UofM News

Finding the Hidden Patterns in Maps and Networks

By Laura Bailey
U-M News Service

Individual county results from the 2004 election weren't really pure red or blue, but more like purple, with very narrow margins determining whether a county went Republican or Democrat. (CLICK IMAGE for enlargement.)

On the morning of Nov. 4, 2004, while Democrats nursed the hangover of defeat, U-M Physics Professor Mark Newman busily prepared his election map of red and blue states.

Newman’s cartogram was one of the few positive images for Democrats that day. Ninety-nine percent of election results maps showed wide, blood-red swaths across the country dotted with much smaller blue areas denoting Kerry states. But Newman’s election map was different: by employing a common physics formula, he diffused the population equally throughout the country. Picture a gust of wind blowing people from the high population cities (Kerry supporters) and evenly distributing them into the low population, rural, red areas (Bush supporters)

Newman’s diffusion maps painted a much more accurate picture, with red and blue areas almost even. Democrats lost, but they weren’t nearly as outnumbered as election maps suggested.

Newman joined the U-M in September 2002 from a think tank in New Mexico called the Santa Fe Institute. Since then, the research done by Newman and his collaborators into networking and graph theory has yielded characteristically quirky – “that’s what my mother would call it,” he jokes -- findings that examine real world networks and explain the relationships with mathematical and computer models to understand the invisible complexities of relationships.

Mapping the world's countries based on population rather than land area shows China and India to be giants and Russia to be relatively puny. (CLICK IMAGE for enlargement.)

Physics research certainly isn’t known for its connection to popular culture, and for most people, it’s not immediately clear why it matters who is buying what books on Amazon, or which web sites link to which others, until one considers a networking problem like predicting how diseases spread through populations.

Understanding how people interact means we can predict where diseases will migrate, and therefore try to stop their spread, Newman says. But before any of that can happen, the research must catch someone’s attention. Infusing the rarified air around physics research with popular culture is one way to do that.

Physics Chair Myron Campbell says Newman’s approach is novel and advantageous.

“Because his research is so interesting, a lot of students want to work with him,” Campbell says, “and he is able to generate funding….It is incredible, not everyone has that talent that Mark has.”

Besides his election cartograms, Newman and his collaborators have examined social networks among dolphin pods and characters in the book Les Miserables; they’ve determined the degree of separation among collaborating scientists (sort of the Kevin Bacon theory of academia); they’ve developed a new college football ranking system based on networks of teams, their records and scores.

The United States looks fat enough to burst in this cartogram of energy consumption. CLICK IMAGE for enlargement.)

“The question he was really asking is how do you do comparisons when you have incomplete information,” Campbell says, of the football project. He stresses the complexity of the math involved is sometimes obscured by the lighter subject matter Newman uses to test his models. “For example, in the rankings, not every team has played every other team, so you don’t have a complete set of information.”

For a recent project that was published in the prestigious Proceedings of the National Academy of Sciences, Newman developed a computer analysis to separate networks into communities, which yielded some surprises when used on real-world networks like political books, blogs, and metabolic systems. For instance, Newman found that when sorting books sold on Amazon into left- and right-wing groups, the most appealing book to conservative buyers was actually written by Democrat Zell Miller, who became notorious within his own party when he endorsed Bush in the last presidential election.

Newman says that because he doesn’t work on specific networks, but rather techniques applicable to many different types of networks, he can choose the examples he likes to illustrate the techniques.

“So, I’m free to choose what examples I like, and in many cases I think it makes sense to choose examples that will be familiar to people; hence the Amazon network, and the blogs, and so forth.”