def bipartite_op_gen_zipf(g, params):
if len(params) != 8:
error('invalid number of arguments for "genzipf"')
zipf_alpha2 = float(params[0])
zipf_N2 = int(params[1])
zipf_xmin2 = int(params[2])
n2 = int(params[3])
zipf_alpha3 = float(params[4])
zipf_N3 = int(params[5])
zipf_xmin3 = int(params[6])
n3 = int(params[7])
z2 = Zipf(zipf_alpha2, zipf_N2, zipf_xmin2)
z3 = Zipf(zipf_alpha3, zipf_N3, zipf_xmin3)
z2_exp = z2.expectation()
z3_exp = z3.expectation()
info(" L2 distrib expectation = %.20f" % (z2_exp))
info(" L3 distrib expectation = %.20f" % (z3_exp))
if (n2 <= 0) and (n3 > 0):
n2 = int(round((n3 * z3_exp) / z2_exp))
info(" n2 auto-computed = %d" % (n2))
elif (n2 > 0) and (n3 <= 0):
n3 = int(round((n2 * z2_exp) / z3_exp))
info(" n3 auto-computed = %d" % (n3))
else:
error(" n2 and n3 cannot both be undefined")
info(" a2=%f, N2=%d, xmin2=%d, n2=%d" % (zipf_alpha2, zipf_N2, zipf_xmin2, n2))
info(" a3=%f, N3=%d, xmin3=%d, n3=%d" % (zipf_alpha3, zipf_N3, zipf_xmin3, n3))
# Check expected number of edges at level 2
# against expected number of edges at level 3
l2_exp = z2_exp * n2
l3_exp = z3_exp * n3
info(" Expected total L2 degree = %.20f" % (l2_exp))
info(" Expected total L3 degree = %.20f" % (l3_exp))
(degrees2, degrees3) = random_matching_degrees(z2, n2, z3, n3)
log(1, " MLE L2 = %f" % (Zipf.mle(degrees2, zipf_xmin2)))
log(1, " MLE L3 = %f" % (Zipf.mle(degrees3, zipf_xmin3)))
return bipartite_cm(degrees2, degrees3)
def _bipartite_op_stats_flat(g, output=None):
# Vertex/edge count
info(" Number of vertices: %d" % (g.vcount()))
info(" Number of edges: %d" % (g.ecount()))
degrees = g.degree()
max_degree = g.maxdegree()
info(" Highest degree: %d" % (max_degree))
# Connectedness
if g.is_connected():
info(" Graph is connected")
else:
info(" Graph is not connected")
clusters = g.clusters()
info(" Number of connected components = %d" % (len(clusters)))
giant = clusters.giant()
info(" Size of largest component = %d" % (giant.vcount()))
# Power law exponent estimators
# mle= Pareto.mle(degrees)
mle = Zipf.mle(degrees)
info(" Maximum Likelihood Estimator:")
info(" alpha (xm=1): %.20f" % (mle))
# Node degrees distributions
if output:
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
_plot_degree_hist(ax, degrees, max_degree)
filename = "degree-hist-%s" % (output)
info(' Create "%s"' % (filename))
fig.savefig(filename)
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
_plot_degree_dist_loglog(ax, degrees, max_degree)
filename = "degree-dist-loglog-%s" % (output)
info(' Create "%s"' % (filename))
fig.savefig(filename)
else:
fig = plt.figure()
ax = plt.subplot(1, 2, 1)
_plot_degree_hist(ax, degrees, max_degree)
ax = plt.subplot(1, 2, 2)
_plot_degree_dist_loglog(ax, degrees, max_degree)
plt.show()
return g
def _bipartite_op_stats_bipartite(g, output=None):
# Vertex/edge count
l2_vertices = [idx for idx in range(g.vcount()) if not (g.vs["type"][idx])]
l3_vertices = [idx for idx in range(g.vcount()) if g.vs["type"][idx]]
info(" Number of L2 vertices: %d" % (len(l2_vertices)))
info(" Number of L3 vertices: %d" % (len(l3_vertices)))
