In [1]:

    

%matplotlib inline


    

In [2]:

    

import networkx as nx
import pandas as pd
import projx as px
import matplotlib.pyplot as plt
import seaborn as sns


    

In [3]:

    

plt.rcParams['figure.figsize'] = (12, 7)


    

In [4]:

    

g = nx.read_gexf("projections/onemode.gexf")


    

In [5]:

    

print(len(g), len(g.edges()))


    

    




(318, 2212)

In [6]:

    

g = list(nx.connected_component_subgraphs(g))[0]


    

In [7]:

    

print(len(g), len(g.edges()))


    

    




(305, 2174)

In [8]:

    

weight_sr = pd.Series([attrs["weight"] for s, t, attrs in g.edges(data=True)])
weight_sr.describe()


    

    
Out[8]:





count    2174.000000
mean        0.203542
std         0.197535
min         0.052632
25%         0.111455
50%         0.142857
75%         0.200000
max         2.602381
dtype: float64

In [17]:

    

font = {'family' : 'normal',
        'weight' : 'bold',
        'size'   : 22}

plt.rc('font', **font)
plt.savefig("img/article/figure6.eps", format='eps', dpi=1000)
cutoffs, densities = px.proj_density(g, 0.0, 0.01, 100)
plt.plot(cutoffs, densities)
plt.ylabel('network density', size=18)
plt.xlabel('deight', size=18)
plt.savefig("img/article/figure6.eps", format='eps', dpi=1000)


    

In [30]:

    

cutoffs, densities = px.proj_density(g, 0.0, 0.01, 20)
plt.plot(cutoffs, densities)
plt.savefig("img/cutlines_detail.png")


    

In [9]:

    

weight_sr.quantile(0.10)


    

    
Out[9]:





0.090909090909100002

In [15]:

    

fourteen_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.14))
nx.write_gexf(fourteen_percent_cut, "projections/fourteen_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(fourteen_percent_cut))
print([len(sub) for sub in subgraphs])
print(nx.density(subgraphs[0]))


    

    




[288, 5, 8]
0.0457075106465

In [10]:

    

ten_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.10))
nx.write_gexf(ten_percent_cut, "projections/ten_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(ten_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[297, 5, 8]

In [11]:

    

twentyfive_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.25))
nx.write_gexf(twentyfive_percent_cut, "projections/twenty_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(twentyfive_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[271, 5, 8]

In [31]:

    

fifty_percent_cut = px.remove_edges(g.copy(), 0.14)
nx.write_gexf(fifty_percent_cut, "projections/fifty_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(fifty_percent_cut))
print([len(sub) for sub in subgraphs])
print(len(subgraphs[0].edges())) / float(2212)
print(nx.density(subgraphs[0]))


    

    




[236]
0.557414104882
0.0444644789037

In [13]:

    

sixty_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.6))
subgraphs = list(nx.connected_component_subgraphs(sixty_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[198, 5, 2]

In [14]:

    

seventy_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.7))
subgraphs = list(nx.connected_component_subgraphs(seventy_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[167, 5, 2]

In [15]:

    

seventyfive_percent_cut = px.remove_edges(g.copy(), 0.2)
subgraphs = list(nx.connected_component_subgraphs(seventyfive_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[167, 5, 2]

In [16]:

    

eighty_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.8))
subgraphs = list(nx.connected_component_subgraphs(eighty_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[139, 5, 2]

In [17]:

    

ninety_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.9))
nx.write_gexf(ninety_percent_cut, "projections/ninety_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(ninety_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[76, 4, 5, 2, 2]

In [18]:

    

ninetyone_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.91))
subgraphs = list(nx.connected_component_subgraphs(ninetyone_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[74, 4, 2, 2, 2]

In [19]:

    

ninetytwo_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.92))
subgraphs = list(nx.connected_component_subgraphs(ninetytwo_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[57, 4, 2, 12, 2]

In [20]:

    

ninetythree_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.93))
subgraphs = list(nx.connected_component_subgraphs(ninetythree_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[49, 4, 2, 12, 2]

In [21]:

    

ninetyfour_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.94))
subgraphs = list(nx.connected_component_subgraphs(ninetyfour_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[47, 4, 5, 4, 2]

In [22]:

    

ninetyfive_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.95))
nx.write_gexf(ninetyfive_percent_cut, "projections/ninetyfive_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(ninetyfive_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[44, 4, 5, 4, 2]

In [23]:

    

ninetysix_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.96))
subgraphs = list(nx.connected_component_subgraphs(ninetysix_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[37, 4, 5, 4, 2]

In [24]:

    

ninetyseven_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.97))
subgraphs = list(nx.connected_component_subgraphs(ninetyseven_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[32, 5, 3]

In [25]:

    

ninetyeight_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.98))
subgraphs = list(nx.connected_component_subgraphs(ninetyeight_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[25, 4, 3, 2]

In [26]:

    

ninetynine_percent_cut = px.remove_edges(g.copy(), weight_sr.quantile(0.99))
nx.write_gexf(ninetynine_percent_cut, "projections/ninetynine_percent_cut.gexf")
subgraphs = list(nx.connected_component_subgraphs(ninetynine_percent_cut))
print([len(sub) for sub in subgraphs])


    

    




[18, 3, 2, 2]