def test_modularity():
"""Test the values that go into the modularity calculation after randomly
creating a graph"""
# Given a partition with the correct labels of the input graph, verify that
# the modularity returns 1
# We need to measure the degree within/between modules
nnods = 120, 240, 360
nmods = 2, 3, 4
av_degrees = 8, 10, 16
for nnod in nnods:
for nmod in nmods:
for av_degree in av_degrees:
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Compute the of nodes per module
nnod_mod = nnod/nmod
#Make a "correct" partition for the graph
part = mod.perfect_partition(nmod,nnod_mod)
#Make a graphpartition object
graph_partition = mod.GraphPartition(g,part)
#call modularity
mod_meas = graph_partition.modularity()
mod_true = 1.0 - 1.0/nmod
npt.assert_almost_equal(mod_meas, mod_true, 2)
def test_modularity():
"""Test the values that go into the modularity calculation after randomly
creating a graph"""
# Given a partition with the correct labels of the input graph, verify that
# the modularity returns 1
# We need to measure the degree within/between modules
nnods = 120, 240, 360
nmods = 2, 3, 4
av_degrees = 8, 10, 16
for nnod in nnods:
for nmod in nmods:
for av_degree in av_degrees:
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Compute the of nodes per module
nnod_mod = nnod / nmod
#Make a "correct" partition for the graph
part = mod.perfect_partition(nmod, nnod_mod)
#Make a graphpartition object
graph_partition = mod.GraphPartition(g, part)
#call modularity
mod_meas = graph_partition.modularity()
mod_true = 1.0 - 1.0 / nmod
npt.assert_almost_equal(mod_meas, mod_true, 2)
def test_mutual_information():
""" Test the function which returns the mutual information in two
partitions
XXX - This test is currently incomplete - it only checks the most basic
case of MI(x, x)==1, but doesn't do any non-trivial checks.
"""
# nnod_mod, av_degrees, nmods
networks = [ [4, [2, 3], [2, 4, 6]],
[8, [4, 6], [4, 6, 8]],
[40, [20], [2]] ]
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod*nmod
for av_degree in av_degrees:
#make a graph object
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Compute the of nodes per module
nnod_mod = nnod/nmod
#Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod,nnod_mod)
#graph_out, mod_array =mod.simulated_annealing(g, temperature =
#temperature,temp_scaling = temp_scaling, tmin=tmin)
#test the perfect case for now: two of the same partition
#returns 1
mi_orig = mod.mutual_information(ppart,ppart)
yield npt.assert_equal(mi_orig,1)
#move one node and test that mutual_information comes out
#correctly
graph_partition = mod.GraphPartition(g,ppart)
graph_partition.node_update(0,0,1)
mi = mod.mutual_information(ppart,graph_partition.index)
yield npt.assert_array_less(mi, mi_orig)
## NOTE: CORRECTNESS NOT TESTED YET
#merge modules and check that mutual information comes out
#correctly/lower
graph_partition2 = mod.GraphPartition(g,ppart)
merged_module, e_new, a_new, d,t,m1,m2,x = graph_partition2.compute_module_merge(0,1)
graph_partition2.apply_module_merge(m1,m2,merged_module,e_new,a_new)
mi2 = mod.mutual_information(ppart,graph_partition2.index)
yield npt.assert_array_less(mi2,mi_orig)
## NOTE: CORRECTNESS NOT TESTED YET
#split modules and check that mutual information comes out
#correclty/lower
graph_partition3 = mod.GraphPartition(g,ppart)
n1 = list(graph_partition3.index[0])[::2]
n2 = list(graph_partition3.index[0])[1::2]
