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    <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>
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