Metcalfe’s Law before Metcalfe
2011/10/14
I copy from the preface of “Structuring Complex Systems” by J. N. Warfield:
“Since the structuring of systems has largely been done in an ad hoc way in the past, it may seem that a theory designed to permit this process to become more explicit, and to be carried out with machine assistance, would be superfluous. [...] when the number of elements to be considered is large, the number of interactions to be considered is at least comparable to the square of the number of elements. The logistics of dealing with so many interactions is by itself an inhibiting factor in conducting a studied structuring exercise and in manipulating the perceived relations.”
My beloved N2 network effect pattern has been noticed before then. But it still seems that Metcalfe was the first to attach value to it.
New eBooks on Graph Theory
2010/07/08
My twitter stream and my INBOX brought to my attention two new books on Graph Theory:
- “Graph Theory and Complex Networks: An Introduction” by Maarten van Steen. It is very interesting to note that this book is also available electronically as a personalised PDF. As the author notes: “When you write a book containing mathematical symbols, thinking big and acting commercially doesn’t seem the right combination. I merely hope to see the material to be used by many students and instructors everywhere and to receive a lot of constructive feedback that will lead to improvements. Acting commercially has never been one of my strong points anyway”.
- The other book is the fourth edition of Reinhard Diestel’s “Graph Theory“. This book is also available electronically in different formats. I bought the student edition for €12.50 (offer expires in Aug 15, 2010).
PS: On a side-note I decided to buy a BeBook Mini
La Ola
2009/11/04
From page 25 of Connected:
A group of physicists who usually study waves on the surface of liquids were sufficiently intrigued that they decided to study a collection of filmed examples of La Ola in enormous soccer stadiums; they noticed that these waves usually rolled in a clockwise direction and consistently moved at a speed of “twenty seats per second”.*
Damn! I have participated numerous times in such waves and never, ever thought of that!
[*] – “Mexican waves in an excitable medium“, Nature 419, 131-132 (2002).
The story of a lost manuscript
2009/10/28
In “The development of social network analysis” (for which I have blogged too) Linton C. Freeman, among other things, tracks the efforts of different scientists to lay a mathematical foundation for SNA. For two such efforts he writes:
“both Fararo (circa 1964) and I separately set out to specify the common mathmatical properties of all these seemingly different studies. Fararo circulated but never published his paper. Mine was presented several times and eventually published, but not until twenty-five years later.”
The unpublished manuscript in question was entitled “Theory of Webs and Social Systems Data“. I contacted Professor Fararo for the unpublished manuscript. He told me that he had lost his copy and that I might be lucky by asking Professor Freeman, which I did. When I contacted Professor Freeman he was away from home, but promised to look for it. Indeed about a week later he found the manuscript, had it scanned and emailed it to me. Like I told to my wife who is an archaeologist, I think this is what it feels when they (archaeologists) make a discovery.
Prior to writing this blog post, I told this story to two friends of mine. Funnily enough they asked me the same question:
- Name one Greek Professor who (a) would answer to your email and (b) would go into all that effort to locate something written circa 1965-1966 and send it to you.
This humble blog post stands to publicly thank both Professors for their kind replies and help.
Update: After getting permission, I uploaded the document on Scribd.
The development of social network analysis
2009/10/21
As promised, I finished reading “The development of social network analysis“. The book, written by Linton C. Freeman follows the development of the field from pre-Moreno times and the introduction of structural thought into social studies up to the late 90s. According to the book cover it is based on the Keynote Lecture that Freeman gave in April 2000 at the twentieth annual meeting of the INSNA.
The study of social structure has come of age
This is the last sentence of the book. Before reaching it, Freeman takes us on a journey that roughly begins with the works of Auguste Comte who apparently planted the first seeds of structural thought. Since then the field of structural thought has been restarted a number of times, and for a variety of reasons, among them being megalomania, shift of interest, interdepartmental politics and job security, main scene politics (like the Jenner committee that essentially ended a whole group).
A whole chapter is devoted to the life of Jacob Levy Moreno, who many think of as the father of the field, although it is later shown that there were earlier studies with similar aims and results and that the systematic approach and development of his ideas is most probably owed to the work of Helen Jennings and Paul Lazarsfeld.