split_modules,e_new,a_new,d,t,m,n1,n2 = graph_partition3.compute_module_split(0,n1,n2)
graph_partition3.apply_module_split(m,n1,n2,split_modules,e_new,a_new)
mi3 = mod.mutual_information(ppart,graph_partition3.index)
yield npt.assert_array_less(mi3,mi_orig)
def SA():
""" Test the simulated annealing script"""
#nnod_mod, av_degrees, nmods
#networks = [ [4, [2, 3], [2, 4, 6]]]#,
#networks = [ [8, [4, 6], [4, 6, 8]]]
#networks = [[40, [20], [2]]]
networks = [[32, [16], [4]]]
#networks = [[64, [12], [6]]]
btwn_fracs = [0]
temperature = 10
temp_scaling = 0.9995
tmin = 1e-4
nochange_ratio_min = 0.01
#keep time
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod * nmod
for av_degree in av_degrees:
for btwn_frac in btwn_fracs:
t1 = time.clock()
g = mod.random_modular_graph(nnod, nmod, av_degree,
btwn_frac)
#Compute the # of nodes per module
nnod_mod = nnod / nmod
#Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod, nnod_mod)
graph_out, energy_array, rej_array, temp_array = mod.simulated_annealing(
g,
temperature=temperature,
temp_scaling=temp_scaling,
tmin=tmin,
nochange_ratio_min=nochange_ratio_min)
print "perfect partition", ppart
print "SA partition", graph_out.index
t2 = time.clock()
print 'Elapsed time: ', float(t2 - t1) / 60, 'minutes'
print 'partition similarity: ', mod.mutual_information(
ppart, graph_out.index)
return graph_out, g, energy_array, rej_array, ppart, temp_array
def SA():
""" Test the simulated annealing script"""
# nnod_mod, av_degrees, nmods
# networks = [ [4, [2, 3], [2, 4, 6]]]#,
# networks = [ [8, [4, 6], [4, 6, 8]]]
# networks = [[40, [20], [2]]]
networks = [[32, [16], [4]]]
# networks = [[64, [12], [6]]]
btwn_fracs = [0]
temperature = 10
temp_scaling = 0.9995
tmin = 1e-4
nochange_ratio_min = 0.01
# keep time
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod * nmod
for av_degree in av_degrees:
for btwn_frac in btwn_fracs:
t1 = time.clock()
g = mod.random_modular_graph(nnod, nmod, av_degree, btwn_frac)
# Compute the # of nodes per module
nnod_mod = nnod / nmod
# Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod, nnod_mod)
graph_out, energy_array, rej_array, temp_array = mod.simulated_annealing(
g,
temperature=temperature,
temp_scaling=temp_scaling,
tmin=tmin,
nochange_ratio_min=nochange_ratio_min,
)
print "perfect partition", ppart
print "SA partition", graph_out.index
t2 = time.clock()
print "Elapsed time: ", float(t2 - t1) / 60, "minutes"
print "partition similarity: ", mod.mutual_information(ppart, graph_out.index)
return graph_out, g, energy_array, rej_array, ppart, temp_array
def test_sim_anneal_simple():
"""Very simple simulated_annealing test with a small network"""
#
nnod, nmod, av_degree, btwn_frac = 24, 3, 4, 0
g = mod.random_modular_graph(nnod, nmod, av_degree, btwn_frac)
#Compute the # of nodes per module
nnod_mod = nnod/nmod
#Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod,nnod_mod)
temperature = 10
temp_scaling = 0.95
tmin=1
graph_out, graph_dict = mod.simulated_annealing(g,
temperature = temperature, temp_scaling = temp_scaling,
tmin=tmin, extra_info = True, debug=True)
# Ensure that there are no empty modules
util.assert_no_empty_modules(graph_out.index)
mi = mod.mutual_information(ppart, graph_out.index)
def danon_benchmark():
"""This test comes from Danon et al 2005. It will create the line plot of
Mututal Information vs. betweenness fraction to assess the performance of
the simulated annealing algorithm."""
