaw.pdf(graphe.degree().values())
def power_law_plot(graph,
log=True,
linear_binning=False,
bins=90,
draw=True,
x_min=None):
degree = list(dict(graph.degree()).values())
#powerlaw does not work if a bin is empty
#sum([1 if x == 0 else 0 for x in list(degree)])
corrected_degree = [x for x in degree if x != 0]
if x_min is not None:
corrected_degree = [x for x in corrected_degree if x > x_min]
# fit powerlaw exponent and return distribution
pwl_distri = pwl.pdf(corrected_degree, bins=bins)
if draw:
degree_distribution = Counter(degree)
# Degree distribution
x = []
y = []
for i in sorted(degree_distribution):
x.append(i)
y.append(degree_distribution[i] / len(graph))
#plot our distributon compared to powerlaw
#plt.figure(figsize=(10,7))
plt.yscale('log')
plt.xscale('log')
plt.plot(x, y, 'ro')
plt.xticks(fontsize=15)
plt.yticks(fontsize=15)
plt.xlabel('$k$', fontsize=16)
plt.ylabel('$P(k)$', fontsize=16)
if linear_binning:
pwl.plot_pdf(corrected_degree,
linear_bins=True,
color='black',
linewidth=2)
else:
pwl.plot_pdf(corrected_degree, color='black', linewidth=2)
return pwl_distri
def analyze_pk(g, figfile):
ks = [x[1] for x in g.degree()]
results = powerlaw.Fit(ks, discrete=True)
figPDF = results.power_law.plot_pdf(label=r"fit($\alpha$: %.2f, $x_{min}$: %d)" % (results.alpha, results.xmin))
figPDF.set_ylabel("P(k)")
figPDF.set_xlabel("k")
cdf = {z[0]:z[1] for z in zip(*powerlaw.cdf(ks))}
cdf_xmin = cdf[results.xmin]
bin_edges, prob = powerlaw.pdf(ks)
x = [ (bin_edges[i]+bin_edges[i+1])/2.0 for i in range(0, len(bin_edges)-1) ]
plt.plot(x, prob/(1.0-cdf_xmin), label="data")
plt.legend()
plt.savefig(figfile)
return (results.power_law.alpha, results.power_law.xmin)
def plot_basics(filepath, ax, c):
tweetcounts = np.genfromtxt(filepath, usecols=(1,), comments=None, dtype=np.int32, unpack=True)
###
x, y = powerlaw.pdf(tweetcounts, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax.scatter(x, y, color=c, s=.5)
# ax.set_xscale('log')
ax.set_yscale('log')
# powerlaw.plot_pdf(tweetcounts, ax=ax, color='b', linewidth=2)
# ###
#
# from mpl_toolkits.axes_grid.inset_locator import inset_axes
# ax1in = inset_axes(ax, width="30%", height="30%", loc=3)
# ax1in.hist(tweetcounts, density=True, color='b')
# ax1in.set_xticks([])
# ax1in.set_yticks([])
#
# ###
# fit = powerlaw.Fit(tweetcounts, xmin=1, discrete=True)
# fit.power_law.plot_pdf(ax=ax, linestyle=':', color='g')
#
# ####
# fit = powerlaw.Fit(tweetcounts, discrete=True)
# fit.power_law.plot_pdf(ax=ax, linestyle='--', color='g')
#
# ax.set_xlabel(r"Tweetcount")
# ax.set_ylabel(u"p(X)")
#
# alpha = fit.power_law.alpha
# xmin = fit.power_law.xmin
# textstr = 'alpha: {0:.4f}\nxmin: {1}\nperiod: {2}'.format(alpha, xmin, text)
# props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)
# ax.text(0.5, 0.95, textstr, transform=ax.transAxes, fontsize=14, verticalalignment='top', bbox=props)
# ####
return
def create_cits_plots(data, title_=""):
# fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,7) )
fig, ax1 = plt.subplots(1, 1, figsize=(7,7) )
fit = powerlaw.Fit(data, discrete=True)
