Title: Fireflies, Finches, and Ferrers Digraphs

Abstract:

In this talk, I will explore network sampling algorithms which have found use in answering questions about the distribution of finch species on islands, as well as synchronization of blinking fireflies. My focus will be on graph structures associated with these algorithms, and in particular on a generalization of split graphs to the directed case. These split digraphs can be identified solely by their degree sequences, as in the undirected case, with their structure appearing in the approximate uniform sampling of directed graphs from a fixed degree sequence. I will conclude with a discussion of corrected Ferrer digraphs, also known as threshold digraphs, and their relation to split digraphs.