All the pioneers and heroes of SNA parade through the book, the flow of names and their interrelations is so vast that half way through the book I regretted not taking notes of the names and their relations in order to produce something like the TCS genealogy coupled with some visualization. Luckily, in page 131 such a pruned graph is presented by the author.
Professor Freeman characterizes social network analysis as an approach that involves four defining properties:
- It involves the intuition that links among social actors are important.
- It is based on the collection and analysis of data that record social relations that link actors.
- It draws heavily on graphic imagery to reveal and display the patterning of those links.
- It develops mathematical and computational models to describe and explain those patterns.
All the efforts of structural thought (almost all of them lacking combination of all four characteristics) are presented, most of them being in USA with a few in Europe, up until the great restart of the discipline by Harrison White and his team at Harvard. The central role that Barry Wellman played in unifying all the approaches to the structural thought, through organizing meetings with key persons, forming the INSNA and the Connections newsletter is covered. Plus the EIES system (of interest to those who seek fragments of Internet history) is also covered at some extent, showing the role that technology can play in forming both a discipline and (human) networks.
“But how do I find out?”
2009/09/29
“But how do I find out what I search for?”, a friend asked the other day, “Google cannot help me find information that I need”. This friend is in the process of completing a thesis on social networks.
Google, Yahoo! Search, Bing and the rest are tools that help us search information already available. Unfortunately they are not mind readers, plus vast though it may be, indexed information on the web is not all available information. Years ago, when put in the same situation, my post started with “I have a silly question” and got back two answers, the answer to my question and that “Silly questions are the ones never asked; there are no silly questions”. So whenever in trouble, when your favorite search engine (or your ability to ask it) seems limited, ask the ultimate search engine:
People
The best answers I have ever got for questions that troubled me were from humans, be it in person, telephone, the USENET or even mailing lists. My advice to her was to locate and subscribe to a mailing list relevant to her subject (in her case SOCNET) and ask people there. Impressive things happen when you ask people instead of machines. Ideas spring and flourish and (human) networks form. Just do not ask anyone to do your homework for you.
Studies in the Economics of Transportation
2009/09/25
While reading Nagurney‘s “Comment on Catching the Network Science Bug“, I was fascinated that “Studies in the Economics of Transportation”, which was written in 1956 was mentioned. After all, Network Science is supposed to be “newer” than that.
For anyone interested the book is available from the RAND classics section. A more readable PDF is located here.
I will not claim that I have given the book anything more than a brief look. However I read “A Retrospective on Beckmann, McGuire and Winsten’s Studies in the Economics of Transportation“.
This was not the first time that I saw this book being cited: It is also cited in Preface to “On a Paradox of Traffic Planning” (a preface to the English translation of Braess‘s “On a Paradox of Traffic Planning“ which introduces Braess’s Paradox).
Sometimes the titles stick to your head, I guess.
Scale-Free Networks: A Decade and Beyond
2009/08/07
Barry Wellman posted on SOCNET a link to “Scale-Free Networks: A Decade and Beyond” by Albert-László Barabási. I quote two excerpts that I find interesting:
“the scale-free nature of networks of key scientific interest, from protein interactions to social networks and from the network of interlinked documents that make up the WWW to the interconnected hardware behind the Internet, has been established beyond doubt“
Regarding the scale-free nature of the Internet much has been written. However lately I came across two papers that specifically refute Barabási’s opinion on the matter:
- Mathematics and the Internet: A Source of Enormous Confusion and Great Potential [pdf]
- The ‘‘robust yet fragile’’ nature of the Internet [pdf]
So at least for the Internet the scale-free nature has not been established beyond doubt (The links for these papers were posted on Interesting-People). If anyone wishes to dive more into Internet topology stuff (and related mathematics) go read them! They provide a wealth of references too.
However, the second excerpt that I singled out is a prediction and a fascinating one I must say:
“If I dare to make a prediction for the next decade, it this: Thanks to the proliferation of the many electronic devices that we use on a daily basis, from cell phones to the Global Positioning Systems and the Internet, that capture everything from our communications to our whereabouts, the complex system that we are most likely to tackle first in a truly quantitative fashion may not be the cell or the Internet but rather society itself.”
Hmm… I think we know what the (long term) target of the next papers by Barabási’s team will be.
Steven Strogatz blogs at NY Times
2009/06/17
Steven Strogatz has a series of guest blog posts over at the NY Times. Highly interesting stuff (at least for me!)
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