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import numpy as np
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import matplotlib.pyplot as plt
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
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P_t = 0.15
M = np.linspace(1,100)
P_d = 1/M
pt = plt.plot(M, 1/(P_t+P_d-P_t*P_d), M, [1/P_t]*len(M), lw=4, alpha=0.6)
plt.xlabel('Original graph mixing time')
plt.ylabel('Expected number of steps')
plt.grid()
plt.axis([M[0], M[-1], 0, 10]);
plt.legend(['Combined death/teleportation process', 'Teleportation process']);
plt.savefig(filename='/Users/migish/Desktop/combined-mixing-time.pdf')
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