Directed Random Dot Product Graphs

In this paper we consider three models for random graphs that utilize the inner product as their fundamental object. We analyze the behavior of these models with respect to clustering, the small world property, and degree distribution. These models are motivated by the random dot product graphs developed by Kraetzl, Nickel, and Scheinerman. We extend their results to fully parameterize the conditions under which clustering occurs, characterize the diameter of graphs generated by these models, and describe the behavior of the degree distribution.