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Edit and run

Re-exploratory Analysis

As the start of our second pass through the epicycle, we wish to refine and expand our exploratory analysis. We will compute vertex and edge features on our graphs across multiple scales and multiple datasets.

Setup





In [9]:



    


from scipy.stats import gaussian_kde
from ipywidgets import widgets

import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
import collections
import os

%matplotlib inline

font = {'weight' : 'bold',
        'size'   : 18}

import matplotlib
matplotlib.rc('font', **font)



    











In [10]:



    


# Initializing dataset names
dnames = list(['../data/desikan/MRN114', '../data/desikan/KKI2009', '../data/desikan/SWU4'])
print "Datasets: " + ", ".join(dnames)
print "D = " + str(len(dnames))

# Getting graph names
fs = dict()
for dd in dnames:
        fs[dd] = [root+'/'+fl for root, dir, files in os.walk(dd) for fl in files if fl.endswith(".graphml")]
# fs[dnames[1]]



    


















    






Datasets: ../data/desikan/MRN114, ../data/desikan/KKI2009, ../data/desikan/SWU4
D = 3

















In [11]:



    


def loadGraphs(filenames, printer=False):
    gstruct = collections.OrderedDict()
    for idx, files in enumerate(filenames):
        if printer:
            print "Loading: " + files
        gstruct[files] = nx.read_graphml(files)
    return gstruct

MRN114 Dataset





In [12]:



    


mygs = loadGraphs(fs[fs.keys()[0]], printer=False) # only loads graphs for kki dataset
mygs.keys()



    


















    
Out[12]:








['../data/desikan/MRN114/MRN114_M87102217_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87102806_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87103074_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87105476_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87107085_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87108094_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87111487_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87111924_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87114047_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87114064_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87115498_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87115517_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87117119_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87117167_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87120962_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87121943_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87121956_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87122092_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87123042_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87123449_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87123913_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87124633_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87124781_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87124827_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87125134_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87128444_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87129719_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87129789_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87131806_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87134068_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87135647_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87136332_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87136832_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87139021_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87139257_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87141220_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87141664_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87141793_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87141858_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87141906_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87141949_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87142764_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87143273_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87144889_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87144896_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87145479_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87145575_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87146520_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87146993_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87147006_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87148745_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87149014_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87149025_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87150194_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87150415_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87150639_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87151117_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87151146_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87151453_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87152844_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87153569_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87154559_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87155496_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87155949_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87156106_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87157827_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87158338_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87158534_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87159410_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87159580_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87160332_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87160375_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87161235_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87161902_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87162915_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87164412_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87164886_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87165017_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87165441_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87166115_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87168759_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87174803_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87176019_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87176708_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87178630_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87179511_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87179597_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87179713_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87181205_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87181216_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87182922_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87183189_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87183485_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87184910_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87185000_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87186642_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87187090_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87187750_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87187984_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87188000_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87188762_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87190609_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87190745_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87191087_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87191258_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87192333_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87192557_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87192637_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87192995_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87193409_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87196363_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87196591_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87199297_1_desikan_sg.graphml',
 '../data/desikan/MRN114/MRN114_M87199728_1_desikan_sg.graphml']

Number of Non-Zero (NNZ) edge weights





In [13]:



    


nnz = collections.OrderedDict((key, len(nx.edges(mygs[key]))) for key in mygs)



    











In [14]:



    


fig = plt.figure(figsize=(12,6))
plt.bar(range(len(nnz)),nnz.values(), alpha=0.7, color='#888888')
plt.title('Number of Non-Zeros in MRN114 Dataset', y = 1.04)
plt.ylabel('Count')
plt.xlabel('Graph')
plt.xlim((0, len(nnz.keys())))
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-nnz.png')
plt.show()

Vertex Degree





In [15]:



    


degrees = collections.OrderedDict((key, np.array(nx.degree(mygs[key]).values())) for key in mygs)

avg_degrees = [np.mean(degrees[key]) for key in degrees]