networks = [[32, [16], [6]]]
btwn_fracs = [float(i)/100 for i in range(0,80,3)]
temperature = 0.1
temp_scaling = 0.9995
tmin=1e-4
num_reps = range(1)
mi_arr=np.empty((len(btwn_fracs),len(num_reps)))
#keep time
for rep in num_reps:
t1 = time.clock()
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod*nmod
for av_degree in av_degrees:
x_mod = []
for ix,btwn_frac in enumerate(btwn_fracs):
print 'btwn_frac: ',btwn_frac
g = mod.random_modular_graph(nnod, nmod, av_degree,btwn_frac)
#Compute the # of nodes per module
nnod_mod = nnod/nmod
#Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod,nnod_mod)
graph_out, graph_dict =mod.simulated_annealing(g,
temperature = temperature,temp_scaling = temp_scaling,
tmin=tmin, extra_info = True)
#print "SA partition",graph_out.index
mi = mod.mutual_information(ppart,graph_out.index)
t2 = time.clock()
print 'Elapsed time: ', (float(t2-t1)/60), ' minutes'
print 'partition similarity: ',mi
mi_arr[ix,rep] = mi
## plot_partition(g,graph_out.index,'mi: '+ str(mi),'danon_test_6mod'+str(btwn_frac)+'_graph.png')
x_mod.append(betweenness_to_modularity(g,ppart))
## mi_arr_avg = np.mean(mi_arr,1)
## plt.figure()
## plt.plot(btwn_fracs,mi_arr_avg)
## plt.xlabel('Betweenness fraction')
## plt.ylabel('Mutual information')
## plt.savefig('danon_test_6mod/danontest_btwn.png')
## plt.figure()
## plt.plot(x_mod,mi_arr_avg)
## plt.xlabel('Modularity')
## plt.ylabel('Mutual information')
## plt.savefig('danon_test_6mod/danontest_mod.png')
#plt.figure()
#plt.plot(graph_dict['energy'], label = 'energy')
#plt.plot(graph_dict['temperature'], label = 'temperature')
#plt.xlabel('Iteration')
return mi_arr
def test_apply_module_merge():
"""Test the GraphPartition operation that merges modules so that it returns
a change in modularity that reflects the difference between the modularity
of the new and old parititions"""
# nnod_mod, av_degrees, nmods
networks = [ [3, [2], [3, 4]],
[4, [2, 3], [2, 4, 6]],
[8, [4, 6], [4, 6, 8]] ]
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod*nmod
for av_degree in av_degrees:
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Make a "correct" partition for the graph
part = mod.perfect_partition(nmod,nnod/nmod)
#Make a random partition for the graph
part_rand = dict()
while len(part_rand) <= 1: #check if there is only one module
part_rand = mod.rand_partition(g)
#List of modules in the partition
r_mod=range(len(part))
#Loop through pairs of modules
for i in range(1): # DB: why is this necessary?
#select two modules to merge
mod_per = np.random.permutation(r_mod)
m1 = mod_per[0]; m2 = mod_per[1]
#make a graph partition object
graph_partition = mod.GraphPartition(g,part)
#index of nodes within the original module (before merge)
n1_init = list(graph_partition.index[m1])
n2_init = list(graph_partition.index[m2])
n_all_init = n1_init+n2_init
#calculate modularity before merging
mod_init = graph_partition.modularity()
#merge modules
merge_module,e1,a1,delta_energy_meas,type,m1,m2,m2 = \
graph_partition.compute_module_merge(m1,m2)
graph_part2 = copy.deepcopy(graph_partition)
graph_part2.apply_module_merge(m1,m2,merge_module,e1,a1)
#index of nodes within the modules after merging
n_all = list(graph_part2.index[min(m1,m2)])
# recalculate modularity after splitting
mod_new = graph_part2.modularity()
# difference between new and old modularity
delta_energy_true = -(mod_new - mod_init)
# Test the measured difference in energy against the
# function that calculates the difference in energy
npt.assert_almost_equal(delta_energy_meas,
delta_energy_true)
# Check that the list of nodes in the two original modules
# is equal to the list of nodes in the merged module
n_all_init.sort()
n_all.sort()
npt.assert_equal(n_all_init, n_all)
# Test that the keys are equivalent after merging modules
npt.assert_equal(r_mod[:-1],
sorted(graph_part2.index.keys()))
# Test that the values in the mod_e and mod_a matrices for
# the merged module are correct.
npt.assert_equal(graph_part2.mod_e[min(m1,m2)],e1)
npt.assert_equal(graph_part2.mod_a[min(m1,m2)],a1)
def test_apply_module_split():
"""Test the GraphPartition operation that splits modules so that it returns
a change in modularity that reflects the difference between the modularity
of the new and old parititions.
