Simulating a mixture of sparse + dense network from a mixture of GGPs



In [1]:

    
from operator import itemgetter

import numpy as np
from scipy.special import gamma
import matplotlib.pyplot as plt
import seaborn as sns; sns.set()

from sgp import GGPrnd, BSgraphrnd, GGPgraphrnd, GGPmixtureGraphrnd
from sgp.GraphUtil import compute_growth_rate, degree_distribution, degree_one_nodes

%matplotlib inline

Set up hyper-params for the mixture graph

Expected weight from dense-GGP is -d_sigma / d_tau



In [2]:

    
s_alpha = 20
s_tau = 1
s_sigma = 0.5

d_alpha = 100
d_tau = 1
d_sigma = -0.2

G, D, w, w_rem, params, sparse_nodes, dense_nodes = GGPmixtureGraphrnd(s_alpha, s_sigma, s_tau, d_alpha, d_sigma, d_tau)

How many sparse & dense nodes in the graph?



In [3]:

    
n = G.shape[0]
n_s = len(sparse_nodes); n_d = len(dense_nodes)
print('sparse nodes', n_s)
print('dense nodes', n_d)









    



sparse nodes 531
dense nodes 338



In [4]:

    
plt.figure(figsize=(12, 12))
ax = sns.heatmap(G.toarray(), square=True, xticklabels=False, yticklabels=False)
ax.set_xticks([n_s])
ax.set_xticklabels(['Sparse|Dense'])
ax.set_yticks([n_d])
ax.set_yticklabels(['Dense|Sparse'], rotation='vertical')
ax.hlines(n_d, xmin=0, xmax=n, linestyles='dashed', color='blue')
ax.vlines(n_s, ymin=0, ymax=n, linestyles='dashed', color='blue')









    Out[4]:





<matplotlib.collections.LineCollection at 0x118e77f60>

The sparse nodes are sorted by their weights.

Compute the growth rate of random graph



In [5]:

    
g_rate = compute_growth_rate(G)
plt.plot(g_rate)
plt.title('Growth rate of the graph')
plt.xlabel('# of nodes')
plt.ylabel('# of edges')









    Out[5]:





<matplotlib.text.Text at 0x11e80b470>

Compute degree distribution of random graph



In [6]:

    
d, d_list = degree_distribution(G)
plt.loglog(d_list[1:])
plt.title('Node degree distribution (in+outdegree)')
plt.xlabel('Degree of node')
plt.ylabel('# of nodes')









    Out[6]:





<matplotlib.text.Text at 0x1069011d0>



In [7]:

    
print('Number of nodes with degree one', degree_one_nodes(G))









    



Number of nodes with degree one 86



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