Earthquake_standardization (guebin)

• 1. Data
• 2. $f(x)$
• 3. Haversine Fomula 사용한 거리 정의
• 4. Definition of a weighted adjacency matrix $W$
• 5. The weight edge function with temporal edge $(v_t,v_{t+1})$
• 6. Definition of Graph Laplacian matrix
• 7. Eigendecomposition
• 8. Principal components Analysis
• 2004, $n=571$
• 2005, $n=533$
• 2006, $n=512$
• 2007, $n=608$
• 2008, $n=508$
• 2009, $n=517$
• 2010, $n=560$
• 2011, $n=712$

import tqdm

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import networkx as nx

import time 

import warnings
warnings.simplefilter("ignore", np.ComplexWarning)

from haversine import haversine

1. Data

df = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/earthquakes-23k.csv')

_df = df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).query('Year=="2011"').reset_index().iloc[:,1:]

N=len(_df)

2. $f(x)$

f_true = np.array(_df.loc[:,"Magnitude"])

f=f_true

f@f ## SST 

711.9999999999998

(f-np.mean(f))@(f-np.mean(f)) ## SSE

711.9999999999998

(f*0-np.mean(f))@(f*0-np.mean(f)) ## SSH

3.230784269135488e-28

3. Haversine Fomula 사용한 거리 정의

#     lat = np.array(_df.Latitude)
#     long = np.array(_df.Longitude)
#     return haversine((lat[i],long[i]),(lat[j],long[j]))

locations = np.array(_df.iloc[:,[1,2]])

dist_matrix = np.zeros((N,N))

for i in range(N):
    for j in range(i,N): 
        dist_matrix[i,j]=haversine(locations[i],locations[j])

dist_matrix = dist_matrix + dist_matrix.T

dist_matrix

array([[    0.        , 16163.02258435,  1598.13598041, ...,
        12441.76996155, 16724.50892335,  6903.40785825],
       [16163.02258435,     0.        , 15223.89949838, ...,
         7460.01592618,  6282.10848548, 11122.58071073],
       [ 1598.13598041, 15223.89949838,     0.        , ...,
        10925.94867364, 18298.02127011,  5308.49485366],
       ...,
       [12441.76996155,  7460.01592618, 10925.94867364, ...,
            0.        , 10553.19437367,  5793.83248054],
       [16724.50892335,  6282.10848548, 18298.02127011, ...,
        10553.19437367,     0.        , 16312.45397939],
       [ 6903.40785825, 11122.58071073,  5308.49485366, ...,
         5793.83248054, 16312.45397939,     0.        ]])

4. Definition of a weighted adjacency matrix $W$

$$W_{u,v}=\begin{cases}{exp(-\frac{[dist(u,v)]^2}{2\theta^2})} & \quad \text{if } dist(u,v) \leq κ \\ 0 & \quad \text{otherwise} \end{cases}$$

#     return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) ) if dist(i,j) <= kappa else 0

theta,kappa = 50, 100000

W = np.exp( -(dist_matrix/theta)**2)

plt.hist(W.reshape(-1))

(array([497870.,   2070.,   1346.,    984.,    822.,    670.,    624.,
           560.,    550.,   1448.]),
 array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ]),
 <BarContainer object of 10 artists>)

5. The weight edge function with temporal edge $(v_t,v_{t+1})$

$$W_{u_r,v_s}=\begin{cases} {W_{u,v}} & \quad \text{ if } u,v \in V_t \\ W_{u,v} \odot \beta & \quad \text{if }u=v \text{ and } r=s-1 \\ 0 & \quad \text{otherwise} \end{cases}$$

#     if _df.Year[i] == _df.Year[j]:
#         return 1
#     elif abs(int(_df.Year[i]) - int(_df.Year[j])) == 1:
#         return b
#     else:
#         return 0

_df.groupby("Year").aggregate(len)

	Date	Latitude	Longitude	Magnitude
Year
2011	712	712	712	712

Nlst = _df.groupby("Year").aggregate(len).Date.tolist()
Nlst = [0]+np.cumsum(Nlst).tolist()

Nlst

[0, 712]

beta =np.zeros((N,N))
beta

array([[0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       ...,
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.]])

for i in range(len(Nlst)-1):
    beta[Nlst[i]:Nlst[i+1],Nlst[i]:Nlst[i+1]]= 1

beta

array([[1., 1., 1., ..., 1., 1., 1.],
       [1., 1., 1., ..., 1., 1., 1.],
       [1., 1., 1., ..., 1., 1., 1.],
       ...,
       [1., 1., 1., ..., 1., 1., 1.],
       [1., 1., 1., ..., 1., 1., 1.],
       [1., 1., 1., ..., 1., 1., 1.]])