Also test that the module that was split now contains the correct nodes,
the correct modularity update, the correct energy,and that no empty modules
result from it."""
# nnod_mod, av_degrees, nmods
networks = [ [3, [2], [2, 3, 4]],
[4, [2, 3], [2, 4, 6]],
[8, [4, 6], [4, 6, 8]] ]
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod*nmod
for av_degree in av_degrees:
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Make a "correct" partition for the graph
part = mod.perfect_partition(nmod,nnod/nmod)
#Make a random partition for the graph
part_rand = mod.rand_partition(g, nnod/2)
#List of modules in the partition that have two or more nodes
r_mod = []
for m, nodes in part_rand.iteritems():
if len(nodes)>2:
r_mod.append(m)
# Note: The above can be written in this more compact, if
# slightly less intuitively clear, list comprehension:
# r_mod = [ m for m, nodes in part_rand.iteritems() if
# len(nodes)>2 ]
#Module that we are splitting
for m in r_mod:
graph_partition = mod.GraphPartition(g,part_rand)
#index of nodes within the original module (before split)
n_init = list(graph_partition.index[m])
#calculate modularity before splitting
mod_init = graph_partition.modularity()
# assign nodes to two groups
n1_orig,n2_orig = graph_partition.determine_node_split(m)
# make sure neither of these is empty
yield nt.assert_true(len(n1_orig)>= 1)
yield nt.assert_true(len(n2_orig)>= 1)
#make sure that there are no common nodes between the two
node_intersection = set.intersection(n1_orig,n2_orig)
yield nt.assert_equal(node_intersection,set([]))
#make sure that sum of the two node sets equals the
#original set
node_union = set.union(n1_orig,n2_orig)
yield npt.assert_equal(np.sort(list(node_union)),np.sort(n_init))
# split modules
split_modules,e1,a1,delta_energy_meas,type,m,n1,n2 = \
graph_partition.compute_module_split(m,n1_orig,n2_orig)
#note: n1 and n2 are output from this function (as well as
#inputs) because the function is called from within another
#(rand_mod) def but then output to the simulated script, so
#the node split needs to be passed along.
#as a simple confirmation, can make sure they match
yield npt.assert_equal(n1_orig,n1)
yield npt.assert_equal(n2_orig,n2)
#split_moduels should be a dictionary with two modules
#(0,1) that contain the node sets n1 and n2 respectively.
#test this.
yield npt.assert_equal(split_modules[0],n1)
yield npt.assert_equal(split_modules[1],n2)
#make a new graph partition equal to the old one and apply
#the module split to it (graph_part2)
graph_part2 = copy.deepcopy(graph_partition)
graph_part2.apply_module_split(m,n1,n2,split_modules,e1,a1)
#make a third graph partition using only the original graph
#and the partition from graph_part2
graph_part3 = mod.GraphPartition(g,graph_part2.index)
#index of nodes within the modules after splitting
n1_new = list(graph_part2.index[m])
n2_new = list(graph_part2.index[len(graph_part2)-1])
n_all = n1_new + n2_new
# recalculate modularity after splitting
mod_new = graph_part2.modularity()
mod_new_3 = graph_part3.modularity()
# difference between new and old modularity
delta_energy_true = -(mod_new - mod_init)
# Test that the measured change in energy by splitting a
# module is equal to the function output from module_split
yield npt.assert_almost_equal(delta_energy_meas,
delta_energy_true)
# Test that the nodes in the split modules are equal to the
# original nodes of the module
yield npt.assert_equal(np.sort(list(n1)), n1_new)
yield npt.assert_equal(np.sort(list(n2)), n2_new)
n_init.sort()
n_all.sort()
# Test that the initial list of nodes in the module are
# equal to the nodes in m1 and m2 (split modules)
yield npt.assert_equal(n_init,n_all)
# Test that the computed modularity found when
# apply_module_split is used is equal to the modularity you
# would find if using that partition and that graph
yield npt.assert_almost_equal(mod_new,mod_new_3)
# Check that there are no empty modules in the final
# partition
for m in graph_part2.index:
yield nt.assert_true(len(graph_part2.index[m]) > 0)
def test_mutual_information():
""" Test the function which returns the mutual information in two
partitions
XXX - This test is currently incomplete - it only checks the most basic
case of MI(x, x)==1, but doesn't do any non-trivial checks.
