Simple fat-tailed log-binning

Question

I tried to simplify the log-binning from Plotting log-binned network degree distributions The output shows both the original and the log-binned distributions. However, the latter does not decrease monotonically as it is supposed to, and deviates greatly from the original. What is the best solution to this problem?

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

m = 3
N = 900

G = nx.barabasi_albert_graph(N, m)

degree_list=nx.degree(G).values()

kmin=min(degree_list)
kmax=max(degree_list)

bins=[float(k-0.5) for k in range(kmin,kmax+2,1)]
density, binedges = np.histogram(degree_list, bins=bins, density=True)
bins = np.delete(bins, -1)

logBins = np.logspace(np.log10(kmin), np.log10(kmax),num=20)
logBinDensity, binedges = np.histogram(degree_list, bins=logBins, density=True)
logBins = np.delete(logBins, -1)

fig = plt.figure()
ax = fig.add_subplot(111)
ax.set_xscale('log')
ax.set_yscale('log')

plt.plot(bins,density,'x',color='black')
plt.plot(logBins,logBinDensity,'x',color='blue')
plt.show()

Answer 1

The noise is due to the smallness of N, while the offset at small values is due to the logbin widths being less than one. Add

for x in range(len(logBins)):
    logBins[x] = mt.ceil(logBins[x])