Patterns of scientific collaboration shed light on the structure of society.
In his 1990 play Six Degrees of Separation John Guare claimed that: "Everybody on this planet is separated by only six other people." No one is sure whether this is true because friendship networks are notoriously hard to track. But now at least one social network has been shown to have this 'small world' character: the scientific community.
Mark Newman of the Santa Fe Institute in New Mexico analysed the network generated by collaborations on scientific papers. His findings, reported in the Proceedings of the National Academy of Sciences USA 1, may reveal an important aspect of how scientific ideas are spread.
He found a web of connections that he believes helps to ensure efficient dissemination of new ideas, standards and ethics. "Science would probably not work at all if scientific communities were not densely interconnected," Newman says. And the network bears an uncanny resemblance to the premise of Six Degrees of Separation.
Guare's play was inspired by a celebrated study of networking by psychologist Stanley Milgram. In 1967 Milgram sent packages to random people in Nebraska, asking them to forward the package to a stockbroker in Boston, known to Milgram but not to the Nebraskans.
Milgram did not provide an address. He merely indicated the rough location of the intended recipient, and asked his correspondents to pass the package on to someone they knew who might have a better chance of knowing the stockbroker.
Some of the packages reached their destination, and on average they passed through the hands of only six people en route. In the United States, at least, it seemed that there were indeed just six degrees of separation between any two people. Several researchers have since tried to verify this observation by mapping out friendship networks in full, but this is too labour-intensive and unreliable to supply firm conclusions.
Newman focused on a less fuzzily defined social network. He looked at several huge electronic databases of scientific publications, and tracked the networks of collaborations that they record. Newman considered any two scientists who co-authored a paper to be directly linked in the network. There is no ambiguity here about who is 'friends' with whom.
His analysis has a distinguished precedent. The mathematical sciences have long enjoyed the concept of the Erdös number, which measures how many co-authorship steps an individual is from the eminent and prolific Hungarian mathematician Paul Erdös (who made a groundbreaking study of networks).
People who have written a paper with Erdös have an Erdös number (EN) of 1, those who co-authored with a co-author of Erdös have an EN of 2, and so on. Albert Einstein, for example, has an EN of 2, and the German physicist Werner Heisenberg has an EN of 4.
Informal studies such as Newman's give a strong indication that the scientific community is very incestuous. Many people have published papers with many others, so the co-authorship network is highly interconnected, with several alternative routes between any two points (that is, any two people). Networks like this are often 'small worlds', in which one can usually find a short route between any two points.
Newman finds that the average 'distance' (the number of connected points) between any two people chosen at random ranges from just four (for the high-energy physics community) to about nine (for computer scientists), and is generally about five or six. Just as in Six Degrees of Separation
It is possible that the network of contacts in the scientific community is similar to that in any other profession, and perhaps in social life in general.
Newman,M. E. J. The structure of scientific network collaborations. Proceedings of the National Academy of Sciences USA 98,404- 409 2001.
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Ball, P. Science is all about networking. Nature (2001). https://doi.org/10.1038/news010118-2