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Directed graph limits and directed threshold graphs
We look at the recently developed concept of graphons first discussed by Lovász and Szegedy in 2004. These are continuous versions of adjacency matrices which arise as limits of sequences of graphs. We develop the concepts that generalize graphons to directed graphs. Several papers by Diaconis and Janson have looked at the limits of sequences from certain graph classes. We develop a class of directed graphs analogous to threshold graphs and then characterize their graphons. We finish by defining integer partition homomorphisms and giving an analog to graphons for integer partitions.
Boeckner, Derek, "Directed graph limits and directed threshold graphs" (2013). ETD collection for University of Nebraska - Lincoln. AAI3559217.