W = W * beta

plt.imshow(W)

<matplotlib.image.AxesImage at 0x7f4a8ee12370>

6. Definition of Graph Laplacian matrix

• $L = D - W$

d = W.sum(axis=1)
D = np.diag(d)

plt.imshow(D-W)

<matplotlib.image.AxesImage at 0x7f4a8ed7d400>

L = np.diag(1/np.sqrt(d)) @ (D-W) @ np.diag(1/np.sqrt(d))

plt.plot(f)
plt.plot(L@f)

[<matplotlib.lines.Line2D at 0x7f4a40abd2b0>]

7. Eigendecomposition

• ${\bf L} = {\boldsymbol\Psi} {\boldsymbol\Lambda} {\boldsymbol\Psi}^\top$

λ, Ψ = np.linalg.eigh(L)
Λ = np.diag(λ)

8. Principal components Analysis

• $comp_k = f @ np.outer(Ψ[:,k], Ψ[:,k]) $
  • $k = 1, 2, 3, n$
• $p = \sum_{1}^{n} comp_{1}^{2},\sum_{1}^{n} comp_{2}^{2},…,\sum_{1}^{n} comp_{n}^{2}$
• $p = \frac{p}{\sum(p)}$

n=600
plt.plot(f,'.')
plt.plot(Ψ[:,0:n]@Ψ[:,0:n].T@f,'x')

[<matplotlib.lines.Line2D at 0x7f4a3f27efd0>]

fhats=[Ψ[:,[i]]@Ψ[:,[i]].T@f for i in tqdm.tqdm(range(N))]
fhats=np.array(fhats)

100%|██████████| 712/712 [00:00<00:00, 1066.12it/s]

powers=np.apply_along_axis(lambda x: np.sum(x**2), 1, fhats)

plt.plot(λ,powers)

[<matplotlib.lines.Line2D at 0x7f4aad595be0>]

thresh = 1

powers[powers>thresh].sum() / powers.sum()

0.9970187978218614

sum(powers>thresh)

249

sum(powers>thresh) / N

0.3497191011235955

fhats2=fhats.copy()

fhats2[np.where(powers<thresh)]=0

fhats2

array([[ 0.        , -0.07347129,  0.02208522, ...,  0.00216121,
         0.        , -0.00121784],
       [ 0.        , -0.46091157, -0.28804336, ...,  0.37583026,
         0.        , -0.07181023],
       [ 0.        ,  0.11199477,  0.00084155, ..., -0.06273662,
         0.        ,  0.30789697],
       ...,
       [ 0.        ,  0.        ,  0.        , ...,  0.        ,
         0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        , ...,  0.        ,
         0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        , ...,  0.        ,
         0.        ,  0.        ]])

plt.plot(f)
plt.plot(fhats2.sum(axis=0))

[<matplotlib.lines.Line2D at 0x7f4a40b07370>]

plt.plot(f)
plt.plot(fhats2[λ<0.1].sum(axis=0))

[<matplotlib.lines.Line2D at 0x7f4aad57fd60>]

_df["low"] = fhats2[λ<0.1].sum(axis=0)
_df["high"] = fhats2[λ>=0.1].sum(axis=0)
_df["res"] = f-fhats2.sum(axis=0)

#!conda install -c conda-forge basemap -y
#!conda install conda -y

import os
import conda

conda_file_dir = conda.__file__
conda_dir = conda_file_dir.split('lib')[0]
proj_lib = os.path.join(os.path.join(conda_dir, 'share'), 'proj')
os.environ["PROJ_LIB"] = proj_lib

from mpl_toolkits.basemap import Basemap

m = Basemap(projection='cyl', resolution=None,
            llcrnrlat=-90, urcrnrlat=90,
            llcrnrlon=-180, urcrnrlon=180)

from itertools import chain
def draw_map(m, scale=0.2):
    # draw a shaded-relief image
    m.shadedrelief(scale=scale)
    
    # lats and longs are returned as a dictionary
    lats = m.drawparallels(np.linspace(-90, 90, 13))
    lons = m.drawmeridians(np.linspace(-180, 180, 13))

    # keys contain the plt.Line2D instances
    lat_lines = chain(*(tup[1][0] for tup in lats.items()))
    lon_lines = chain(*(tup[1][0] for tup in lons.items()))
    all_lines = chain(lat_lines, lon_lines)
    
    # cycle through these lines and set the desired style
    for line in all_lines:
        line.set(linestyle='-', alpha=0.3, color='w')

_G1 = nx.Graph(W[:len(_df.query('Year<="2011"')),:len(_df.query('Year<="2011"'))]-np.identity(len(_df.query('Year=="2011"'))))
_pos1 = nx.spring_layout(_G1,iterations=20)
m_pos1 = list(zip(_df.query('Year=="2011"').Longitude,_df.query('Year=="2011"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2011"').low,node_size = 10,cmap="Reds",ax=ax,alpha=1)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2011"').high,node_size = 10,cmap="Reds",ax=ax,alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2011"').res,node_size = 10,cmap="Reds",ax=ax,alpha=1)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2004, $n=571$

_G1 = nx.Graph(_W[:len(_df.query('Year<="2004"')),:len(_df.query('Year<="2004"'))]-np.identity(len(_df.query('Year=="2004"'))))
_pos1 = nx.spring_layout(_G1,iterations=20)
m_pos1 = list(zip(_df.query('Year=="2004"').Longitude,_df.query('Year=="2004"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2005, $n=533$

_G2 = nx.Graph(_W[len(_df.query('Year<="2004"')):len(_df.query('Year<="2005"')),len(_df.query('Year<="2004"')):len(_df.query('Year<="2005"'))]-np.identity(len(_df.query('Year=="2005"'))))
_pos2 = nx.spring_layout(_G2,iterations=20)
m_pos2 = list(zip(_df.query('Year=="2005"').Longitude,_df.query('Year=="2005"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2006, $n=512$

_G3 = nx.Graph(_W[len(_df.query('Year<="2005"')):len(_df.query('Year<="2006"')),len(_df.query('Year<="2005"')):len(_df.query('Year<="2006"'))]-np.identity(len(_df.query('Year=="2006"'))))
_pos3 = nx.spring_layout(_G3,iterations=20)
m_pos3 = list(zip(_df.query('Year=="2006"').Longitude,_df.query('Year=="2006"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2007, $n=608$

_G4 = nx.Graph(_W[len(_df.query('Year<="2006"')):len(_df.query('Year<="2007"')),len(_df.query('Year<="2006"')):len(_df.query('Year<="2007"'))]-np.identity(len(_df.query('Year=="2007"'))))
_pos4 = nx.spring_layout(_G4,iterations=20)
m_pos4 = list(zip(_df.query('Year=="2007"').Longitude,_df.query('Year=="2007"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp3,node_size =10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2008, $n=508$

_G5 = nx.Graph(_W[len(_df.query('Year<="2007"')):len(_df.query('Year<="2008"')),len(_df.query('Year<="2007"')):len(_df.query('Year<="2008"'))]-np.identity(len(_df.query('Year=="2008"'))))
_pos5 = nx.spring_layout(_G5,iterations=20)
m_pos5 = list(zip(_df.query('Year=="2008"').Longitude,_df.query('Year=="2008"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2009, $n=517$

_G6 = nx.Graph(_W[len(_df.query('Year<="2008"')):len(_df.query('Year<="2009"')),len(_df.query('Year<="2008"')):len(_df.query('Year<="2009"'))]-np.identity(len(_df.query('Year=="2009"'))))
_pos6 = nx.spring_layout(_G6,iterations=20)
m_pos6 = list(zip(_df.query('Year=="2009"').Longitude,_df.query('Year=="2009"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2010, $n=560$

_G7 = nx.Graph(_W[len(_df.query('Year<="2009"')):len(_df.query('Year<="2010"')),len(_df.query('Year<="2009"')):len(_df.query('Year<="2010"'))]-np.identity(len(_df.query('Year=="2010"'))))
_pos7 = nx.spring_layout(_G7,iterations=20)
m_pos7 = list(zip(_df.query('Year=="2010"').Longitude,_df.query('Year=="2010"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

2011, $n=712$

_G8 = nx.Graph(_W[len(_df.query('Year<="2010"')):len(_df.query('Year<="2011"')),len(_df.query('Year<="2010"')):len(_df.query('Year<="2011"'))]-np.identity(len(_df.query('Year=="2011"'))))
_pos8 = nx.spring_layout(_G8,iterations=20)
m_pos8 = list(zip(_df.query('Year=="2011"').Longitude,_df.query('Year=="2011"').Latitude))

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp1,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp2,node_size = 10,ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp3,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp4,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp5,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp6,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()

with plt.style.context('seaborn-dark'):
    fig,ax = plt.subplots(figsize = (16,8))
    nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp7,node_size = 10, ax=ax,cmap='bwr')
    plt.colorbar(nodes)
    plt.axis()
    ax.set_axis_on()
    ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)
plt.show()