plt.suptitle(title_,fontsize=30)
a = fit.power_law.alpha
xmin = fit.power_law.xmin
pdf = powerlaw.pdf(data)
bins = pdf[0]
widths = bins[1:] - bins[0:-1]
centers = bins[0:-1] + 0.5*widths
xc,yc = find_pdf_at_x(xmin, pdf[0], pdf[1])
x_, y_ = fitted_pl_xy(a, xc, yc, xmin, np.max(pdf[0]) )
#### AX1
ax1.set_xlabel("Number of citations", fontsize=20)
ax1.set_ylabel("Probability density function", fontsize=20)
ax1.plot(centers,pdf[1],'o')
powerlaw.plot_pdf(data, ax=ax1, color='b',label='APS data')
ax1.plot(x_, y_, 'r--', label=r'Power law fit: $x^{-%4.3f}$' % ( a ) )
# ax1.plot(xc,yc,'o',color='grey')
ax1.plot([xmin,xmin],[10**(-16),1],'--',color="grey", label=r'$\rm x_{min}=%d$' % (xmin))
ax1.legend(loc=0, fontsize=15)
#### AX2
# ax2.set_xlabel(r'$\rm x_{min}$', fontsize=20)
# ax2.set_ylabel(r'$\rm D, \sigma, \alpha$', fontsize=20)
# ax2.plot(fit.xmins, fit.Ds, label=r'$D$')
# ax2.plot(fit.xmins, fit.sigmas, label=r'$\sigma$', linestyle='--')
# ax2.plot(fit.xmins, fit.sigmas/fit.alphas, label=r'$\sigma /\alpha$', linestyle='--')
# ax2.legend(loc=0, fontsize=15)
# ax2.set_xlim( [0, 200] )
# ax2.set_ylim( [0, .25] )
fig.text(0.95, 0.05, '(c) 2018, P.G.',fontsize=10, color='gray', ha='right', va='bottom', alpha=0.5)
plt.show()
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.1, .95)
# annotate_coord = (1.1, .95)
ax1 = fig.add_subplot(n_graphs, n_data, data_inst, visible=False)
x, y = pdf(data, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data > 0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp(ax1.get_xticklabels(), visible=False)
# ABC
# if data_inst == 1:
# ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
# ax1.set_ylabel(u"p(X)")
# from mpl_toolkits.axes_grid.inset_locator import inset_axes
# ax1in = inset_axes(ax1, width="30%", height="30%", loc=3)
# ax1in.hist(data, density=True, color='b')
# ax1in.set_xticks([])
# ax1in.set_yticks([])
# ax1.set_xlabel(units)
ax2 = fig.add_subplot(n_graphs,
n_data,
n_data + data_inst,
sharex=ax1,
visible=False)
plot_pdf(data, ax=ax2, color='b', linewidth=2, label="pdf of data")
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2,
linestyle=':',
color='g',
label="power law fit")
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2,
linestyle='--',
color='g',
label="power law fit--opt xmin")
from pylab import setp
setp(ax2.get_xticklabels(), visible=True)
# if data_inst == 1:
ax2.annotate("B",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax2.set_ylabel(u"p(X)") # (10^n)")
handles, labels = ax2.get_legend_handles_labels()
ax2.legend(handles, labels, loc=3)
ax2.set_xlabel(units)
ax3 = fig.add_subplot(n_graphs, n_data, n_data * 2 +
data_inst) # , sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3,
linestyle='--',
color='g',
label="power law fit\n(opt-min)")
fit.exponential.plot_pdf(ax=ax3,
linestyle='--',
color='r',
label="exponential fit\n(opt-min)")
fit.plot_pdf(ax=ax3, color='b', linewidth=2, label="PDF\n(opt-min)")
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
handles, labels = ax3.get_legend_handles_labels()
ax3.legend(handles, labels, loc=3, fontsize=12)
