<p>And there are now other approaches than modularity, designed to overcome the limitations mentionned by job, such as <a href="http://en.wikipedia.org/wiki/Surprise_%28networks%29" rel="nofollow">surprise</a>; or the B- and <a href="http://arxiv.org/abs/0907.3708" rel="nofollow">C-scores</a> (designed to be significance indices).</p>
Metrics for hierarchical graphs connectivity
<p>this is my first question on Stack Overflow. This is not really a programming question but since most of us have to deal with theoretical problems at some point and there might be some graph theory specialists around, I thought I might give it a go.</p>

<p>I am currently doing some research on multilingual websites and I found some interesting patterns in the website structure. The graphs below are the website graphs of two different multilingual websites. Sorry, I don't have enough rep points to post images so I leave them as links. I used the Force Atlas algorithm for the layout. Vertices are colored according to the page language. The shaded areas correspond to the subgraphs of a specific language.</p>

<p>Here is the graph of the website where different language versions of the same content are very closely linked. Hence the planes representing the different language versions are overlapping.</p>

<p><a href="http://www.ai.soc.i.kyoto-u.ac.jp/~julien/phd/images/tight.png" rel="nofollow">http://www.ai.soc.i.kyoto-u.ac.jp/~julien/phd/images/tight.png</a></p>

<p>In this second graph, we have a website where language versions of a website are almost independent, thus we have almost no overlap.</p>

<p><a href="http://www.ai.soc.i.kyoto-u.ac.jp/~julien/phd/images/loose.png" rel="nofollow">http://www.ai.soc.i.kyoto-u.ac.jp/~julien/phd/images/loose.png</a></p>

<p>So here is my question:</p>

<p><strong>Is there a specific metric to quantify this overlap? If so, what is it named?</strong></p>

<p>Since I used a force-based layout, the number of edges between the language subgraphs. So I guess something like taking the ratio of the number of edges within the subgraph to the number edges going outside/coming inside a specific subgraph might do the trick. I am sure I am not the first to get this idea so I was wondering if this metric had a name. I could then Google it from there :)</p>

<p>Thank you in advance!</p>