Why might the critical-point behavior of coauthorship networks be universal? The symmetry group of the associated concept space
In December 2008, Luis Bettencourt and David Kaiser reported their findings from studies of research collaboration networks, which included their discovery that, as coauthorship networks in a particular field reach the point of forming a single giant component of interconnected authors that dwarfs all other coauthor groups in that field, the growth near that point depends in a universal way on the average number of coauthors per author. In particular, the fraction of coauthor links that belong to the giant component appears to be proportional to ( - kc)0.35, where kc, which marks the critical point, depends on the research field. The remarkable fact is that the exponent, 0.35, fits the data for networks in several quite distinct fields. This value apparently isn’t common to networks in general, though. I had wondered what features of a network do determine the exponent’s value.
Many physical systems exhibit critical-point transitions like the formation of a giant component in networks—e.g., iron magnets lose their magnetism at a certain critical temperature, and the sharp difference between the densities of water and water vapor disappears above a critical pressure. ...Read more...