This talk is meant to survey a variety of research among what is commonly phrased “higher-order graph algorithms.” We’ll begin by establishing well-known relationships among different approaches for matrices, stochastic, and standard graph algorithms — for instance, the equivalence between finite-space, discrete time Markov chains and weighted graphs. Then look at what happens with higher-order generalizations of these ideas where we tend to find that different higher-order generalizations often tend to be more different than their pairwise or matrix origins with fewer connections.