ax3.set_xlabel(units, fontsize=15)
# if data_inst == 1:
ax3.annotate("C",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax3.set_ylabel(u"p(X)", fontsize=15)
def main():
G = nx.Graph()
fileIn = open('brazil.txt','r')
for line in fileIn:
m,f,t = line.split(' ')
G.add_node(m,gender='m')
G.add_node(f,gender='f')
G.add_edge(m,f)
degree_sequence_female =sorted([d for n,d in G.degree().iteritems() if G.node[n]['gender']== 'f' ], reverse=True) # degree sequence
degree_sequence_male =sorted([d for n,d in G.degree().iteritems() if G.node[n]['gender']== 'm' ], reverse=True) # degree sequence
male_fraction = float(len(degree_sequence_male))/(len(degree_sequence_male) + len(degree_sequence_female))
print male_fraction
e_male,e_female = analytic_exponent(G,male_fraction)
pdf_female = powerlaw.pdf(degree_sequence_female)
x_fe = list(pdf_female[0]) ; y_fe = list(pdf_female[1])
del x_fe[-1]
pdf_male = powerlaw.pdf(degree_sequence_male)
x_ma = list(pdf_male[0]) ; y_ma = list(pdf_male[1])
del x_ma[-1]
data_fe = degree_sequence_female
plt.scatter(x_fe,y_fe,color=maj_color )
fit_fe = powerlaw.Fit(data_fe, discrete=True ,xmax = 200 , xmin = 20 )
alpha_fe = fit_fe.power_law.alpha
figFIT = fit_fe.power_law.plot_pdf(color=maj_color, linestyle='--' , label=r"(workers) Fit: %.2f, Model: %.2f"%(alpha_fe,e_female) )
data_ma = degree_sequence_male
plt.scatter(x_ma,y_ma,color=min_color )
fit_ma = powerlaw.Fit(data_ma, discrete=False ,xmax = 200 , xmin = 20)
alpha_ma = fit_ma.power_law.alpha
fit_ma.power_law.plot_pdf(color=min_color, linestyle='--' , label=r"(buyers) Fit: %.2f, Model: %.2f"%(alpha_ma,e_male) )
plt.xlim([1,200])
#plt.tight_layout()
handles, labels = figFIT.get_legend_handles_labels()
leg = figFIT.legend(handles, labels, loc=3 )
leg.draw_frame(False)
figFIT.text(9,0.18,'A) Sexual contacts',fontsize = 24)
figFIT.text(2,0.001,r'$f_{min} = 0.40$',fontsize = 26)
figFIT.set_ylabel("$p(k)$" , size = 26)
figFIT.set_xlabel("degree $(k)$ " , size = 26)
figname = 'deg_dist_brazil_scatter'
plt.savefig(figname+'.eps', bbox_inches='tight')
plt.savefig(figname+'.svg', bbox_inches='tight')
def main():
G = nx.Graph()
fileIn = 'sampled_APS_pacs052030.gexf'
G = nx.read_gexf(fileIn)
degree_sequence_maj = sorted([
d for n, d in G.degree().iteritems() if G.node[n]['pacs'] == '05.30.-d'
],
reverse=True) # degree sequence
degree_sequence_min = sorted([
d for n, d in G.degree().iteritems() if G.node[n]['pacs'] == '05.20.-y'
],
reverse=True) # degree sequence
maj_fraction = float(len(degree_sequence_maj)) / (
len(degree_sequence_maj) + len(degree_sequence_min))
maj_maj = maj_min = min_min = 0
for e in G.edges():
n1, n2 = e
g1 = G.node[n1]['pacs']
g2 = G.node[n2]['pacs']
if g1 == g2:
if g1 == '05.20.-y':
min_min += 1
else:
maj_maj += 1
else:
maj_min += 1
h_aa = 0.88
h_bb = 1
e_min = 3.4
e_maj = 2.8
data_min = degree_sequence_min
data_pdf = powerlaw.pdf(data_min)
x = list(data_pdf[0])
y = data_pdf[1]
del x[-1]
#scatter(x,y,color='r' )
#plot(range(10),range(10))
data_maj = degree_sequence_maj
maj_pdf = powerlaw.pdf(data_maj)
x_maj = list(maj_pdf[0])
