{"id":22276,"date":"2023-06-05T14:43:16","date_gmt":"2023-06-05T18:43:16","guid":{"rendered":"https:\/\/alumni.cornell.edu\/cornellians\/?p=22276"},"modified":"2023-06-05T14:43:17","modified_gmt":"2023-06-05T18:43:17","slug":"small-world","status":"publish","type":"post","link":"https:\/\/alumni.cornell.edu\/cornellians\/small-world\/","title":{"rendered":"Look Back: How Two Cornellians Cracked the \u2018Small World\u2019 Problem"},"content":{"rendered":"\n

In the 1990s, a prof and a grad student developed a model that upended understanding of social networks\u2014and much more<\/p>\n\n\n\n

This story was condensed from <\/em>a feature<\/em><\/a> in the <\/em>Cornell Chronicle.<\/p>\n\n\n\n

By Caitlin Hayes<\/strong><\/p>\n\n\n\n

More than 25 years ago, Professor Steven Strogatz<\/a> and then-graduate student Duncan Watts, PhD \u201997<\/a>, embarked on research so daring in its interdisciplinarity, and so broad in its reach, that at first they didn\u2019t tell anyone about it. <\/p>\n\n\n\n

The problem they were working on involved \u201csix degrees of separation\u201d\u2014the idea that any one person in the world could connect to any other person through a chain of only six links, identified in 1967 by social psychologist Stanley Milgram. <\/p>\n\n\n\n

But Milgram didn\u2019t explain the structure of these social networks and how such a large world, with more than 3 billion people at the time, could be made so small.<\/p>\n\n\n\n

\"Prof
In the past quarter-century, Strogatz has gone on to even wider fame as a scholar and author. (Jason Koski \/ Cornell University)<\/em><\/figcaption><\/figure>\n\n\n\n
<\/div>\n\n\n\n

\u201cWe kept the project between us because of the examples we were using, and we were not experts in social science. We knew very little about the literature around Milgram\u2019s small-world problem,\u201d says Strogatz, the Winokur Professor for the Public Understanding of Science and Mathematics<\/a> in the College of Arts and Sciences. \u201cSo we were very na\u00efve. And we thought that would give us an advantage\u2014that by being na\u00efve, we might ask unusual questions. And we wouldn\u2019t go down the same path everybody else had gone down.\u201d<\/p>\n\n\n\n

They were right.<\/p>\n\n\n\n

In 1998, Strogatz and Watts proposed a mathematical model that would not only provide a way of seeing and understanding a wide range of networks, but would mobilize scientific communities across disciplines to turn toward their study. The work, along with a few subsequent papers, ushered in the modern era of network science\u2014the results of which are ubiquitous in today\u2019s world.<\/p>\n\n\n\n

\u201cI look at papers that have had the most impact, and it\u2019s those that have marshaled and mobilized tens of thousands of incredibly creative people,\u201d says Jon Kleinberg \u201993, the Tisch University Professor of Computer Science in the Cornell Ann S. Bowers College of Computing and Information Science. \u201cThe power of network thinking is everywhere now\u2014it\u2019s in the systems we build, the online platforms, the way we reason about financial crises and global pandemics like COVID. That way of thinking in the community is really the lasting impact of this work.\u201d<\/p>\n\n\n\n

\n

The power of network thinking is everywhere now.<\/p>\nProfessor Jon Kleinberg \u201993<\/strong><\/cite><\/blockquote>\n\n\n\n

\u201cCollective Dynamics of \u2018Small-World\u2019 Networks<\/a>\u201d published in Nature<\/em> on June 4, 1998 and was immediately picked up by major news outlets, including the New York Times<\/em>, Discover Magazine<\/em>, and BusinessWee<\/em>k. It\u2019s been cited more than 50,000 times, and the \u201cWatts-Strogatz model\u201d continues to be fundamental in any introduction to modern network science.<\/p>\n\n\n\n

The main finding in the paper was that a large network could be made small very quickly with just a few random connections, or connections beyond those that are nearby or clustered. <\/p>\n\n\n\n

A disease might spread in a small community, but one or two people bringing it outside that community will have an outsized impact on the spread of the disease. Information can travel much more quickly and efficiently in the brain\u2014or on the Internet\u2014with the introduction of a small number of connections outside a cluster of neurons or nodes. <\/p>\n\n\n\n

The research came at a time when the interconnectedness of the world was increasing and becoming more felt\u2014with the explosive growth of the Internet, global markets, and international travel, the latter of which enabled the spread of diseases like HIV. <\/p>\n\n\n\n

\"Duncan
Watts speaking on a \u201cSix Degrees\u201d panel at Cornell\u2019s Charter Day in 2015. (Cornell University)<\/em><\/figcaption><\/figure>\n\n\n\n
<\/div>\n\n\n\n

\u201cEverybody was starting to get the feeling in their respective disciplines that we have these gigantic networks that are at the root of all kinds of mysteries, but we didn\u2019t know what these networks were like; they were too big,\u201d Strogatz says. \u201cWe provided this abstract picture that was encapsulating what people see in a lot of real networks, but the paper was also successful because of its incompleteness. People could see all kinds of ways to improve what we did or try to apply it. It was a very stimulating, fruitful paper, partly because it raised more questions than it answered.\u201d<\/p>\n\n\n\n

Prior to this model, researchers had often resorted to classifying networks as either regular\u2014totally symmetrical\u2014or random, without a way of visualizing or quantifying the (much more common) middle ground.<\/p>\n\n\n\n

\u201cTheories in epidemiology at the time made these extreme assumptions that everyone was mixing at random with everyone else, which never seemed realistic,\u201d Strogatz says. \u201cBut no one knew what network to assume because nothing had been measured. By default, people would often assume whatever network they were looking at was random, not because they really believed it but because they were just throwing up their hands.\u201d<\/p>\n\n\n\n

\n

We provided this abstract picture that was encapsulating what people see in a lot of real networks.<\/p>\nProfessor Steven Strogatz<\/strong><\/cite><\/blockquote>\n\n\n\n

Strogatz and Watts, now the Stevens University Professor at the University of Pennsylvania\u2019s Annenberg School for Communication, used three networks as test cases for their model. <\/p>\n\n\n\n

They chose systems from different disciplines: a map of the nervous system of the worm C. elegans<\/em>; the power grid of the western U.S.; and the network of 250,000 actors in the Internet Movie Database, taking inspiration from \u201cSix Degrees of Kevin Bacon,\u201d then a popular game in which people would trace any actor\u2019s connections back to Bacon.<\/p>\n\n\n\n

Watts analyzed the three networks and found that each could be classified as a \u201csmall world,\u201d looking and behaving like their model.<\/p>\n\n\n\n

\u201cWe predicted in the paper that it would not be a rarity, it would be what you\u2019d expect, that most networks will turn out to be small worlds,\u201d Strogatz says. \u201cIn science that\u2019s really sticking your neck out. Because we didn\u2019t know\u2014we only had three examples. But people did try out lots of different networks, and one after another\u2014bing, bing, bing\u2014they were all small worlds.\u201d <\/p>\n\n\n\n

And even 25 years later, the work continues to generate questions.<\/p>\n\n\n\n

Says Strogatz: \u201cUnderstanding complex systems, enormous systems of many interacting parts, whether it\u2019s an immune system, an ecosystem, an economy\u2014that will keep us occupied for the whole of the 21st century.\u201d<\/p>\n\n\n\n

Published June 5, 2023<\/p>\n\n\n\n

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