***** To join INSNA, visit http://www.sfu.ca/~insna/ ***** On Mon, 2003-01-27 at 10:29, Martina Morris wrote: > Intuitively, though, the scale free property implies tail behavior that is > physically impossible in social contact networks. Indeed, it implies that > there is a small, but non-zero, probability that someone can have more > contacts than there are members of the population. And this property > underlies many of the "newsworthy" analytic results that follow -- i.e., > that there can be no effective interventions for sexually transmitted > diseases. This is a good point. Further, Pareto-like distributions have properties in the _lower_ tail which are also clearly false for most interpersonal networks. If the world were truly scale-free, then the population mode would have to consist of the minimum-degree state...more people would have to have no friends, for instance, than any other number.[*] Furthermore, the next most common degree value would have to be 1, then 2, etc., etc., etc. This is trivially true for any monotonically decreasing degree distribution, and is quite incompatible with most substantively interesting interpersonal relations. While one might be able to write-off the limiting behavior in the upper tail as an approximation, the lower tail behavior accounts for much of the probability mass of the distribution...thus, it's very difficult to ignore! No matter how you slice it, it doesn't fit. With respect to the question of degree distribution, Elisa Bienenstock and I have been looking at this too (though we may be too late, which is OK :-)). Based on purely preliminary results, the one class of graphs I've tested for which the power-law could be a vaguely plausible model is a set of semantic networks. My guess is that, when the dust settles on all this, the consensus will be that these models are reasonable for certain kinds of citation networks and concept networks, but not for most substantively interesting interpersonal networks. Time will tell. -Carter [*] Unless everyone has at least one friend, in which case 1 would become the mode. _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.sfu.ca/~insna/). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.