del x_maj[-1]
y_maj = maj_pdf[1]
data_min = degree_sequence_min
data_pdf = powerlaw.pdf(data_min)
plt.scatter(x, y, color=min_color)
#figPDF = powerlaw.plot_pdf(data_min,color='r', linewidth=2 )
fit_min = powerlaw.Fit(data_min, xmax=30, xmin=4)
alpha_min = fit_min.power_law.alpha
figFIT = fit_min.power_law.plot_pdf(color=min_color,
linestyle='--',
label=r"(CSM) Fit: %.2f, Model: %.2f" %
(alpha_min, e_min))
data_maj = degree_sequence_maj
plt.scatter(x_maj, y_maj, color=maj_color)
#powerlaw.plot_pdf(data_maj,color='b', linewidth=2 )
fit_maj = powerlaw.Fit(data_maj, xmax=80, xmin=5)
alpha_maj = fit_maj.power_law.alpha
fit_maj.power_law.plot_pdf(color=maj_color,
linestyle='--',
label=r"(QSM) Fit: %.2f , Model: %.2f" %
(alpha_maj, e_maj))
handles, labels = figFIT.get_legend_handles_labels()
leg = figFIT.legend(handles, labels, loc=3)
leg.draw_frame(False)
plt.xlim([1, 40])
figFIT.text(7, 0.18, 'C) Scientific citation', fontsize=24)
figFIT.text(2, 0.01, r'$f_{min} = 0.38$', fontsize=26)
figFIT.set_ylabel(r"$p(k)$", size=26)
figFIT.set_xlabel(r"degree $(k)$", size=26)
figname = 'deg_dist_APS_05'
plt.savefig(figname + '.eps', bbox_inches='tight')
plt.savefig(figname + '.svg', bbox_inches='tight')
def plot_basics(data, data_inst, fig, units):
### Setup ###
from powerlaw import plot_pdf, Fit, pdf
import pylab
pylab.rcParams['xtick.major.pad'] = '8'
pylab.rcParams['ytick.major.pad'] = '8'
#pylab.rcParams['font.sans-serif']='Arial'
from matplotlib.font_manager import FontProperties
panel_label_font = FontProperties().copy()
panel_label_font.set_weight("bold")
panel_label_font.set_size(30.0)
panel_label_font.set_family("sans-serif")
n_data = 2
n_graphs = 4
annotate_coord = (-.4, .95)
#############
ax1 = fig.add_subplot(n_graphs, n_data, data_inst)
x, y = pdf(data, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data > 0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp(ax1.get_xticklabels(), visible=False)
if data_inst == 1:
ax1.annotate("A",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax2 = fig.add_subplot(n_graphs, n_data, n_data + data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
_ = fit.power_law.pdf()
ax2.set_xlim((1, max(x)))
setp(ax2.get_xticklabels(), visible=False)
if data_inst == 1:
ax2.annotate("B",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax2.set_ylabel(u"p(X)") # (10^n)")
ax3 = fig.add_subplot(n_graphs, n_data,
n_data * 2 + data_inst) #, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.lognormal.plot_pdf(ax=ax3, linestyle=':', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
if data_inst == 1:
ax3.annotate("C",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax3.set_xlabel(units)
def plplot(data, title, save=False, save_path=None):
data = np.array(data)
fig = plt.figure(figsize=(18,6))
fig.suptitle(title)
# === A ===
ax1 = fig.add_subplot(1,3,1)
# 线性x轴
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
# 双log-绘制概率密度曲线
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
ax1.set_xlabel('A')
# 绘制histogram小图
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
