def draw_cdf_JI_helper(ases_in_use, mode, color, marker): #mode is for title
#plt.title(title)
colors = ['b']
lis_legend = []
lis = []
total_dots = 0
#names = ("BGP","iBGP","eBGP")
for count,as_ in enumerate(ases_in_use):
print count,len(as_)
#c2 = 0
for lg1,lg2 in itertools.combinations(as_.get_attr(LGS),2):
total_dots += 1
#print c2
#c2 += 1
lg1.update_prefix_as_path()
p1 = lg1.get_prefixes()
lg2.update_prefix_as_path()
p2 = lg2.get_prefixes()
lis.append(JI(p1,p2))
if JI(p1,p2) == 0:
print lg1,lg2
lg1.release()
lg2.release()
print "total dots",total_dots#658
dist,prob = pl.cdf(lis)
#plt.scatter(dist,prob,c='b',marker='x')
return plt.scatter(dist,prob,c=color,marker=marker)
'''
def plot_aggregated_counts_distributions_ccdf():
#agg_distributions = read_pickle(HOME+'output/aggregated_counts_distribution.obj')
#for i in agg_distributions.values():
# print len(i)
colors = {'source_article': 'r', 'target_article': 'b'}
labels = {
'source_article': 'source article',
'target_article': 'target article'
}
fig = plt.figure()
ax = fig.add_subplot(111)
#for category in ['source_article', 'target_article']:
# data = agg_distributions[category]
# data = [int(x[0]) for x in data]
# powerlaw.plot_ccdf(data, ax, label=labels[category],color=colors[category])
category_distributions = read_pickle(
HOME + 'output/category_counts_distribution.obj')
data = category_distributions['counts']
data = [int(x[0]) for x in data]
#to consider the edges that have zero transitions we substract the number transitions from the number of edges in wikipeida
number_of_edges = 339463340
listofzeros = [0] * (number_of_edges - len(data))
print len(data)
print len(listofzeros)
zeros = np.zeros((number_of_edges - len(data)))
data = np.append(zeros, data)
#data = data.extend(listofzeros)
print data
#hist, bin_edges = np.histogram(data, bins=100, normed=True)
#ones = np.ones(100)
#ccdf = ones - np.cumsum(data)
#cdf = np.cumsum(hist)
#print cdf
#print ccdf
bins, CDF = powerlaw.cdf(data, survival=True)
plt.plot(bins, CDF)
plt.xscale('symlog')
#powerlaw.plot_cdf(data, ax, label='transitions', color='r')
# further plotting
#ax.set_xlabel(r'Number of transitions $n$')
#ax.set_ylabel(r'$P(X \geq n)$')
plt.legend(fancybox=True, loc='lower left', ncol=1, prop={'size': 5})
#leg = plt.gca().get_legend()
#ltext = leg.get_texts() # all the text.Text instance in the legend
#plt.setp(ltext, fontsize='small') # the legend text fontsize
plt.tight_layout()
plt.savefig('output/agg_counts_distributions.pdf', bbox_inches='tight')
def plot_aggregated_counts_distributions_ccdf():
#agg_distributions = read_pickle(HOME+'output/aggregated_counts_distribution.obj')
#for i in agg_distributions.values():
# print len(i)
colors= {'source_article':'r','target_article':'b'}
labels = {'source_article': 'source article', 'target_article':'target article'}
fig = plt.figure()
ax = fig.add_subplot(111)
#for category in ['source_article', 'target_article']:
# data = agg_distributions[category]
# data = [int(x[0]) for x in data]
# powerlaw.plot_ccdf(data, ax, label=labels[category],color=colors[category])
category_distributions = read_pickle(HOME+'output/category_counts_distribution.obj')
data = category_distributions['counts']
data = [int(x[0]) for x in data]
#to consider the edges that have zero transitions we substract the number transitions from the number of edges in wikipeida
number_of_edges = 339463340
listofzeros = [0] * (number_of_edges - len(data))
print len(data)
print len(listofzeros)
zeros = np.zeros((number_of_edges - len(data)))
