Chris Fields Research

Research questions, recent publications ...

Mathematician Paul Erdős (1913 - 1996) is well-known as the author of at least 1,525 research papers with 511 different collaborators. In tribute to Erdős' vast productivity and collaborative zeal, the ''Erdős Number'' of any researcher is defined as follows: Paul Erdős himself has (uniquely) Erdős Number 0, any co-author with Erdős has Erdős Number 1, any co-author with an Erdős co-author has Erdős Number 2, etc. Considerable data on the Erdős Numbers of prominent researchers, including lists of all individuals with Erdős Numbers of 1 or 2, are maintained by the Erdős Number Project at Oakland University.

The *Erdős Collaboration Graph* is the graph constructed by representing researchers as vertices and joint publications as edges connecting their co-authors. The Erdős Collaboration Graph is a social network in which the interdependency is productive (of published papers) research collaboration. The length of the shortest path from the vertex representing any individual included in the Erdős Collaboration Graph to the vertex representing Erdős is that individual's Erdős Number; however, the Erdős Collaboration Graph also allows the determination of paths between any two individuals who are included in the web of collaboration that includes Paul Erdős. For example, with an Erdős Number of 3, I have a path of length 4 through Erdős to Alfred Tarski and a path of length 5 through Erdős to Albert Einstein (data from the archive of the Erdős Number Project). The extent to which the Erdős Collaboration Graph captures *all* research collaboration, i.e. includes all researchers who have published jointly-authored papers, is unknown.

A subgraph of the Erdős Collaboration Graph showing some paths connecting me to Erdős is shown below. Eight paths (1 of length 3 and 7 of length 4) connect me to Erdős via collaborative links in bioinformatics and genomics; one path (of length 3) is via a collaborative link in nuclear physics.

The data on collaborative links up to Erdős Number 2 used to construct this subgraph are from the 2010 records of the Erdős Number Project. The additional data are listed below, keyed by the edge labels shown in the subgraph.

Many of the connections in my Erdős lineage result from my involvement in the early stages of the Human Genome Project. As discussed in Some effects of the Human Genome Project on the Erdős collaboration graph, this "big science" collaboration gave researchers across biology lower Erdős numbers.

An interesting feature of the graph of my Erdős lineage is that it is composed entirely of cycles: every vertex is between at least two other vertices. Cycles indicate interactions between members of different academic lineages. The subgraph below shows another cycle that combines molecular biology collaborations with nuclear physics collaborations; the unlabeled links are again from the Erdős Number Project. In How small is the center of science? Short cross-disciplinary cycles in co-authorship graphs, I show that short cycles like this one cross many boundaries between scientific disciplines. This leads to a question: how "real" are the disciplinary boundaries that are often taken so seriously?

Nobel prize winners and other prominent scientists are naturally regarded as "central" to their disciplines. In Close to the edge: Co-authorship proximity of Nobel laureates in Physiology or Medicine, 1991 - 2010, to cross-disciplinary brokers, I show that Nobel laureates in biomedicine are also close to the boundaries of biomedicine - on average, less than three co-authorship steps away. Co-authorship proximity of A. M. Turing Award and John von Neumann Medal winners to the disciplinary boundaries of computer science shows that recipients of either the A. M. Turing Award or the John von Neumann Medal in computer science are even closer to the edges of their discipline. The graph below, from Nobel numbers: Time-dependent centrality measures on co-authorship graphs, shows a small section of the boundary between the biomedical sciences and physics containing co-authorship paths that traverse either me or my colleague Eric Lander. Nobel laureates in either Physiology or Medicine (lower part of graph) or Physics (upper part of graph) are indicated by two-digit award dates. Being close to the boundaries of their respective disciplines makes these Nobel laureates close to each other. Do other boundaries between disciplines also look like this? If so, what does this mean for the "shape" of disciplines in co-authorship space?

Any of my collaborators can use the subgraphs above and the references below to establish that his/her Erdős Number is at most 4, as well to discover perhaps surprisingly short paths to many other scientists.

A:B:

C: Branscomb, E., T. Slezak, R. Paestar,

D: Gardner, M. J., H. Tettelin, D. J. Carucci, L. M. Cummings, L. Aravind,

E:

F:

G: Cassandra L. Smith, C. L., S. K. Lawrance, G. A. Gillespie,

H: International Human Genome Sequencing Consortium (including

I: Mikkelsen, T. S., M. J. Wakefield, B. Aken

J: Mount, S. M.,

K: Martin-Gallardo, A., W. R. McCombie, J. Gocayne, M. FitzGerald, S. Wallace, B. M. Lee, J. Lamerdin, S. Trapp, J. Kelley, L.-I. Liu, M. Dubnick, L. Dow, A. R. Kerlavage, P. De Jong,

L: Adams, M., M. Dubnick, A. Kerlavage, R. Moreno, J. Kelley, T. Utterback, J. Nagle,

M: McCombie, W. R., A. Martin-Gallardo, J. Gocayne, M. FitzGerald, M. Dubnick, J. Kelley, L. Castilla, L.-I. Liu, S. Wallace, S. Trapp, D. Tagle, L. Whaley, S. Cheng, J. Gusella, A.-M. Frischauf, A. Poustka, H. Lehrach,

N:

O: Schein, J. E.,

P:

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R:

S:

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U:

V: