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    <p>If you want to use the configuration model something like this should work in NetworkX:</p> <pre><code>import random import networkx as nx z=[int(random.gammavariate(alpha=9.0,beta=2.0)) for i in range(100)] G=nx.configuration_model(z) </code></pre> <p>You might need to adjust the mean of the sequence z depending on parameters in the gamma distribution. Also z doesn't need to be graphical (you'll get a multigraph), but it does need an even sum so you might have to try a few random sequences (or add 1)...</p> <p>The NetworkX documentation notes for configuration_model give another example, a reference and how to remove parallel edges and self loops:</p> <pre><code>Notes ----- As described by Newman [1]_. A non-graphical degree sequence (not realizable by some simple graph) is allowed since this function returns graphs with self loops and parallel edges. An exception is raised if the degree sequence does not have an even sum. This configuration model construction process can lead to duplicate edges and loops. You can remove the self-loops and parallel edges (see below) which will likely result in a graph that doesn't have the exact degree sequence specified. This "finite-size effect" decreases as the size of the graph increases. References ---------- .. [1] M.E.J. Newman, "The structure and function of complex networks", SIAM REVIEW 45-2, pp 167-256, 2003. Examples -------- &gt;&gt;&gt; from networkx.utils import powerlaw_sequence &gt;&gt;&gt; z=nx.create_degree_sequence(100,powerlaw_sequence) &gt;&gt;&gt; G=nx.configuration_model(z) To remove parallel edges: &gt;&gt;&gt; G=nx.Graph(G) To remove self loops: &gt;&gt;&gt; G.remove_edges_from(G.selfloop_edges()) </code></pre> <p>Here is an example similar to the one at <a href="http://networkx.lanl.gov/examples/drawing/degree_histogram.html" rel="noreferrer">http://networkx.lanl.gov/examples/drawing/degree_histogram.html</a> that makes a drawing including a graph layout of the largest connected component:</p> <pre><code>#!/usr/bin/env python import random import matplotlib.pyplot as plt import networkx as nx def seq(n): return [random.gammavariate(alpha=2.0,beta=1.0) for i in range(100)] z=nx.create_degree_sequence(100,seq) nx.is_valid_degree_sequence(z) G=nx.configuration_model(z) # configuration model degree_sequence=sorted(nx.degree(G).values(),reverse=True) # degree sequence print "Degree sequence", degree_sequence dmax=max(degree_sequence) plt.hist(degree_sequence,bins=dmax) plt.title("Degree histogram") plt.ylabel("count") plt.xlabel("degree") # draw graph in inset plt.axes([0.45,0.45,0.45,0.45]) Gcc=nx.connected_component_subgraphs(G)[0] pos=nx.spring_layout(Gcc) plt.axis('off') nx.draw_networkx_nodes(Gcc,pos,node_size=20) nx.draw_networkx_edges(Gcc,pos,alpha=0.4) plt.savefig("degree_histogram.png") plt.show() </code></pre>
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    1. POGenerating a graph with certain degree distribution?
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    1. POGenerating a graph with certain degree distribution?
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    1. CO@Aric: Thank you. I understand why it needs an even sum but can you please explain why a multigraph will do? From my understanding, multigraph allows self-loops and multiple edges from a node so I am a little confused.
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    2. CO@Aric: I can understand that in a multigraph, multiple edges can be merged to form a single edge and loops are erased but will this lead to a simple graph? I am asking this because I tried setting `z = [3,2,2,1]` to generate a simple graph with these degrees but instead I got a graph with `1 2 2 1` degrees.
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    3. COYou are correct that multigraphs may have self-loops and parallel edges.
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