"""
# nnod_mod, av_degrees, nmods
networks = [[4, [2, 3], [2, 4, 6]], [8, [4, 6], [4, 6, 8]],
[40, [20], [2]]]
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod * nmod
for av_degree in av_degrees:
#make a graph object
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Compute the of nodes per module
nnod_mod = nnod / nmod
#Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod, nnod_mod)
#graph_out, mod_array =mod.simulated_annealing(g, temperature =
#temperature,temp_scaling = temp_scaling, tmin=tmin)
#test the perfect case for now: two of the same partition
#returns 1
mi_orig = mod.mutual_information(ppart, ppart)
npt.assert_equal(mi_orig, 1)
#move one node and test that mutual_information comes out
#correctly
graph_partition = mod.GraphPartition(g, ppart)
graph_partition.node_update(0, 0, 1)
mi = mod.mutual_information(ppart, graph_partition.index)
npt.assert_array_less(mi, mi_orig)
## NOTE: CORRECTNESS NOT TESTED YET
#merge modules and check that mutual information comes out
#correctly/lower
graph_partition2 = mod.GraphPartition(g, ppart)
merged_module, e_new, a_new, d, t, m1, m2, x = graph_partition2.compute_module_merge(
0, 1)
graph_partition2.apply_module_merge(m1, m2, merged_module,
e_new, a_new)
mi2 = mod.mutual_information(ppart, graph_partition2.index)
npt.assert_array_less(mi2, mi_orig)
## NOTE: CORRECTNESS NOT TESTED YET
#split modules and check that mutual information comes out
#correclty/lower
graph_partition3 = mod.GraphPartition(g, ppart)
n1 = set(list(graph_partition3.index[0])[::2])
n2 = set(list(graph_partition3.index[0])[1::2])
split_modules, e_new, a_new, d, t, m, n1, n2 = graph_partition3.compute_module_split(
0, n1, n2)
graph_partition3.apply_module_split(m, n1, n2, split_modules,
e_new, a_new)
mi3 = mod.mutual_information(ppart, graph_partition3.index)
npt.assert_array_less(mi3, mi_orig)
def danon_benchmark():
"""This test comes from Danon et al 2005. It will create the line plot of
Mututal Information vs. betweenness fraction to assess the performance of
the simulated annealing algorithm."""