# === A ===
# === B ===
annotation = ''
ax2 = fig.add_subplot(1,3,2, sharey=ax1)
# 双log-绘制概率密度曲线
print(title)
print(pdf(data))
print()
plot_pdf(data, ax=ax2, color='b', linewidth=2)
# 拟合power-law函数并绘图
fit = Fit(data, xmin=1, discrete=True, parameter_range={'alpha':[None,None]})
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
params1 = (fit.power_law.alpha, fit.power_law.xmin, fit.power_law.sigma)
# alpha为拟合系数
# xmin表示最小的x值(使不为0)，此处指定为1
# sigma为标准差
annotation += '\':\' - alpha={:.2f}, xmin= {}, sigma={:.2f}'.format(*params1)
# p = fit.power_law.pdf()
fit = Fit(data, discrete=True, parameter_range={'alpha':[-5,10]})
# 区别于ax2中的第一条拟合线 - 此处的xmin并非指定，而是自动计算的optimal
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
params2 = (fit.power_law.alpha, fit.power_law.xmin, fit.power_law.sigma)
annotation += '\n\'--\' - alpha={:.2f}, xmin= {}, sigma={:.2f}'.format(*params2)
ax2.set_xlabel('B')
ax2.set_ylabel(u"p(X)")# (10^n)")
ax2.set_xlim(ax1.get_xlim())
annotate_coord = (0.05, 0.88)
ax2.annotate(annotation, annotate_coord, xycoords="axes fraction")
# === B ===
# === C ===
ax3 = fig.add_subplot(1,3,3, sharey=ax1)#, sharex=ax1)#, sharey=ax2)
plot_pdf(data[data>0], ax=ax3, color='b', linewidth=2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
ax3.set_xlabel('C')
# === C ===
if save:
plt.savefig(save_path)
else:
plt.show()
return params1, params2
def draw(sample,
xmin,
xmax,
model,
ax=None,
lim1=4,
color='green',
normalized=False):
"""
Fits the data contained in "sample" (i.e. sizes or durations of the avalanches) with the model chosen.
xmin : the maximum xmin that can be considered in the power law fit.
lim1 : upper limit of the range in which to search the power law parameter
ax = object of the type AxesSubplot (returned by fig.add_subplot())
"""
ypred = pwl.Fit(sample,
xmin=(1, xmin + 1),
xmax=xmax,
parameter_range={"alpha": [1, lim1]},
discrete=True)
if normalized == True:
new = []
for i in range(len(sample)):
if sample[i] >= ypred.xmin:
new.append(sample[i])
sample = new
if ax == None:
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ns = len(pwl.pdf(sample)[0]) - 1 # == nbins + 1
print(ns)
ax.set_xscale('log')
nbins = np.logspace(np.log10(min(sample)), np.log10(max(sample)), ns)
ax.hist(sample,
density=True,
histtype='stepfilled',
log=True,
bins=nbins,
color=color,
alpha=0.25)
pwl.plot_pdf(sample,
color='r',
linewidth=2,
label='pdf',
linear_bins=False)
if model == 'power_law':
ypred.power_law.plot_pdf(color='blue',
linestyle='-',
linewidth=2,
label='Power Law fit')
print(
ypred.distribution_compare('power_law',
'exponential',
normalized_ratio=True))
print('Parameters are (alpha)', ypred.power_law.alpha, 'xmin',
ypred.power_law.xmin)
elif model == 'lognormal':
ypred.lognormal.plot_pdf(color='blue',
linestyle='-',
linewidth=2,
label='Lognormal fit')
print('Parameters are (mu,sigma)', ypred.lognormal.mu, 'and',
ypred.lognormal.sigma)
elif model == 'exponential':
ypred.exponential.plot_pdf(color='blue',
linestyle='-',
linewidth=2,
label='Exponential fit')
print('Parameters are (lambda)', ypred.exponential.Lambda)
