<p>How do you know that the degree distribution of your PPI network approximates a power-law? It could be any other fat-tailed distribution as well. Also, the <code>$xmin</code> value of the resulting power law fit indicates that the best fit is achieved by a lower cutoff at degree=178 and whatever happens at degrees below 178 is not approximated by the exponent that the method fitted.</p>

<p>If you want to create a random network that has <em>exactly</em> the same degree distribution as your graph, you can try using <code>degree.sequence.game</code> to generate one from scratch (make sure you use <code>method="vl"</code> or <code>method="simple.no.multiple</code> if you want to avoid multiple edges between the same pair of nodes), or use <code>rewire.edges</code> to rewrite the edges of your graph.</p>

<p>Re power laws, I recommend reading <a href="http://arxiv.org/abs/0706.1062.pdf" rel="nofollow">this paper</a> about power-law-like distributions in empirical data.</p>
create random graph with "same" power-law degree distribution
<p>I have an undirected graph (a Protein-Protein Interaction network, PPi) for which I know the degree distribution approximates a power-law distribution. I want to create 1,000 random graphs replicating the number of nodes, edges and "similar" power-law outdegree distribution. </p>

<p>My real graph <code>g.lcc</code> has:</p>

<pre><code>&gt; g.lcc
#IGRAPH UN-- 12551 166189 -- 
#+ attr: name (v/c), V3 (e/n)
</code></pre>

<p>What I did so far was:</p>

<pre><code>#Calculate the alpha for my distribution
alpha &lt;- power.law.fit(degree(g.lcc, mode="out"))
#$continuous
#[1] FALSE

#$alpha
#[1] 4.529602

#$xmin
#[1] 178

#$logLik
#[1] -1123.405

#$KS.stat
#[1] 0.0446421

#$KS.p
#[1] 0.7825008
</code></pre>

<p>Then I run <code>statitc.power.law.game</code> using as <code>exp.out</code> the alpha generated with <code>power.law.fit</code>:</p>

<pre><code>random.g &lt;- static.power.law.game(12551, 166189, 4.53, exponent.in=-1, finite.size.correction=T)
</code></pre>

<p>However when I do that the two distributions are not even similar...</p>

<p>Any help??</p>

<p>P.S attached two images with real.ppi and random.g</p>

<p><img src="https://i.stack.imgur.com/ruoVx.png" alt="Random graph"> <img src="https://i.stack.imgur.com/vSHOD.png" alt="Real PPI"></p>