by David Kaiser (MIT) and Luis Bettencourt (LANL)

For some time, we and OSTI have been interested in the question of how new scientific ideas spread. What does it take for the "next big thing" to leap from one person's head to an active community of researchers? Do those shared ideas or techniques bind the community together more tightly than before, perhaps even helping to define a new research field that didn't exist before? And if so, how might we detect and measure such shifts in the space of researchers and ideas?

One interesting possibility is to study changes in the structure of collaboration networks over time. For example, imagine that Alice writes a scientific article with Bashir. Some time later, Bashir writes a different article with Carlos, while Alice writes a new paper with Dwayne. Those four authors are now connected by co-authorship links: Alice directly with Bashir and Dwayne, and--thanks to Bashir's separate article with Carlos--Alice and Carlos are connected, too. We may call that collection of nodes (authors) and links (co-authorship ties) a collaboration network.

We might expect that the pattern of change over time in these collaboration networks would vary widely with scientific field or discipline. After all, articles in theoretical physics tend to have far fewer co-authors than do articles on biomedical topics. Fields also have different average rates at which researchers write articles in any given year. And yet we have found some surprising regularities lurking beneath what otherwise appear to be rather different modes of behavior.

We have published some of these findings in a recent paper--L. Bettencourt, D. Kaiser, and J. Kaur, "Scientific discovery and topological transitions in collaboration networks," Journal of Informetrics, volume 3 (2009): 210-221--and describe our results here. See also our original OSTI report: "The dynamics of scientific discovery: the spread of ideas and structural transitions in collaboration networks."

http://www.osti.gov/innovation/research/diffusion/OSTIBettencourtKaiser.pdf

In examples that range from theoretical physics, to cutting-edge materials science and engineering, to biomedical research, we have found that the connections between authors in each field evolve quite similarly. Collaboration networks in each of these domains "densify" over time, that is, they show an increase in the average number of links per node. Likewise, in all fields that we might otherwise consider to be productive, the sizes of the connected portions of the collaboration graphs grow and stabilize.

Over time, in other words, Alice will be connected with more and more researchers in her field via co-authorship links. Some will be direct ties--people with whom Alice has co-written articles herself--and some will be distant 'cousins' (Yolanda, Zachary), researchers who have written papers with some of Alice's co-authors or with their co-authors, and so on down the line. We may define the diameter of that connected group as the average path length connecting any two nodes--how many intermediaries it takes to connect Alice to some distant author, with whom she has not written a paper herself. We have found that in productive fields of research, that diameter stabilizes or decreases over time: as more and more authors enter the field and begin to collaborate with each other, the community grows more tightly woven together.Most interesting of all, the network as a whole typically undergoes what is called a topological transition--akin to a physical process called percolation--in which a giant component emerges, with most authors connected via co-authorship links to that main cluster. The transition proceeds much like a physical phase transition--say, liquid water freezing into ice--once the average number of links per author reaches a critical threshold.

This rapid structural transition in collaboration networks likely occurs when a critical mass of ideas or techniques becomes shared among researchers--when a "trading zone" allows specialists to leverage complementary skills toward a common goal. (The historian of science, Peter Galison, coined the term "trading zone" to describe these kinds of collaborative processes.) The process then becomes self-reinforcing as researchers such as graduate students and postdocs circulate among research groups. In this way, clusters of ideas and people become tightly linked by ties of communication and collaboration, enabling new ideas to take off and entire new fields of research to coalesce.

We are excited about this topological measure of a field's evolution for two reasons. First, the topological phase transition appears to be a robust signature, clearly discernible early in a field's development--thus enabling us to identify "hot" new emerging fields and potential transformations, amid a sea of thousands or even millions of unrelated papers. We believe that this method has advantages over other approaches. Early on, for example, the jargon that may later accompany new fields is typically not yet settled, and often refers to older concepts, making identification based on natural language analysis (such as searching for keywords) unreliable. Moreover, most new research directions turn out to be red herrings, eventually ending up as dead ends--so relying solely on "bursts" of activity (citation, co-authorship, or otherwise) is likely to be insufficient. Those fields that undergo the percolation-like transition appear to make it "over the hump" and become successful, productive research communities.

Second, preliminary analysis indicates that the topological transition can help distinguish between successful fields and dead ends. For example, the subject of cold fusion has generated comparable numbers of articles and authors as other fields we have investigated. If we measured a field's health by numbers of published articles or participating authors, in other words, we would find little difference between, say, cold fusion, research on H5N1 influenza ("bird flu"), or research in various topics within theoretical physics. But unlike those other fields, the collaboration network for cold fusion never percolated. The critical mass of shared concepts and techniques never emerged; the network of researchers in the area never coalesced into a coherent, connected structure. For this reason, we suspect that the topological transition may serve as a significant indicator of whether a new field of scientific research is likely to be a "good bet," a robust endeavor worthy of the attention of new young scientists and policymakers alike.

In future work, we would like to explore whether additional means of communicating information and sharing techniques--beyond formal co-authorship--might accelerate the structural transition in collaboration networks. Could interactive tools on the web, from blogging to videoconferencing and more, help strengthen collaborative ties, connecting researchers with shared interests and giving fields the extra boost they need to succeed?

Technical note: Preliminary research indicates that the topological transition in collaboration networks might display universality, that is, cases that are different in detail all exhibit the same form of critical behavior. In particular, near their transitions, the cases we have examined so far all fit a remarkably simple curve. The fraction of links in the largest cluster scales as (k - k_c) to some power, where k is the average number of links per node, and k_c is the critical connectivity--the tipping point, above which the entire network will rapidly coalesce into a single giant connected component. The critical connectivity, k_c, is like a critical temperature for a phase transition, such as water freezing to ice. Much as with physical systems near phase transitions, the numerical value of k_c varies case by case, but the exponent is shared across a wide range of examples. Put another way, although water and liquid Helium freeze at rather different temperatures, they both freeze by means of the same basic process. See our report for details.

Luis M. A. Bettencourt is with the Theoretical Division, Los Alamos National Laboratory and the Santa Fe Institute.

David I. Kaiser is with the Program in Science, Technology and Society, and the Department of Physics, Massachusetts Institute of Technology.