Earthquake

• - 데이터 출처 : https://github.com/plotly/datasets/blob/master/earthquakes-23k.csv
  • 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 numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import networkx as nx

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

from haversine import haversine

Abstract

- 데이터 출처 : https://github.com/plotly/datasets/blob/master/earthquakes-23k.csv

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>="2004" & Year<="2011"').reset_index().iloc[:,1:]

2. $f(x)$

f = _df.loc[:,"Magnitude"]

f@f ## SST 

156631.04369999998

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

790.9921195483727

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

155840.05158045172

3. Haversine Fomula 사용한 거리 정의

def dist(i,j):
    return haversine((_df.Latitude[i],_df.Longitude[i]),(_df.Latitude[j],_df.Longitude[j]))

4. Definition of a weighted adjacency matrix $W$

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

def weight(i,j,theta=100000,kappa=100000):
    return np.exp( -np.abs(dist(i,j))**2 / (2*theta**2) ) if dist(i,j) <= kappa else 0

W = np.array([[weight(i,j) for i in range(len(_df))] for j in range(len(_df))])

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

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

def beta(i,j,b):
    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

_beta = np.array([[beta(i,j,1) for i in  range(len(_df))] for j in range(len(_df))])

_W = W @ _beta

6. Definition of Graph Laplacian matrix

• $L = D - W$

D = np.diag(_W.sum(axis=1))

L = D - _W

7. Eigendecomposition

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

λ, Ψ = np.linalg.eig(L)

Λ = np.diag(λ)

8. Principal components Analysis

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

def p(i):
    return sum((f @ np.outer( Ψ[:,i], Ψ[:,i]))**2)

array_1 = np.array([p(i) for i in range(1,len(_df))])
varprop = array_1/array_1.sum()
_index = pd.DataFrame({'index':range(1,len(_df)),'varprop':varprop}).sort_values('varprop',ascending=False)
_indexlst = _index.iloc[:25,0].tolist()

_df["comp1"] = f @ np.outer( Ψ[:,0], Ψ[:,0])
_df["comp2"] = f @ np.outer( Ψ[:,_indexlst[0]], Ψ[:,_indexlst[0]])
_df["comp3"] = f @ np.outer( Ψ[:,_indexlst[1]], Ψ[:,_indexlst[1]])
_df["comp4"] = f @ np.outer( Ψ[:,_indexlst[2]], Ψ[:,_indexlst[2]])
_df["comp5"] = f @ np.outer( Ψ[:,_indexlst[3]], Ψ[:,_indexlst[3]])
_df["comp6"] = f @ np.outer( Ψ[:,_indexlst[4]], Ψ[:,_indexlst[4]])
_df["comp7"] = f @ np.outer( Ψ[:,_indexlst[5]], Ψ[:,_indexlst[5]])

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()