elif model == 'stretched_exponential':
ypred.stretched_exponential.plot_pdf(color='blue',
linestyle='-',
linewidth=2,
label='Stretched_exponential fit')
print('Parameters are (lambda,beta)',
ypred.stretched_exponential.Lambda, 'and',
ypred.stretched_exponential.beta)
elif model == 'truncated_power_law':
ypred.truncated_power_law.plot_pdf(color='blue',
linestyle='-',
linewidth=2,
label='Truncated_power_law fit')
print('Parameters are (alpha,lambda)', ypred.truncated_power_law.alpha,
'and', ypred.truncated_power_law.Lambda)
plt.legend()
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.4, .95)
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
plot_pdf(data[data>0], ax=ax1, linear_bins=True, color='r', linewidth=.5)
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
#ax1.set_xticks(ax1.get_xticks()[::2])
ax1.set_yticks(ax1.get_yticks()[::2])
locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontsize=14)
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
p = fit.power_law.pdf()
#ax2.set_ylim(min(p), max(p))
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
from pylab import setp
setp( ax2.get_xticklabels(), visible=False)
#ax2.set_xticks(ax2.get_xticks()[::2])
if ax2.get_ylim()[1] >1:
ax2.set_ylim(ax2.get_ylim()[0], 1)
ax2.set_yticks(ax2.get_yticks()[::2])
#locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax2.annotate("B", annotate_coord, xycoords="axes fraction", fontsize=14)
ax2.set_ylabel(r"$p(X)$")# (10^n)")
ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
#p = fit.power_law.pdf()
ax3.set_ylim(ax2.get_ylim())
ax3.set_yticks(ax3.get_yticks()[::2])
ax3.set_xlim(ax1.get_xlim())
#locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax3.annotate("C", annotate_coord, xycoords="axes fraction", fontsize=14)
#if ax2.get_xlim()!=ax3.get_xlim():
# zoom_effect01(ax2, ax3, ax3.get_xlim()[0], ax3.get_xlim()[1])
ax3.set_xlabel(units)
def build(path="../data/influence_data.csv"):
G = create_graph()
# print(nx.degree_histogram(G))
deg_dist = nx.degree_histogram(G)
# _, deg_dist = get_inout_degrees(G)
degree = list(dict(nx.degree(G)).values())
# degree = deg_dist
degree = [d for d in degree if d > 0]
plt.plot(range(0, len(degree)),
sorted(degree, reverse=True),
'ko',
color='#40916c',
alpha=0.7)
plt.legend(['degree'])
plt.xlabel('id')
plt.ylabel('degree')
plt.tight_layout() # 去除pdf周围白边
plt.savefig("../img/degree_distrubition.pdf")
# plt.show()
plt.figure()
import powerlaw
fit = powerlaw.Fit(degree, xmin=3, discrete=True)
print(f'alpha: {fit.power_law.alpha}')
print(f'x-min: {fit.power_law.xmin}')
print(f'D: {fit.power_law.D}')
fit.plot_pdf(color='#2d6a4f', lw=3, linestyle=':', label='curve')
x, y = powerlaw.pdf(degree, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
plt.scatter(x,
y,
color='#74c69d',
marker='s',
alpha=0.6,
s=50,
label='original degree')
fit.power_law.plot_pdf(color='#1b4332',
linestyle='-',
label='$\gamma=1.8$',
lw=2)
# fit.power_law.plot_pdf(color='#1b4332', linestyle='-',
# label='$gamma=%.3f$' % fit.power_law.alpha, lw=2)
plt.legend()
plt.xlabel('ln(id)')
plt.ylabel('ln(degree)')