    











In [22]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in degrees.keys():
    dens = gaussian_kde(degrees[key])
    x = np.linspace(0, 1.2*np.max(degrees[key]), 1000)
    plt.plot(x, dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Degree Sequence in MRN114 Dataset', y = 1.04)
plt.ylabel('Probability')
plt.xlabel('Vertex Degree')
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-degree.png')
plt.show()

Edge weight





In [17]:



    


e_weights = collections.OrderedDict((key, [mygs[key].get_edge_data(e[0],e[1])['weight']
             for e in mygs[key].edges()]) for key in mygs)
avg_e_weights = [{'N': len(e_weights[key]),
                  'mean':np.mean(e_weights[key]),
                  'std':np.std(e_weights[key])} for key in e_weights]



    











In [20]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in e_weights.keys():
    dens = gaussian_kde(e_weights[key])
    x = np.linspace(0, 1.2*np.max(e_weights[key]), 1000)
    plt.plot(x/1000, 1000*dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Edge Weight Distributions in MRN114 Dataset', y = 1.04)
plt.ylabel('Probability (10^(-3)')
plt.xlabel('Edge Weight (10^3)')
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-edgeweight.png')
plt.show()

Edge count





In [23]:



    


e_count = collections.OrderedDict((key, len(e_weights[key])) for key in e_weights)



    











In [24]:



    


fig = plt.figure(figsize=(12,6))
plt.bar(range(len(e_count)),e_count.values(), alpha=0.7, color='#888888')
plt.title('Edge Count in MRN114 Dataset', y = 1.04)
plt.ylabel('Count')
plt.xlabel('Graph')
plt.xlim((0, len(e_count.keys())))
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-edges.png')
plt.show()

Clustering Coefficient





In [25]:



    


ccoefs = collections.OrderedDict((key, nx.clustering(mygs[key]).values()) for key in mygs)
avg_ccoefs = [np.mean(ccoefs[key]) for key in ccoefs]



    











In [26]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in ccoefs.keys():
    dens = gaussian_kde(ccoefs[key])
    x = np.linspace(0, 1.2*np.max(ccoefs[key]), 1000)
    plt.plot(x, dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Clustering Coefficient in MRN114 Dataset', y = 1.04)
plt.ylabel('Probability')
plt.xlabel('Clustering Coefficient')
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-cc.png')
plt.show()

Scan Statistic-i





In [27]:



    


i = 1
def scan_statistic(mygs, i):
    ss = collections.OrderedDict()
    for key in mygs.keys():
        g = mygs[key]
        tmp = np.array(())
        for n in g.nodes():
            subgraph = nx.ego_graph(g, n, radius = i)
            tmp = np.append(tmp, np.sum([subgraph.get_edge_data(e[0],e[1])['weight'] for e in subgraph.edges()]))
        ss[key] = tmp
    return ss

ss1 = scan_statistic(mygs, i)



    











In [28]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in ss1.keys():
    dens = gaussian_kde(ss1[key])
    x = np.linspace(0, 1.2*np.max(ss1[key]), 1000)
    plt.plot(x/10**6, 1*10**6*dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Scan Statistic-1 Distributions in MRN114 Dataset', y = 1.04)
plt.ylabel('Probability (10^(-6))')
plt.xlabel('Scan Statistic-1 (10^(6))')
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-ss1.png')
plt.show()



    


















    
























In [19]:



    


i = 2
ss2 = scan_statistic(mygs, i)



    











In [23]:



    


fig = plt.figure(figsize=(6,6))
plt.hold(True)
for key in ss2.keys():
    dens = gaussian_kde(ss2[key]+1)
    x = np.linspace(0, 1.2*np.max(ss2[key]), 1000)
    plt.plot(x/10**6, 10**6*dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Scan Statistic-2 Distributions in KKI2009 Dataset', y = 1.04)
plt.ylabel('Probability (10^(-6))')
plt.xlabel('Scan Statistic-2 (10^(6))')
plt.show()



