***** To join INSNA, visit http://www.sfu.ca/~insna/ ***** Thanks Mark for the clarification and note about what might eventually be interesting about the scale-free research. I should say that, when I said that human interaction networks are obviously not scale-free, I certainly did not mean to suggest that they are normally distributed. As we well know from many network studies, indegree is usually skewed to the right and sometimes very much so (I have even co-authored an obscure paper that shows this to be the case in a college campus network and that members of the network misperceive the implications for their relative popularity). And yet, as Martina pointed out, there are obvious limits to how skewed they can be-- limits that do not apply to such things as the network of hyperlinks that constitute the web. And Carter's observations reinforce this point. A final thought per Mark's example using outdegree: I would hypothesize that outdegree and indegree are actually pretty different in terms of their right-skewness. Consider the "fame network" I alluded to [Name generator asked of all people on the planet about one another: "Please identify all other people that you recognize."]. I would submit that indegree will be a lot more right-skewed than outdegree. -----Original Message----- From: Social Networks Discussion Forum [mailto:[log in to unmask]] On Behalf Of Mark S. Handcock Sent: Monday, January 27, 2003 3:26 PM To: [log in to unmask] Subject: Re: Erroneous facts / NyT article on social networks (scale free) ***** To join INSNA, visit http://www.sfu.ca/~insna/ ***** Martina and Ezra make some important points about the importance of interdisciplinary approaches to network models and the sociology of science. In that context, here is a brief response to David's particular questions. The notion of "scale free networks" is often used broadly and vaguely. One very common use focuses on the univariate distribution some characteristic of a network such as the aggregate distribution of out-degree of the nodes. If the distribution can be approximately summarized by a measure of level and modest symmetric variation about that level this literature refers to it as having a characteristic "scale". Often this is associated with a notion that the distribution is Gaussian. The term "scale free" is used to describe distributions that do not have this shape e.g., very non-Gaussian distributions. Hence networks were the distribution of out-degrees (say) is very right skewed are often called "scale free networks". Much confusion occurs because of this. Many people with little experience with network processes find right-skewed distributions surprising. However, I have not spoken with a social network person who expected them all to be approximately Gaussian in shape. In this sense it is not new nor surprising. In particular, statisticians are bemused by the entire enterprise and write it of as just more bad science. Statisticians made a cottage industry at the beginning of last century characterizing discrete distributions to represent such behavior. I suggest looking at the presidential address of Maurice Kendall in his 1960 inaugural address to the Royal Statistical Society (on JSTOR JRSS 1961). Kendall reflected that after many years of simple curve fitting exercises that for statistical modeling in the social sciences to mature as a scientific discipline, it must move into tests of processual models. Unfortunately, this message has been often been lost in the passage of time and the segmentation of scientific enterprise. So here is what is new about "scale free" networks. Some of the more scientifically people in the "scale free" pool focus on the stochastic models that may underlay these phenomena, some are getting to the point of testing them empirically against alternative models. It is still at its early stages. I should also note that the focus has been on very simple models for the network (e.g., that it is randomly mixing with respect to the degree distribution of the nodes). These are unlikely to be true in most real networks of interest where network structure and attribute based mixing are important. In musing on your second question: "what networks tend to be scale free, and what networks not?", the real question is what import is it if, say, the degree distribution is right-skewed. Or more generally, what can we say usefully about a network based on characterizing summary statistics like these. In this sense the social network community has been doing this for a long time. The "scale free" folks are just getting started. Mark ------------------------------------------------- Mark S. Handcock Professor of Statistics and Sociology Department of Statistics, C014-B Padelford Hall University of Washington, Box 354322 Phone: (206) 221-6930 Seattle, WA 98195-4322. FAX: (206) 685-7419 Web: www.stat.washington.edu/handcock internet: [log in to unmask] ----- Original Message ----- From: "David Lazer" <[log in to unmask]> To: <[log in to unmask]> Sent: Monday, January 27, 2003 8:58 AM Subject: Re: Erroneous facts / NyT article on social networks > ***** To join INSNA, visit http://www.sfu.ca/~insna/ ***** > > A couple of questions: > > (1) what exactly is and is not new in the recent research in scale free > networks? clearly, the importance of "hubs" has been known for a long > time, although the power law research clearly accents those findings. As > the e-mails below discuss, there was some work on this going back on "scale > free" type ideas to at least the 1940s, and I've heard some allusions to > work going back to the 1920s. exactly what was found, however, is still a > vague to me, and certainly had not been part of the core of social network > attention for a while. Some other power law type research, e.g. city size, > earthquake distribution, war casualty distributions, etc, goes back many > decades, with spikes in attention with the work on "self-organized > criticality" in the 90s, and, before that, on firm size in the econ lit in > the 1950s and 60s. (I also bet that number of responses to socnet e-mails > is power law distributed, most queries generating few responses, and a few, > such as this generating a large number.) > > (2) what networks tend to be scale free, and what networks not? The > interpersonal data I tend to work with I'm pretty sure tend to be normally > distributed. Many other kinds of networks, as Barabasi and others have > shown, are power law distributed in in-degree. If one were to survey > social network data sets, and categorize them by type of distribution of > in-degree, what would the categories be, and what would be the variables > underlying those categories? Has this been done? > > David > > > > [log in to unmask] > Sent by: To: [log in to unmask] > [log in to unmask] cc: > .EDU Subject: Re: Erroneous facts / NyT article on social networks > > > 01/26/2003 09:24 > PM > Please respond > to buttsc > > > > > > > ***** To join INSNA, visit http://www.sfu.ca/~insna/ ***** > > Mark Newman wrote: > > And Rapoport touched on the same ideas even earlier in his work > > on friendship networks, although he didn't specifically discuss > > power-law degree sequences. > > > > Indeed. For that matter, there was a lot of very wonderful technical > work by physicists, biologists, and others on both social and biological > networks back in the late 1940s/early 1950s in the _Bulletin of > Mathematical Biophysics_ (of which Rapoport's work was part). My sense > is that there is a fair amount of awareness of this literature within > the modern network community, but I'm not sure to what extent the > "scale-free" crowd is cognizant of it.... > > > Still, as David Gibson points out, one shouldn't blame Duncan Watts for > > this. In fact, Duncan gives ample credit to the pioneers of the field > > in his new book. > > I also noted that he was quoted as asking people to tone down the > hype....not that I expect the message to sink in. Looks like we're in > for a bubble/crash cycle here -- I hope someone here is collecting data > on this! > > -Carter > > _____________________________________________________________________ > 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. > > _____________________________________________________________________ > 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. _____________________________________________________________________ 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. _____________________________________________________________________ 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.