# plt.title(
# 'Power Law Curve in Double Logarithmic Coordinates')
plt.savefig("../img/powerlaw.pdf", dpi=600)
plt.show()
# 计算皮尔逊 指数
# from scipy.stats import pearsonr
# r, p = pearsonr(x, y)
# print(f'pearsonr r: {r}, p: {p}')
# 线性回归
# slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)
# print(slope, intercept, r_value, p_value, std_err)
# 分布
# DataFitAndVisualization(X, Y)
# plt.loglog(x, y, color="steelblue", linewidth=2) # 在双对数坐标轴上绘制度分布曲线
r1, p1 = fit.distribution_compare('power_law', 'exponential', nested=True)
r2, p2 = fit.distribution_compare('power_law', 'lognormal', nested=True)
r3, p3 = fit.distribution_compare('power_law',
'truncated_power_law',
nested=True)
r4, p4 = fit.distribution_compare('power_law',
'stretched_exponential',
nested=True)
print(r1, p1)
print(r2, p2)
print(r3, p3)
print(r4, p4)
def powerFit(Gx,
mode='power_law',
xmin=None,
xmax=None,
linear=False,
indeg=True,
undir=False,
units=None):
# set-up
pylab.rcParams['xtick.major.pad'] = '24'
pylab.rcParams['ytick.major.pad'] = '24'
#pylab.rcParams['font.sans-serif']='Arial'
from matplotlib import rc
rc('font', family='sans-serif')
rc('font', size=14.0)
rc('text', usetex=False)
panel_label_font = FontProperties().copy()
panel_label_font.set_weight("bold")
panel_label_font.set_size(12.0)
panel_label_font.set_family("sans-serif")
# fit power law distribution using the powerlaw package
try:
if indeg == True:
data = np.array(
sorted([d for n, d in Gx.in_degree()], reverse=True))
elif indeg == False and undir == False:
data = np.array(
sorted([d for n, d in Gx.out_degree()], reverse=True))
elif indeg == False and undir == True:
data = np.array(sorted([d for n, d in Gx.degree()], reverse=True))
except:
data = Gx
####
annotate_coord = (-.4, .95)
fig = plt.figure(figsize=(16, 8))
linf = fig.add_subplot(1, 2, 1)
x, y = powerlaw.pdf(data[data > 0], linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
linf.scatter(x, y, color='r', s=5.5)
powerlaw.plot_pdf(data[data > 0],
color='b',
linewidth=2,
linear_bins=linear,
ax=linf)
linf.annotate(" ",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
linf.set_ylabel(u"p(X)") # (10^n)")
linf.set_xlabel(units)
if xmin != None and xmax == None:
fit = powerlaw.Fit(data, discrete=True, xmin=xmin)
elif xmax != None and xmin == None:
fit = powerlaw.Fit(data, discrete=True, xmax=xmax)
elif xmax != None and xmin != None:
fit = powerlaw.Fit(data, discrete=True, xmin=xmin, xmax=xmax)
else:
fit = powerlaw.Fit(data, discrete=True)
fitf = fig.add_subplot(1, 2, 2, sharey=linf)
fitf.set_xlabel(units)
powerlaw.plot_pdf(data, color='b', linewidth=2, ax=fitf)
if mode == 'truncated_power_law':
fit.truncated_power_law.plot_pdf(color='r', linestyle='--', ax=fitf)
print('alpha = ', fit.truncated_power_law.alpha)
print('Lambda = ', fit.truncated_power_law.Lambda)
print('xmin,xmax = ', fit.xmin, fit.xmax)
print('Kolmogorov-Smirnov distance = ', fit.truncated_power_law.D)
elif mode == 'power_law':
fit.power_law.plot_pdf(color='r', linestyle='--', ax=fitf)
print('alpha = ', fit.power_law.alpha)
print('sigma = ', fit.power_law.sigma)