networks = [[32, [16], [6]]]
btwn_fracs = [float(i) / 100 for i in range(0, 80, 3)]
temperature = 0.1
temp_scaling = 0.9995
tmin = 1e-4
num_reps = range(1)
mi_arr = np.empty((len(btwn_fracs), len(num_reps)))
#keep time
for rep in num_reps:
t1 = time.clock()
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod * nmod
for av_degree in av_degrees:
x_mod = []
for ix, btwn_frac in enumerate(btwn_fracs):
print 'btwn_frac: ', btwn_frac
g = mod.random_modular_graph(nnod, nmod, av_degree,
btwn_frac)
#Compute the # of nodes per module
nnod_mod = nnod / nmod
#Make a "correct" partition for the graph
ppart = mod.perfect_partition(nmod, nnod_mod)
graph_out, graph_dict = mod.simulated_annealing(
g,
temperature=temperature,
temp_scaling=temp_scaling,
tmin=tmin,
extra_info=True)
#print "SA partition",graph_out.index
mi = mod.mutual_information(ppart, graph_out.index)
t2 = time.clock()
print 'Elapsed time: ', (float(t2 - t1) /
60), ' minutes'
print 'partition similarity: ', mi
mi_arr[ix, rep] = mi
## plot_partition(g,graph_out.index,'mi: '+ str(mi),'danon_test_6mod'+str(btwn_frac)+'_graph.png')
x_mod.append(betweenness_to_modularity(g, ppart))
## mi_arr_avg = np.mean(mi_arr,1)
## plt.figure()
## plt.plot(btwn_fracs,mi_arr_avg)
## plt.xlabel('Betweenness fraction')
## plt.ylabel('Mutual information')
## plt.savefig('danon_test_6mod/danontest_btwn.png')
## plt.figure()
## plt.plot(x_mod,mi_arr_avg)
## plt.xlabel('Modularity')
## plt.ylabel('Mutual information')
## plt.savefig('danon_test_6mod/danontest_mod.png')
#plt.figure()
#plt.plot(graph_dict['energy'], label = 'energy')
#plt.plot(graph_dict['temperature'], label = 'temperature')
#plt.xlabel('Iteration')
return mi_arr
def test_apply_module_merge():
"""Test the GraphPartition operation that merges modules so that it returns
a change in modularity that reflects the difference between the modularity
of the new and old parititions"""
# nnod_mod, av_degrees, nmods
networks = [[3, [2], [3, 4]], [4, [2, 3], [2, 4, 6]],
[8, [4, 6], [4, 6, 8]]]
for nnod_mod, av_degrees, nmods in networks:
for nmod in nmods:
nnod = nnod_mod * nmod
for av_degree in av_degrees:
g = mod.random_modular_graph(nnod, nmod, av_degree)
#Make a "correct" partition for the graph
part = mod.perfect_partition(nmod, nnod / nmod)
#Make a random partition for the graph
part_rand = dict()
while len(part_rand) <= 1: #check if there is only one module
part_rand = mod.rand_partition(g)
#List of modules in the partition
r_mod = range(len(part))
#Loop through pairs of modules
for i in range(1): # DB: why is this necessary?
#select two modules to merge
mod_per = np.random.permutation(r_mod)
m1 = mod_per[0]
m2 = mod_per[1]
#make a graph partition object
graph_partition = mod.GraphPartition(g, part)
#index of nodes within the original module (before merge)
n1_init = list(graph_partition.index[m1])
n2_init = list(graph_partition.index[m2])
n_all_init = n1_init + n2_init
#calculate modularity before merging
mod_init = graph_partition.modularity()
#merge modules
merge_module,e1,a1,delta_energy_meas,type,m1,m2,m2 = \
graph_partition.compute_module_merge(m1,m2)
graph_part2 = copy.deepcopy(graph_partition)
graph_part2.apply_module_merge(m1, m2, merge_module, e1,
a1)
#index of nodes within the modules after merging
n_all = list(graph_part2.index[min(m1, m2)])
# recalculate modularity after splitting
mod_new = graph_part2.modularity()
# difference between new and old modularity
delta_energy_true = -(mod_new - mod_init)
# Test the measured difference in energy against the
# function that calculates the difference in energy
npt.assert_almost_equal(delta_energy_meas,
delta_energy_true)
# Check that the list of nodes in the two original modules
# is equal to the list of nodes in the merged module
n_all_init.sort()
n_all.sort()
npt.assert_equal(n_all_init, n_all)
# Test that the keys are equivalent after merging modules
npt.assert_equal(r_mod[:-1],
sorted(graph_part2.index.keys()))
# Test that the values in the mod_e and mod_a matrices for
# the merged module are correct.
npt.assert_equal(graph_part2.mod_e[min(m1, m2)], e1)
npt.assert_equal(graph_part2.mod_a[min(m1, m2)], a1)
