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Small-world networks
There is a sense in which small-world networks are trivial, for we inhabit them on a daily basis by virtue of our social networks. Disciplines of study are small-world networks, for example: they are highly clustered into graduate programs and academic departments, dense clusters of faculty and students. And yet, each person in a given program comes there from another program, either from graduate school or a position at another school.
All of my friends from graduate school are connected, whether they know it or not, to the members of Syracuse's Writing Program. And vice versa. And each of those friends holds a position in another program, the collected members of which are connected to me through my friends. In a matter of three degrees (each connection between two people is a degree), the graduate students at Syracuse, for instance, are connected to the faculty and graduate students at Purdue University, the University of Texas, Penn State University, and so on. Each of the SU students knows someone (me) who knows someone (my friend) who knows the people at those institutions and many more besides. And I am only one of eleven faculty in the program at SU, from a relatively small graduate program. Multiply the extent of my own network by the number of faculty at each institution, and it's difficult to imagine that there is anyone in our field who couldn't be connected to anyone else in much more than 3 or 4 steps.
Observations like these become much less trivial or obvious when we reflect upon the ways that clustering and connectivity occur in both the structure and the dynamics of our programs (to borrow terms from Watts once more). Structurally, for example, a core curriculum serves to reinforce the density of the cluster. Students who attend the same class can be assured of a relatively common and shared experience, but a core curriculum is supposed to ensure that students in different cohorts, taking a course in different incarnations, also share that experience. Elective courses, on the other hand, are likely to change more frequently, and more radically, with the passage of time, serving to connect the intellectual work of the program with a broader range of topics and areas within a discipline. Program dynamics include not only tenure (which both rewards and insures a continuity in a program's faculty) but also the custom against hiring one's own graduates (every faculty hire forges a new tie between a program and the new hire's socio-disciplinary network).
Watts, then, provides us with a vocabulary for framing our social networks, but what does this accomplish? In terms of the questions that I've tried to set forth here, this suggests that small-world networks, like the one that we refer to as our discipline, function as deictic systems. Our programs and departments change regularly, with every decision about curriculum and hiring, with each new person who joins the local network and each member who leaves. And yet, they remain stable as well, persisting to a greater or lesser degree despite (and sometimes, because of) those changes.
I would argue that Watts' discussion of clustering and connectivity correspond roughly to my earlier discussion of centripetal and centrifugal forces, respectively. And if this is indeed the case, then the idea of small-world networks has important implications for Miller's pendulum, or rather my attempt to extend her metaphor beyond the scope of her essay. Small-world networks cannot exist along the swing of that pendulum, for according to Watts, they represent systems that move, for a brief time, both towards centripetality and centrifugality. This seeming paradox has important implications for our understanding of social software, particularly if (and as) we adapt it for pedagogical purposes, the focus for the remainder of this essay.

Comments
If I remember right, Barabasi (in _Linked_) moves from early presumptions by Erdos and Renyi about random network formation to the more selective quality of small worlds. I was thinking about this especially in the paragraph on curriculum here. It seems like there's a combination of selectivity and randomness. In the previous section, the stuff on social software as affording both activity *and* serendipity comes close to this. Would you say a random/serendipitous quality applies to these institutional situations, too?
Posted by: Derek at June 12, 2005 07:49 PM
Absolutely, Derek.
But I also think we're constantly negotiating the temptation to see curriculum as progressive as well. We tend to downplay serendipity when it comes to institutional situations, partly because it messes with our ability to change (and to justify changing) those situations...
Posted by: collin at June 13, 2005 02:03 AM