data = np.append(zeros, data)
#data = data.extend(listofzeros)
print data
#hist, bin_edges = np.histogram(data, bins=100, normed=True)
#ones = np.ones(100)
#ccdf = ones - np.cumsum(data)
#cdf = np.cumsum(hist)
#print cdf
#print ccdf
bins, CDF = powerlaw.cdf(data, survival=True)
plt.plot(bins, CDF)
plt.xscale('symlog')
#powerlaw.plot_cdf(data, ax, label='transitions', color='r')
# further plotting
#ax.set_xlabel(r'Number of transitions $n$')
#ax.set_ylabel(r'$P(X \geq n)$')
plt.legend(fancybox=True, loc='lower left', ncol=1, prop={'size':5})
#leg = plt.gca().get_legend()
#ltext = leg.get_texts() # all the text.Text instance in the legend
#plt.setp(ltext, fontsize='small') # the legend text fontsize
plt.tight_layout()
plt.savefig('output/agg_counts_distributions.pdf', bbox_inches='tight')
def draw_avg_geo_as_dist_helper(lg_pairs, d, color, mode):
values = []
for lg1,lg2 in lg_pairs:
lg1.update_prefix_as_path()
p1 = lg1.get_prefixes()
lg2.update_prefix_as_path()
p2 = lg2.get_prefixes()
overlap = p1 & p2
if len(overlap) == 0:#no overlapping prefixes
continue
if mode == GEODIST:
for p in overlap:
coord_p = d[p]
coord_lg1 = getattr(lg1,LAT_LON)
coord_lg2 = getattr(lg2,LAT_LON)
if coord_lg1 == (0.0, 0.0) or coord_lg2 == (0.0, 0.0) or coord_p == (0.0 , 0.0):#if one of the location is unknown
continue
dist1 = geopy.distance.great_circle(coord_lg1,coord_p).km
dist2 = geopy.distance.great_circle(coord_lg2,coord_p).km
avg_dist = (dist1+dist2) / 2.0
#print lg1,lg2,p,avg_dist
values.append(avg_dist)
elif mode == ASDIST:
for p in overlap:
s1 = lg1.get_as_paths_set(p)
s2 = lg2.get_as_paths_set(p)
len1 = len(s1)
len2 = len(s2)
avg_asdist = (len1+len2) / 2.0
#print lg1,lg2,p,avg_asdist
values.append(avg_asdist)
else:
print "wrong!"
return
lg1.release()
lg2.release()
dist,prob = pl.cdf(values)
return plt.scatter(dist,prob,c=color,marker='x')
def draw_cdf(ases, title, lower=-1, upper=100):
'''
args:
ases:
list of AS objects
title:
title of the figure
lower:
lower bound of num of LGs in the ASes to be selected
upper:
upper bound of num of LGs in the ASes to be selected
'''
ases_in_use = []
for as_ in ases:
if len(as_) >= lower and len(as_) <= upper:
ases_in_use.append(as_)
#plt.title(title)
plt.xlabel("number of neighbors")
plt.ylabel("cdf")
colors = ['r','b','g']
lis_legend = []
names = ("BGP","iBGP","eBGP")
lgs = []
for as_ in ases_in_use:
lgs += as_.get_attr(LGS)
for i in range(len(names)):
lis = []
for lg in lgs:
n = len(lg.get_attr(NEI_SET)[i])
lis.append(float(n))
dist,prob = pl.cdf(lis)
lis_legend.append(plt.scatter(dist,prob,c=colors[i],marker='x'))
plt.legend(tuple(lis_legend),names,scatterpoints=1,loc="lower right")
plt.autoscale()
plt.margins(0.03)
#plt.title("Degree distribution based on BGP, eBGP, and iBGP neighbors")
#plt.xlim(0,15000)
#plt.ylim(0,1)
plt.show()
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)
#Used powerlaw package: https://github.com/jeffalstott/powerlaw
import networkx as nx
import matplotlib.pyplot as plt
import powerlaw as pl
#The graph is read as a weighted edgelist
G = nx.Graph()
G = nx.read_weighted_edgelist('as-22july06.mtx')
#Each node in the dataset has a corresponding degree - deg references to each
#node and iterates through the degrees of the graph and sorts it
sorted_degree = sorted([deg for node, deg in G.degree()])
#cdf - cumulative distribution function is a function under the powerlaw function
pl.cdf(data=sorted_degree, survival=False)
# plot_cdf function plots the cdf - also under the powerlaw package
pl.plot_cdf(sorted_degree)
plt.show()