info(" Number of edges: %d" % (g.ecount()))
l2_degrees = g.degree(l2_vertices)
l3_degrees = g.degree(l3_vertices)
l3_degrees = [i for i in l3_degrees if i > 0]
max_l2_degree = g.maxdegree(l2_vertices)
max_l3_degree = g.maxdegree(l3_vertices)
if max_l2_degree > max_l3_degree:
max_degree = max_l2_degree
else:
max_degree = max_l3_degree
info(" Highest L2 degree: %d" % (max_l2_degree))
info(" Highest L3 degree: %d" % (max_l3_degree))
l2_degrees_hist = numpy.histogram(l2_degrees, bins=max_degree, range=(0, max_degree))
l3_degrees_hist = numpy.histogram(l3_degrees, bins=max_degree, range=(0, max_degree))
# Connectedness
if g.is_connected():
info(" Graph is connected")
else:
info(" Graph is not connected")
clusters = g.clusters()
info(" Number of connected components = %d" % (len(clusters)))
giant = clusters.giant()
info(" Size of largest component = %d" % (giant.vcount()))
# L2/L3 power law exponents estimators
info(" Maximum Likelihood Estimator:")
l2_xmin_range = range(1, 4)
l2_mle = _estimate_pareto_params(l2_degrees, l2_xmin_range)
for xmin in l2_xmin_range:
info(" alpha (L2, xm=%d): %.20f" % (xmin, l2_mle[xmin]))
# l3_mle= Pareto.mle(l3_degrees)
l3_mle = Zipf.mle(l3_degrees)
info(" alpha (L3, xm=1): %.20f" % (l3_mle))
# L2/L3 degrees distributions
if output:
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
_plot_degree_hist(ax, l2_degrees, max_degree)
for xmin in l2_xmin_range:
_plot_pareto_pdf(ax, l2_mle[xmin], xmin, l2_degrees, max_degree, hist=False)
filename = "l2-degree-hist-%s" % (output)
info(' Create "%s"' % (filename))
fig.savefig(filename)
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
_plot_degree_dist_loglog(ax, l2_degrees, max_degree)
for xmin in l2_xmin_range:
_plot_pareto_pdf(ax, l2_mle[xmin], xmin, l2_degrees, max_degree)
filename = "l2-degree-dist-loglog-%s" % (output)
info(' Create "%s"' % (filename))
fig.savefig(filename)
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
_plot_degree_hist(ax, l3_degrees, max_degree)
_plot_pareto_pdf(ax, l3_mle, 1, l3_degrees, max_degree, hist=False)
filename = "l3-degree-hist-%s" % (output)
info(' Create "%s"' % (filename))
fig.savefig(filename)
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
_plot_degree_dist_loglog(ax, l3_degrees, max_degree)
_plot_pareto_pdf(ax, l3_mle, 1, l3_degrees, max_degree)
filename = "l3-degree-dist-loglog-%s" % (output)
info(' Create "%s"' % (filename))
fig.savefig(filename)
else:
fig = plt.figure()
ax = plt.subplot(2, 2, 1)
_plot_degree_hist(ax, l2_degrees, max_degree)
ax = plt.subplot(2, 2, 2)
_plot_degree_dist_loglog(ax, l2_degrees, max_degree)
for xmin in l2_xmin_range:
_plot_pareto_pdf(ax, l2_mle[xmin], xmin, l2_degrees, max_degree)
ax = plt.subplot(2, 2, 3)
_plot_degree_hist(ax, l3_degrees, max_degree)
ax = plt.subplot(2, 2, 4)
_plot_degree_dist_loglog(ax, l3_degrees, max_degree)
_plot_pareto_pdf(ax, l3_mle, 1, l3_degrees, max_degree)
plt.show()
return g
def _estimate_pareto_params(degrees, beta_range):
alphas = {}
for beta in beta_range:
# alphas[beta]= Pareto.mle(degrees, beta)
alphas[beta] = Zipf.mle(degrees, beta)
return alphas
