"""This program performs item 4 in 4.4 exercise 4.

"Make a graph that replicates the line marked C(p)/C(0) in Figure 2 of the
paper. In other words, confirm that the clustering coefficient drops off slowly
for small values of p."

"""
import random
import matplotlib.pyplot as pyplot

from Graph import Vertex
from SmallWorldGraph import SmallWorldGraph


title = 'C(p)/C(0)'

# compute C(0)
n = 1000
k = 10
vs = [Vertex(str(i)) for i in range(n)]
g = SmallWorldGraph(vs, k, 0.0)
c0 = g.clustering_coefficient()
print 'c0 =', c0

# compute data
p_vals = [0,
          0.0001, 0.0002, 0.0004, 0.0006, 0.0008,
          0.001, 0.002, 0.004, 0.006, 0.008,
          0.01, 0.02, 0.04, 0.06, 0.08,
          0.1, 0.2, 0.4, 0.6, 0.8,
          1.0]

c_vals = []
for p in p_vals:
    g = SmallWorldGraph(vs, k, p)
    c_vals.append(g.clustering_coefficient() / c0)

# plot graph
pyplot.clf()
pyplot.xscale('log')
pyplot.yscale('log')
pyplot.title('')
pyplot.xlabel('p')
pyplot.ylabel('C(p)/C(0)')
pyplot.plot(p_vals, c_vals, label=title, color='green', linewidth=3)
pyplot.legend(loc=4)
pyplot.show()