<p>You could use any of the objective functions optimized when performing community detection, see (<a href="http://arxiv.org/abs/0906.0612" rel="nofollow">Fortunato 09</a>). The most widespread one is certainly the <em>modularity</em> (<a href="http://arxiv.org/abs/cond-mat/0308217" rel="nofollow">Newman &amp; Girvan 03</a>), which is implemented in Gephi (see <a href="https://wiki.gephi.org/index.php/Modularity" rel="nofollow">this page</a>), and most other tools.</p>

<p>Edit: from your comments, you might be more interested in the <a href="http://en.wikipedia.org/wiki/Cut_%28graph_theory%29" rel="nofollow">cut size</a> (number of links between the two communities), or one of its normalized variants such as the conductance, ratio cut, normalized cut. See <a href="http://arxiv.org/abs/0906.0612" rel="nofollow">Fortunato'10</a> (section 4.1) for a review.</p>
Metric to assess interconnectivity between two communities/subgraphs
<p>Consider a large graph with several thousands nodes. Nodes belong to two communities (defined intrinsically by a node attribute). I am looking for a metric (if possible already implemented in gephi, cytoscape, or other software) able to tell me how much these two communities/subgraphs are interconnected (and compare several case studies). I am sure this must be a standard problem for people studying social dynamics in communities or network theory...</p>