"""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 matplotlib.pyplot as pyplot

from Graph import Vertex
from SmallWorldGraph import SmallWorldGraph

# Use Dijkstra or Floyd-Warshall to compute L
DIJKSTRA = True

# 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()
l0 = g.big_l3() if DIJKSTRA else g.big_l2()
print 'c0 =', c0, 'l0 =', l0

# compute data
p_vals = [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 = []
l_vals = []
for p in p_vals:
    g = SmallWorldGraph(vs, k, p)
    c_vals.append(g.clustering_coefficient() / c0)
    l = g.big_l3() if DIJKSTRA else g.big_l2()
    l_vals.append(l / l0)

p_vals.insert(0, 0.0)
c_vals.insert(0, 1.0)
l_vals.insert(0, 1.0)

# 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='C(p)/C(0)', color='green', linewidth=3)
pyplot.plot(p_vals, l_vals, label='L(p)/L(0)', color='blue', linewidth=3)
pyplot.legend(loc=4)
pyplot.show()