def plot_set(ax, graph, group, color):
""" Plots the (I(C), E(C)) points for all communities in the group
"""
I_values = []
E_values = []
for c in group:
I, E, rubish = CD.I_E(graph, c)
E_values.append(E)
I_values.append(I)
ax.plot(I_values, E_values, color + 'o')
def gen_path_single(graph,
seed,
name,
ax,
metric,
comp,
ylim=[0, .3],
legend=False,
width=0.01,
param=None):
""" Generates and plots the I E path and manages the space
Parameters
----------
graph : a networkx graph
seed : a list of nodes to start from
name : the title of the graph
ax : the subplot to put everything
metric : the single community metric to optimize
comp : the comparison function either CD.compare_min or max
legend : whether or not to show the legend
width : the width of the arrow head
"""
# plot metric optimized path
(I_path, E_path, order) = CD.path_I_E(graph,
seed[:],
metric,
comp,
param=param)
print "Last point for ", name, " I ", I_path[-1], " E ", E_path[-1]
CD.plot_path(I_path[:], E_path[:], ax, 'r', name, width)
# plot corner cases
ax.plot(1, 0, 'kD', label='Ideal', markersize=10)
(graph_I, graph_E) = CD.I_E(graph, graph.nodes())
ax.plot(graph_I, 0, 'mD', label='Entire Graph', markersize=10)
# set labels etc
ax.set_title(name, fontsize=24)
plt.xticks([0, .3, .7, 1], ['0', '0.3', '0.7', '1'])
plt.yticks(ylim, [str(y) for y in ylim])
ax.set_xlim(-0.01, 1.01)
ax.set_ylim(ylim[0] - width / 2., ylim[1] + width / 2.)
ax.set_xlabel(r'$I(C)$', fontsize=24)
ax.set_ylabel(r'$E(C)$', fontsize=24)
if legend:
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, labels, loc=2)
plt.show()
# save the figure
plt.savefig(name + ".eps")
plt.savefig(name + ".pdf")
def gen_path_set(graph,
I_path,
E_path,
S_path,
name,
ylim=[0, 1],
legend=False,
width=0.01,
fig=False,
color='r'):
""" Given an I E S path plots
Parameters
----------
I_path : a list of I(S) values
E_path : a list of E(S) values
S_path : a list of |S| values
name : the title and saving file name
ylim : the maximum value of E(S)
legend : whether or not to show legend (not likely)
width : the width of the arrow head
"""
if not fig:
fig = plt.figure()
ax = fig.add_subplot(111)
CD.plot_path(I_path[:], E_path[:], ax, color, name, width)
# plot corner cases
ax.plot(1, 0, 'kD', label='Ideal', markersize=10)
(graph_I, graph_E) = CD.I_E(graph, graph.nodes())
ax.plot(graph_I, 0, 'mD', label='Entire Graph', markersize=10)
# set the dimensions and labels
ax.set_title(name, fontsize=24)
plt.xticks([0, .3, .7, 1], ['0', '0.3', '0.7', '1'])
plt.yticks(ylim, [str(y) for y in ylim])
ax.set_xlim(-.01, 1.01)
ax.set_ylim(ylim[0] - width / 2., ylim[1] + width / 2.)
ax.set_xlabel(r'$I(S)$', fontsize=24)
ax.set_ylabel(r'$E(S)$', fontsize=24)
if legend:
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, labels, loc=2)
plt.show()
# save the figure
plt.savefig(name + ".eps")
plt.savefig(name + ".pdf")
def path_I_E(graph, seed, f, compare, param=None, stop=100):
"""Traces the path of the best f metric community through the IE plane
Parameters
----------
graph - a networkx graph
seed - a set of nodes to start from
f - a metric to optimize
compare - the function that determines if the metric is being improved
param - a box to hand in any parameters f depends on, such as in linearity
Returns
-------
I_values - a list of the subsequent I values
E_values - a list of the subsequent E values
order - the order in which nodes are added
Method
------
At each stage, finds a node that if added to the set decreases conductance
"""
all_nodes = set(graph.nodes())
I_values = []
E_values = []
order = seed[:]
addition = True
while addition != None and len(order) < stop:
(next_I, next_E) = CD.I_E(graph, order)
I_values.append(next_I)
E_values.append(next_E)
addition = greedy_selection(graph, order, f, compare, param)
if type(addition) == int:
order.append(addition)
elif addition != None:
addition = None
if len(order) == 100:
print "The metric was terminated by the maximum number of steps"
return I_values, E_values, order
