Geodesic cycle length distributions in fictional character networks (2303.11597v1)

Abstract: A geodesic cycle in a graph is a cycle with no shortcuts, so that the shortest path between any two nodes in the cycle is the path along the cycle itself. A recently published paper used random graph models to investigate the geodesic cycle length distributions of a unique set of delusional social networks, first examined in an earlier work, as well as some other publicly available social networks. Here I test the hypothesis, suggested in the former work, that fictional character networks, and in particular those from works by a single author, might have geodesic cycle length distributions which are extremely unlikely under random graph models, as the delusional social networks do. The results do not show any support for this hypothesis. In addition, the recently published work is reproduced using a method for counting geodesic cycles exactly, rather than the approximate method used originally. The substantive conclusions of that work are unchanged, but some differences in the results for particular networks are described.