print('xmin,xmax = ', fit.xmin, fit.xmax)
print('Kolmogorov-Smirnov distance = ', fit.power_law.D)
elif mode == 'lognormal':
fit.lognormal.plot_pdf(color='r', linestyle='--', ax=fitf)
print('mu = ', fit.lognormal.mu)
print('sigma = ', fit.lognormal.sigma)
print('xmin,xmax = ', fit.xmin, fit.xmax)
print('Kolmogorov-Smirnov distance = ', fit.lognormal.D)
elif mode == 'lognormal_positive':
fit.lognormal_positive.plot_pdf(color='r', linestyle='--', ax=fitf)
print('mu = ', fit.lognormal_positive.mu)
print('sigma = ', fit.lognormal_positive.sigma)
print('xmin,xmax = ', fit.xmin, fit.xmax)
print('Kolmogorov-Smirnov distance = ', fit.lognormal_positive.D)
elif mode == 'exponential':
fit.exponential.plot_pdf(color='r', linestyle='--', ax=fitf)
print('Lambda = ', fit.exponential.Lambda)
print('xmin,xmax = ', fit.xmin, fit.xmax)
print('Kolmogorov-Smirnov distance = ', fit.exponential.D)
elif mode == 'stretched_exponential':
fit.stretched_exponential.plot_pdf(color='r', linestyle='--', ax=fitf)
print('Lambda = ', fit.stretched_exponential.Lambda)
print('beta = ', fit.stretched_exponential.beta)
print('xmin,xmax = ', fit.xmin, fit.xmax)
print('Kolmogorov-Smirnov distance = ', fit.stretched_exponential.D)
else:
fit = None
print('mode not allowed')
return (data, fit)
def main():
G = nx.read_gexf('DBLP_graph.gexf')
degree_sequence_min = sorted(
[d for n, d in G.degree().iteritems() if G.node[n]['gender'] == 'f'],
reverse=True) # degree sequence
degree_sequence_maj = sorted(
[d for n, d in G.degree().iteritems() if G.node[n]['gender'] == 'm'],
reverse=True) # degree sequence
maj_fraction = float(len(degree_sequence_maj)) / (
len(degree_sequence_min) + len(degree_sequence_maj))
#e_maj,e_min = analytic_exponent(G,maj_fraction)
e_maj = 2.94 #measured analytically
e_min = 3.24
pdf_female = powerlaw.pdf(degree_sequence_min)
x_fe = list(pdf_female[0])
y_fe = list(pdf_female[1])
del x_fe[-1]
pdf_male = powerlaw.pdf(degree_sequence_maj)
x_ma = list(pdf_male[0])
y_ma = list(pdf_male[1])
del x_ma[-1]
data_min = degree_sequence_min
plt.scatter(x_fe, y_fe, color=min_color)
fit_min = powerlaw.Fit(data_min, xmax=60, xmin=6)
alpha_min = fit_min.power_law.alpha
figFIT = fit_min.power_law.plot_pdf(
color=min_color,
linestyle='--',
label=r"(women) Fit: %.2f, Model: %.2f" % (alpha_min, e_min))
data_maj = degree_sequence_maj
plt.scatter(x_ma, y_ma, color=maj_color)
fit_maj = powerlaw.Fit(data_maj, xmax=80, xmin=6)
alpha_maj = fit_maj.power_law.alpha
fit_maj.power_law.plot_pdf(color=maj_color,
linestyle='--',
label=r"(men) Fit: %.2f , Model: %.2f" %
(alpha_maj, e_maj))
plt.ylim([10**(-5), 1])
plt.xlim([1, 120])
handles, labels = figFIT.get_legend_handles_labels()
leg = figFIT.legend(handles, labels, loc=3)
leg.draw_frame(False)
figFIT.text(7, 0.2, 'B) Scientific collaboration', fontsize=24)
figFIT.text(2, 0.01, r'$f_{min} = 0.23$', fontsize=26)
figFIT.set_ylabel(r"$p(k)$", size=26)
figFIT.set_xlabel(r"degree $(k)$", size=26)
figname = 'deg_dist_DBLP_2010_scatter'
plt.savefig(figname + '.eps', bbox_inches='tight')
plt.savefig(figname + '.svg', bbox_inches='tight')
