A few years ago, some mathematicians analyzed the US Congress using network theory, trying to determine which committees were linked by shared members. They discovered that the connections between committees and subcommittees changed markedly when Congress was dominated by Republicans.

What you see above is a network diagram that shows connections between committees in the Republican-dominated 107th House based on how many people are shared between each committee - the darker the line, the more connections. (These connections have been normalized so that larger and smaller committees don't throw off the numbers.) In addition, each committee has been assigned a color for extremism, which Oxford mathematician Mason Porter and his co-authors defined as Democratic or Republican partisanship in terms of how members voted. So committees with the least partisan members are blue, and the most extremely partisan are red. Basically this is a snapshot of the social network in Congress in 2001-2003, after Bush won as President and during the 2001 terrorist attacks.

We talked to Porter via email, and he told io9:

We found changes in terms of the overall structure of the network . . . [there was] an additional hierarchical level that seemed to arise. The interesting thing there is that such a levelâ€”if it genuinely existsâ€”is not one that is imposed by the structure of the body itself. The body itself has individuals, subcomittees, committees, and the full Houseâ€”so the most interesting things to try to examine are (in my opinion) things like connections between different subcommittees and connections between different committees.

That "additional level" that Porter is referring to are the connections between committees. He added:

The close connection between committees like Rules and the Select Committee on Homeland Security was pretty striking.

In a paper that Porter co-authored with colleagues in 2007 [PDF], the researchers write:

Some of the connections . . . are unsurprising. For instance, sets of subcommittees of the same standing committee typically share many of the same members, thereby forming a group or clique in the network. The four subcommittees of the 107th Permanent Select Committee on Intelligence, for example, each include at least half of the full 20-member committee and at least one third of each of the other subcommittees. These tight connections result in normalized interlocks with values in the range 14.4â€“23.6, causing these five nodes to be drawn close together in the visualizations, forming the small pentagon in the middle right of Fig. 2 and lower right of [the image at the top of this post]. The Intelligence Committee and its subcommittees are also tightly connected in the 108th House, appearing again as a small pentagon in [the image below].

They continue:

Some connections between committees, however, are less obvious. For instance, the 9- member Select Committee on Homeland Security, formed in June 2002 during the 107th Congress in the aftermath of the terrorist attacks of September 11, 2001, has a strong connection to the 13-member Rules Committee (with a normalized interlock of 7.4 from two common members), which is the committee charged with deciding the rules and order of business under which legislation is considered by other committees and the full House. The Homeland Security Committee is also connected to the 7-member Legislative and Budget Process Subcommittee of Rules by the same two common members.

In other words, under the Republicans, new connections (and new committees) grew into existence. This isn't too surprising, though some of the connections are revealing.

What's new is that under Republicans, committee appointments shrank, but connections between committees and subcommittees tightened. In another paper [PDF], Porter and colleagues write, "The committee reorganization following the Republican Revolution produced a sharp decline in the typical numbers of committee assignments per Representative compared to the 101stâ€“103rd Houses [and] seems also to have tightened the compartmentalization of the House committee assignments." There may have been fewer committee appointments than under Democrats, but it was much more likely that committees and subcommittees would share members. This creates more modular networks, with areas of tightly connected nodes.

As a result, a new level of the network hierarchy in the House was born. Not only were there the hierarchies of committees, but there was also a hierarchy of links between committees. Porter told io9:

[A situation like this] could arise if there is e.g. a more cohesive set of connections across committees (or a more cohesive set of connections across subcommittees within a larger committee). More specifically, the algorithm we used started with a network and had a tree (a "dendrogram") as an output and the depth of the tree being longer is what "more levels" is.

Below you can see one of the dendograms Porter and his colleagues created, showing the hierarchy of connections between committees.

Porter cautions that these models are not predictive. Just because there seems to have been more back-scratching between committees during a previous Republican House doesn't mean that will happen if the House goes Republican on Election Day today. "I try to be cautious about interpreting it," he said. "I prefer when possible to let the output speak for itself."