Formation of Scientific Fields as a Universal Topological Transition

Scientific fields differ in terms of their subject matter, research techniques, collaboration sizes, rates of growth, and so on. We investigate whether common dynamics might lurk beneath these differences, affecting how scientific fields form and evolve over time. Particularly important in any field's history is the moment at which shared concepts and techniques allow widespread exchange of ideas and collaboration. At that moment, co-authorship networks show the analog of a percolation phenomenon, developing a giant connected component containing most authors. We develop a general theoretical framework for analyzing finite, evolving networks in which each scientific field is an instantiation of the same large-scale topological critical phenomenon. We estimate critical exponents associated with the transition and find evidence for universality near criticality implying that, as various fields approach the topological transition, they do so with the same set of critical exponents consistent with an effective dimensionality $d \simeq 1$. These results indicate that a common dynamics is at play in all scientific fields, which in turn may hold policy implications for ways to encourage and accelerate the creation of scientific and technological knowledge.