Figure 6.1 (a, b, and c) and 6.3 (a, b, c, d, and e)
----------------------------------------------------

:download:`Downloadable Source Code <fig6p1.py>` 

This code does both 6.1 and 6.3 since they use the same data.
It produces an additional figure not included in the text for 6.3.

6.1

.. image:: fig6p1a.png

.. image:: fig6p1b.png
    :width: 45 %
.. image:: fig6p1c.png
    :width: 45 %

6.3

.. image:: fig6p3a.png
    :width: 45 %
.. image:: fig6p3b.png
    :width: 45 %
.. image:: fig6p3c.png
    :width: 45 %
.. image:: fig6p3d.png
    :width: 45 %
.. image:: fig6p3e.png
    :width: 45 %

::
    
        
    import networkx as nx
    import EoN
    from collections import defaultdict
    import matplotlib.pyplot as plt
    import scipy 
    
    colors = ['#5AB3E6','#FF2000','#009A80','#E69A00', '#CD9AB3', '#0073B3','#F0E442']
    
    
    
    def getMs(counts):
        r'''used for figure 6.3 to get the values of M1, Mstar, and M2'''
        N=len(counts)
        M1 = 0
        val1 = 0
        M2 = 0
        val2=0
        Mstar = 0
        valstar = 1
        for index, val in enumerate(counts):
            if index<2:
                continue
            if val < valstar:
                Mstar = index
                valstar = val
            elif index - Mstar > 0.1*N:
                break
        for index, val in enumerate(counts):
            if index>Mstar:
                break
            elif val>val1:
                val1=val
                M1 = index
        for index, val in enumerate(counts):
            if index < Mstar:
                continue
            elif val > val2:
                val2 = val
                M2 = index
        return M1, Mstar, M2
    
    
    iterations = 5*10**4
    p=0.25
    kave = 5.
    labels=['a', 'b', 'c', 'd', 'e']
    
    for N, color, label in zip([100, 400, 1600, 6400, 25600], colors, labels):
        print(N)
        xm = {m:0 for m in range(1,N+1)}
        G = nx.fast_gnp_random_graph(N, kave/(N-1.))
        for counter in range(iterations):
            t, S, I, R = EoN.basic_discrete_SIR_epidemic(G, p)
            xm[R[-1]] += 1./iterations
        items = sorted(xm.items())
        m, freq = zip(*items)
    
        plt.figure(1)
        plt.loglog(m, freq, color = color)
        
        plt.figure(2)
        plt.plot(m, freq, color=color)
        plt.yscale('log')
        
        freq = scipy.array(freq)
        m= scipy.array(m)
        plt.figure(3)
        plt.plot(m/float(N), N*freq, color = color)  #float is required in case python 2.X
        
        M1, Mstar, M2 = getMs(freq)
        plt.figure(4)
        plt.clf()
        plt.axis(xmin = 0,xmax = N, ymax=6./(N), ymin = 0)
        plt.plot(m, freq, color= color)
        plt.fill_between(range(1,Mstar+2), 0, freq[0:Mstar+1], linewidth=0, color = colors[4])
        plt.fill_between(range(Mstar+1,len(freq)+1), 0, freq[Mstar:], linewidth=0, color = colors[5])
        inset = plt.axes([0.55,0.5,0.325,0.35])
        inset.plot(m, freq, color= color)
        inset.fill_between(range(1,Mstar+2), 0, freq[0:Mstar+1], linewidth=0, color = colors[4])
        inset.fill_between(range(Mstar+1,len(freq)), 0, freq[Mstar+1:], linewidth=0, color = colors[5])
        inset.axis(xmin=0., xmax=20, ymin=0, ymax = 0.3)#, ymin=-counts[0]*iterations/100)
        inset.set_xticks([0,5,10,15,20])
        plt.xlabel('Number Infected')
        plt.ylabel('Probability')
        plt.savefig('fig6p3{}.png'.format(label))
    
        
    
    plt.figure(1)
    plt.ylabel(r'$\log_{10} x(m)$')
    plt.xlabel(r'$\log_{10} m$')
    plt.savefig('fig6p1a.png')
    
    plt.figure(2)
    plt.xlabel('$m$')
    plt.ylabel('$\log_{10} x(m)$')
    plt.axis(xmin = 0, xmax = 100)
    plt.savefig('fig6p1b.png')
    
    plt.figure(3)
    plt.xlabel('$m/N$')
    plt.ylabel('$Nx(m)$')
    plt.axis(ymax=10, xmax=1, ymin=0)
    plt.savefig('fig6p1c.png')