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#! /usr/bin/env python
# We will need some things from several places
from __future__ import division, absolute_import, print_function
import sys
if sys.version_info < (3,):
range = xrange
import os
from pylab import * # for plotting
from numpy.random import * # for random sampling
seed(42)
# We need to import the graph_tool module itself
from graph_tool.all import *
# let's construct a Price network (the one that existed before Barabasi). It is
# a directed network, with preferential attachment. The algorithm below is
# very naive, and a bit slow, but quite simple.
# We start with an empty, directed graph
g = Graph()
# We want also to keep the age information for each vertex and edge. For that
# let's create some property maps
v_age = g.new_vertex_property("int")
e_age = g.new_edge_property("int")
# The final size of the network
N = 100000
# We have to start with one vertex
v = g.add_vertex()
v_age[v] = 0
# we will keep a list of the vertices. The number of times a vertex is in this
# list will give the probability of it being selected.
vlist = [v]
# let's now add the new edges and vertices
for i in range(1, N):
# create our new vertex
v = g.add_vertex()
v_age[v] = i
# we need to sample a new vertex to be the target, based on its in-degree +
# 1. For that, we simply randomly sample it from vlist.
i = randint(0, len(vlist))
target = vlist[i]
# add edge
e = g.add_edge(v, target)
e_age[e] = i
# put v and target in the list
vlist.append(target)
vlist.append(v)
# now we have a graph!
# let's do a random walk on the graph and print the age of the vertices we find,
# just for fun.
v = g.vertex(randint(0, g.num_vertices()))
while True:
print("vertex:", int(v), "in-degree:", v.in_degree(), "out-degree:",
v.out_degree(), "age:", v_age[v])
if v.out_degree() == 0:
print("Nowhere else to go... We found the main hub!")
break
n_list = []
for w in v.out_neighbors():
n_list.append(w)
v = n_list[randint(0, len(n_list))]
# let's save our graph for posterity. We want to save the age properties as
# well... To do this, they must become "internal" properties:
g.vertex_properties["age"] = v_age
g.edge_properties["age"] = e_age
# now we can save it
g.save("price.xml.gz")
# Let's plot its in-degree distribution
in_hist = vertex_hist(g, "in")
y = in_hist[0]
err = sqrt(in_hist[0])
figure(figsize=(6,4))
errorbar(in_hist[1][:-1], in_hist[0], fmt="o", yerr=err,
label="in")
gca().set_yscale("log")
gca().set_xscale("log")
gca().set_ylim(1e-1, 1e5)
gca().set_xlim(0.8, 1e3)
subplots_adjust(left=0.2, bottom=0.2)
xlabel("$k_{in}$")
ylabel("$NP(k_{in})$")
tight_layout()
savefig("price-deg-dist.pdf")
savefig("price-deg-dist.svg")
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