Critical thresholds for co-citation clusters and emergence of the giant component

The behavior of co-citation clusters is studied over a wide range of similarity values, and we demonstrate the existence of critical or percolation transitions marked by a sudden expansion of cluster size with a small decrease in similarity which, in most cases, reflects the emergence of a giant component on the overall graph for the dataset. The study was motivated by the question of how to set appropriate thresholds for delineating individual research areas that identify, as far as possible, natural boundaries, in view of the fact that a threshold or criterion appropriate for one area may not be appropriate for another. We explore the rate of change in cluster size as a possible boundary indicator. The relationship of this critical behavior to maps of science is discussed.