<p>Use <a href="http://arxiv.org/pdf/1011.1533.pdf" rel="noreferrer">log binning</a> (<a href="http://arxiv.org/pdf/0706.1062.pdf" rel="noreferrer">see also</a>). Here is code to take a <code>Counter</code> object representing a histogram of degree values and log-bin the distribution to produce a sparser and smoother distribution.</p>

<pre><code>import numpy as np
def drop_zeros(a_list):
    return [i for i in a_list if i&gt;0]

def log_binning(counter_dict,bin_count=35):

    max_x = log10(max(counter_dict.keys()))
    max_y = log10(max(counter_dict.values()))
    max_base = max([max_x,max_y])

    min_x = log10(min(drop_zeros(counter_dict.keys())))

    bins = np.logspace(min_x,max_base,num=bin_count)

    # Based off of: http://stackoverflow.com/questions/6163334/binning-data-in-python-with-scipy-numpy
    bin_means_y = (np.histogram(counter_dict.keys(),bins,weights=counter_dict.values())[0] / np.histogram(counter_dict.keys(),bins)[0])
    bin_means_x = (np.histogram(counter_dict.keys(),bins,weights=counter_dict.keys())[0] / np.histogram(counter_dict.keys(),bins)[0])

    return bin_means_x,bin_means_y
</code></pre>

<p>Generating a classic scale-free network in <code>NetworkX</code> and then plotting this:</p>

<pre><code>import networkx as nx
ba_g = nx.barabasi_albert_graph(10000,2)
ba_c = nx.degree_centrality(ba_g)
# To convert normalized degrees to raw degrees
#ba_c = {k:int(v*(len(ba_g)-1)) for k,v in ba_c.iteritems()}
ba_c2 = dict(Counter(ba_c.values()))

ba_x,ba_y = log_binning(ba_c2,50)

plt.xscale('log')
plt.yscale('log')
plt.scatter(ba_x,ba_y,c='r',marker='s',s=50)
plt.scatter(ba_c2.keys(),ba_c2.values(),c='b',marker='x')
plt.xlim((1e-4,1e-1))
plt.ylim((.9,1e4))
plt.xlabel('Connections (normalized)')
plt.ylabel('Frequency')
plt.show()
</code></pre>

<p>Produces the following plot showing the overlap between the "raw" distribution in blue and the "binned" distribution in red.</p>

<p><img src="https://i.imgur.com/o8piIas.png" alt="Comparison between raw and log-binned"></p>

<p>Thoughts on how to improve this approach or feedback if I've missed something obvious are welcome.</p>
Plotting log-binned network degree distributions
<p>I have often encountered and made long-tailed degree distributions/histograms from complex networks like the figures below. They make the heavy end of these tails, well, very heavy and crowded from many observations:</p>

<p><img src="https://i.stack.imgur.com/R7RzP.png" alt="Classic long-tailed degree distribution"> </p>

<p>However, many publications I read have much cleaner degree distributions that don't have this clumpiness at the end of the distribution and the observations are more evenly-spaced.</p>

<p>!<img src="https://i.imgur.com/RxAq46b.png" alt="Classic long-tailed degree distribution"></p>

<p>How do you make a chart like this using <code>NetworkX</code> and <code>matplotlib</code>?</p>