In [1]:

    

import igraph as ig
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
from math import *

%load_ext autoreload
%autoreload 2
%matplotlib inline


    

In [2]:

    

N = int(30000)
M = np.random.poisson(8, N).tolist()

# generate PA graph
g = ig.Graph.Barabasi(n=N,
                      m=M,
                      directed=True)

# compute citation ages
citation_ages = []
source_ages = []
for e in g.es:
    source = e.source
    target = e.target

    citation_ages.append(source - target)
    
    source_ages.append(source)


    

In [3]:

    

plt.subplot(1,2,1)
plt.hist(citation_ages);
plt.xlim([0, max(citation_ages)])
plt.xlabel('citation age')
plt.ylabel('count')


plt.subplot(1,2,2)
plt.loglog(sorted(citation_ages, reverse=True), '-', marker='.', color='black',
           alpha=.7);
plt.ylabel('log age')
plt.xlabel('log count')


    

    
Out[3]:





<matplotlib.text.Text at 0x1108f08d0>






    

In [4]:

    

plt.scatter(source_ages, citation_ages)
plt.xlabel('source age')
plt.ylabel('citation age')
plt.xlim([0, N])
plt.ylim([0, max(citation_ages)])


    

    
Out[4]:





(0, 29998)






    

In [9]:

    

# np.linspace(0, N, 11)
bins = range(0 , N, 100)
bin_means = stats.binned_statistic(source_ages, citation_ages, statistic='mean', bins=bins).statistic
plt.scatter(bins[:-1], bin_means)
plt.xlim([0, max(bins)])
plt.ylim([0, max(bin_means)])
plt.xlabel('100 days')
plt.ylabel('bin mean')


    

    
Out[9]:





<matplotlib.text.Text at 0x11555f390>






    

In [6]:

    

indegrees = g.indegree()
plt.scatter(range(N), indegrees,
            marker='.',
            color='black')
plt.xlabel('node age')
plt.ylabel('in degree')

plt.xlim([0, N])
plt.ylim([0, 200])


    

    
Out[6]:





(0, 200)






    

In [7]:

    

plt.figure(figsize = [20, 10])

plt.subplot(1,2,1)
dmax = 100
binwidth = 1
plt.hist(indegrees, bins=range(0, dmax + binwidth, binwidth));
plt.xlim([0, dmax])
# plt.ylim([0, 2e5])


plt.subplot(1,2,2)
plt.loglog(sorted(indegrees, reverse=True), '-', marker='.', color='black',
           alpha=.7);
plt.ylabel('log degree')
plt.xlabel('log count')


    

    
Out[7]:





<matplotlib.text.Text at 0x110b30110>






    

In [70]:

    

# layout = []
# indegs = g.indegree()
# for n in range(N):
#     x = n
#     y = - .5 * indegs[n]
#     # y = np.random.uniform()
    
#     layout.append([x, y])

# # vertices
# visual_style = {}
# visual_style['layout'] = layout
# # visual_style['vertex_label'] = range(N)
# # visual_style['vertex_label_size'] = 10
# visual_style['vertex_size'] = 10
# visual_style['vertex_color'] = 'black'
# visual_style['vertex_frame_color'] = 'black'

# visual_style["edge_width"] = .5
# visual_style["edge_arrow_size"] = .5



# visual_style["bbox"] = (300, 300)
# visual_style["margin"] = 20

# ig.plot(g, **visual_style)