Each of the three citations was meant to evoke, distinct though related, approaches to assigning quantities to qualities of networks. The Levine paper[1] focuses on a technique for flattening a food web onto a chain (trophic level). What I find novel is that the technique appears robust to loops (cannibalism like breastfeeding) as well as larger circuits or cliques (scavengers of all types and colors). I am also impressed by the straightforward nature of the calculation familiar to all that work with absorbing Markov chains[KS]: Reorder the transition matrix so that pure source components come first, partition the position vector similarly, find the fundamental matrix and then solve for position. Levine then goes on to point out that the variance of path lengths gives a nice measure of trophic specialization.
I became familiar with the Spring Rank algorithm through conversations with its authors, and became more intimately familiar through recent work applying the algorithm to networks of exchange. The central idea, there, is that we can imagine an exchange network as a mechanical system of weights (individuals) and springs (whose tensions correspond in some way to transactions between individuals). There (and maybe this is how it might correspond to Marcus' criticism) we write the Hamiltonian and solve for position. In the work, my collaborators and I were (are?) doing, we researched how such a model can be used as a suggestion engine for *giving* exactly because one could suggest non-trivial ways to *balance* one's exchange network. Lastly, the reference to gauge-theoretic economic models is one where we can apply an abstract notion of curvature or (cohomologically) measure the distance from *exactness* flows experience on a given circuit. I would not be surprised if this relatively new approach is already finding itself useful in applied economics. My feeling is that the tools already exist (to an extent more than we know, though less than we really want) and that application is where things go awry. Also, I am unsure to what extent these approaches land within the already stated criticism put forth by Marcus. I haven't looked at the Kirkley paper. I suppose I wanted to ground the models in some calculations so that we can more clearly argue their merits. To my mind, assigning qualities to graphs, like assigning qualities to numbers, comes with a certain hermeneutic burden. OTOH, there is a continued effort to discover sensible properties that graphs may have, that is, the field is as rich as any[2]. I am not entirely sure why I feel compelled to highlight this distinction, so please excuse the pedantry. Ultimately, I am probing the group to see what kinds of frameworks each of us has in mind. There are the graphic-theoretic (presently, my favorite to think about) approaches, lawyer-theoretic(?) approaches that ask, "For the benefit of whom?", as well as some axiomatic approaches. Also, we appear to be discussing questions of reciprocity and asking, "Economy, what is it good for"?[$] [1] Reading about Eric's approach to his recent work, I was reminded about the Levine paper. It has been several years since I had thought about the details and attempts to reconstitute the idea for that context have it on my mind for this one. [2] Here, I suppose that I am not only thinking about more recent work like that of Mark Newman or Lovasz or whomever, but also of the rich history (summarized so playfully by Lokatos) going back to Euler and Gauss and ... [$] There is also the question of Evil, money, and their arborescent relationship. I will leave this one alone for now ;) [KS] Kemeny and Snell, 1960 -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/