    


















    






---------------------------------------------------------------------------
LinAlgError                               Traceback (most recent call last)
<ipython-input-23-1676de93be4a> in <module>()
      2 plt.hold(True)
      3 for key in ss2.keys():
----> 4     dens = gaussian_kde(ss2[key]+1)
      5     x = np.linspace(0, 1.2*np.max(ss2[key]), 1000)
      6     plt.plot(x/10**6, 10**6*dens.pdf(x), color='#888888', alpha=0.4)

/usr/local/lib/python2.7/site-packages/scipy/stats/kde.pyc in __init__(self, dataset, bw_method)
    169 
    170         self.d, self.n = self.dataset.shape
--> 171         self.set_bandwidth(bw_method=bw_method)
    172 
    173     def evaluate(self, points):

/usr/local/lib/python2.7/site-packages/scipy/stats/kde.pyc in set_bandwidth(self, bw_method)
    496             raise ValueError(msg)
    497 
--> 498         self._compute_covariance()
    499 
    500     def _compute_covariance(self):

/usr/local/lib/python2.7/site-packages/scipy/stats/kde.pyc in _compute_covariance(self)
    507             self._data_covariance = atleast_2d(np.cov(self.dataset, rowvar=1,
    508                                                bias=False))
--> 509             self._data_inv_cov = linalg.inv(self._data_covariance)
    510 
    511         self.covariance = self._data_covariance * self.factor**2

/usr/local/lib/python2.7/site-packages/scipy/linalg/basic.pyc in inv(a, overwrite_a, check_finite)
    685         inv_a, info = getri(lu, piv, lwork=lwork, overwrite_lu=1)
    686     if info > 0:
--> 687         raise LinAlgError("singular matrix")
    688     if info < 0:
    689         raise ValueError('illegal value in %d-th argument of internal '

LinAlgError: singular matrix

Eigen value





In [29]:



    


laplacian = collections.OrderedDict((key, nx.normalized_laplacian_matrix(mygs[key])) for key in mygs)
eigs = collections.OrderedDict((key, np.sort(np.linalg.eigvals(laplacian[key].A))[::-1]) for key in laplacian)



    











In [30]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in eigs.keys():
#     dens = gaussian_kde(eigs[key])
#     x = np.linspace(0, 1.2*np.max(eigs[key]), 1000)
    plt.plot(eigs[key], 'ro-', markersize=0.4, color='#888888', alpha=0.4)
plt.title('Eigen Values in MRN114 Dataset', y = 1.04)
plt.ylabel('Value')
plt.xlabel('Dimension')
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-eigen.png')
plt.show()

Betweenness Centrality





In [31]:



    


centrality = collections.OrderedDict((key, nx.algorithms.betweenness_centrality(mygs[key]).values())
                                     for key in mygs.keys())



    











In [32]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in centrality.keys():
    dens = gaussian_kde(centrality[key])
    x = np.linspace(0, 1.2*np.max(centrality[key]), 1000)
    plt.plot(x, dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Centrality Distributions in MRN114 Dataset', y = 1.04)
plt.ylabel('Probability')
plt.xlabel('Betweenness Centrality')
plt.tight_layout()
plt.savefig('../figs/distribs/MRN114-centrality.png')
plt.show()

SWU4 Dataset





In [33]:



    


mygs = loadGraphs(fs[fs.keys()[1]], printer=False) # only loads graphs for swu dataset

Number of Non-Zero (NNZ) edge weights





In [34]:



    


nnz = collections.OrderedDict((key, len(nx.edges(mygs[key]))) for key in mygs)



    











In [35]:



    


fig = plt.figure(figsize=(12,6))
plt.bar(range(len(nnz)),nnz.values(), alpha=0.7, color='#888888')
plt.title('Number of Non-Zeros in SWU4 Dataset', y = 1.04)
plt.ylabel('Count')
plt.xlabel('Graph')
plt.xlim((0, len(nnz.keys())))
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-nnz.png')
plt.show()

