Metric to assess interconnectivity between two communities/subgraphs

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...

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You could use any of the objective functions optimized when performing community detection, see (Fortunato 09). The most widespread one is certainly the modularity (Newman & Girvan 03), which is implemented in Gephi (see this page), and most other tools.

Edit: from your comments, you might be more interested in the cut size (number of links between the two communities), or one of its normalized variants such as the conductance, ratio cut, normalized cut. See Fortunato'10 (section 4.1) for a review.

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