Vertex Degree





In [36]:



    


degrees = collections.OrderedDict((key, np.array(nx.degree(mygs[key]).values())) for key in mygs)

avg_degrees = [np.mean(degrees[key]) for key in degrees]



    











In [37]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in degrees.keys():
    dens = gaussian_kde(degrees[key])
    x = np.linspace(0, 1.2*np.max(degrees[key]), 1000)
    plt.plot(x, dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Degree Sequence in SWU4 Dataset', y = 1.04)
plt.ylabel('Probability')
plt.xlabel('Vertex Degree')
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-degree.png')
plt.show()

Edge weight





In [38]:



    


e_weights = collections.OrderedDict((key, [mygs[key].get_edge_data(e[0],e[1])['weight']
             for e in mygs[key].edges()]) for key in mygs)
avg_e_weights = [{'N': len(e_weights[key]),
                  'mean':np.mean(e_weights[key]),
                  'std':np.std(e_weights[key])} for key in e_weights]



    











In [39]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in e_weights.keys():
    dens = gaussian_kde(e_weights[key])
    x = np.linspace(0, 1.2*np.max(e_weights[key]), 1000)
    plt.plot(x/1000, 1000*dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Edge Weight Distributions in SWU4 Dataset', y = 1.04)
plt.ylabel('Probability (10^(-3)')
plt.xlabel('Edge Weight (10^3)')
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-edgeweight.png')
plt.show()

Edge count





In [40]:



    


e_count = collections.OrderedDict((key, len(e_weights[key])) for key in e_weights)



    











In [104]:



    


fig = plt.figure(figsize=(12,6))
plt.bar(range(len(e_count)),e_count.values(), alpha=0.7, color='#888888')
plt.title('Edge Count in SWU4 Dataset', y = 1.04)
plt.ylabel('Count')
plt.xlabel('Graph')
plt.xlim((0, len(e_count.keys())))
plt.savefig('../figs/distribs/SWU4-edges.png')
plt.show()

Clustering Coefficient





In [41]:



    


ccoefs = collections.OrderedDict((key, nx.clustering(mygs[key]).values()) for key in mygs)
avg_ccoefs = [np.mean(ccoefs[key]) for key in ccoefs]



    











In [42]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in ccoefs.keys():
    dens = gaussian_kde(ccoefs[key])
    x = np.linspace(0, 1.2*np.max(ccoefs[key]), 1000)
    plt.plot(x, dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Clustering Coefficient in SWU4 Dataset', y = 1.04)
plt.ylabel('Probability')
plt.xlabel('Clustering Coefficient')
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-cc.png')
plt.show()

Scan Statistic-i





In [43]:



    


i = 1
def scan_statistic(mygs, i):
    ss = collections.OrderedDict()
    for key in mygs.keys():
        g = mygs[key]
        tmp = np.array(())
        for n in g.nodes():
            subgraph = nx.ego_graph(g, n, radius = i)
            tmp = np.append(tmp, np.sum([subgraph.get_edge_data(e[0],e[1])['weight'] for e in subgraph.edges()]))
        ss[key] = tmp
    return ss

ss1 = scan_statistic(mygs, i)



    











In [44]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in ss1.keys():
    dens = gaussian_kde(ss1[key])
    x = np.linspace(0, 1.2*np.max(ss1[key]), 1000)
    plt.plot(x/10**6, 1*10**6*dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Scan Statistic-1 Distributions in SWU4 Dataset', y = 1.04)
plt.ylabel('Probability (10^(-6))')
plt.xlabel('Scan Statistic-1 (10^(6))')
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-ss1.png')
plt.show()



    


















    
























In [19]:



    


i = 2
ss2 = scan_statistic(mygs, i)



    











In [23]:



    


fig = plt.figure(figsize=(6,6))
plt.hold(True)
for key in ss2.keys():
    dens = gaussian_kde(ss2[key]+1)
    x = np.linspace(0, 1.2*np.max(ss2[key]), 1000)
    plt.plot(x/10**6, 10**6*dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Scan Statistic-2 Distributions in KKI2009 Dataset', y = 1.04)
plt.ylabel('Probability (10^(-6))')
plt.xlabel('Scan Statistic-2 (10^(6))')
plt.show()



    


















    






---------------------------------------------------------------------------
LinAlgError                               Traceback (most recent call last)
<ipython-input-23-1676de93be4a> in <module>()
      2 plt.hold(True)
      3 for key in ss2.keys():
----> 4     dens = gaussian_kde(ss2[key]+1)
      5     x = np.linspace(0, 1.2*np.max(ss2[key]), 1000)
      6     plt.plot(x/10**6, 10**6*dens.pdf(x), color='#888888', alpha=0.4)

/usr/local/lib/python2.7/site-packages/scipy/stats/kde.pyc in __init__(self, dataset, bw_method)
    169 
    170         self.d, self.n = self.dataset.shape
--> 171         self.set_bandwidth(bw_method=bw_method)
    172 
    173     def evaluate(self, points):

/usr/local/lib/python2.7/site-packages/scipy/stats/kde.pyc in set_bandwidth(self, bw_method)
    496             raise ValueError(msg)
    497 
--> 498         self._compute_covariance()
    499 
    500     def _compute_covariance(self):

/usr/local/lib/python2.7/site-packages/scipy/stats/kde.pyc in _compute_covariance(self)
    507             self._data_covariance = atleast_2d(np.cov(self.dataset, rowvar=1,
    508                                                bias=False))
--> 509             self._data_inv_cov = linalg.inv(self._data_covariance)
    510 
    511         self.covariance = self._data_covariance * self.factor**2

/usr/local/lib/python2.7/site-packages/scipy/linalg/basic.pyc in inv(a, overwrite_a, check_finite)
    685         inv_a, info = getri(lu, piv, lwork=lwork, overwrite_lu=1)
    686     if info > 0:
--> 687         raise LinAlgError("singular matrix")
    688     if info < 0:
    689         raise ValueError('illegal value in %d-th argument of internal '

LinAlgError: singular matrix

Eigen value





In [45]:



    


laplacian = collections.OrderedDict((key, nx.normalized_laplacian_matrix(mygs[key])) for key in mygs)
eigs = collections.OrderedDict((key, np.sort(np.linalg.eigvals(laplacian[key].A))[::-1]) for key in laplacian)



    











In [46]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in eigs.keys():
#     dens = gaussian_kde(eigs[key])
#     x = np.linspace(0, 1.2*np.max(eigs[key]), 1000)
    plt.plot(eigs[key], 'ro-', markersize=0.4, color='#888888', alpha=0.4)
plt.title('Eigen Values in SWU4 Dataset', y = 1.04)
plt.ylabel('Value')
plt.xlabel('Dimension')
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-eigen.png')
plt.show()

Betweenness Centrality





In [47]:



    


centrality = collections.OrderedDict((key, nx.algorithms.betweenness_centrality(mygs[key]).values())
                                     for key in mygs.keys())



    











In [48]:



    


fig = plt.figure(figsize=(8,6))
plt.hold(True)
for key in centrality.keys():
    dens = gaussian_kde(centrality[key])
    x = np.linspace(0, 1.2*np.max(centrality[key]), 1000)
    plt.plot(x, dens.pdf(x), color='#888888', alpha=0.4)
plt.title('Centrality Distributions in SWU4 Dataset', y = 1.04)
plt.ylabel('Probability')
plt.xlabel('Betweenness Centrality')
plt.tight_layout()
plt.savefig('../figs/distribs/SWU4-centrality.png')
plt.show()



    


















    
























In [ ]:

Content source: Upward-Spiral-Science/grelliam

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