Abstract: We argue that most recommendation approaches can be abstracted as a graph exploration problem. In particular, we describe a graph-theoretic framework with two primary parts: (a) a recommendation graph, modeling all the elements of an (application) domain from a recommendation perspective, including the subjects and objects of recommendations as well as the relationships between them; (b) a set of path operations, inferring new edges, i.e., implicit or unknown relationships, by traversing and combining paths on the graph. The resulting path algebra model provides an abstraction and a common foundation that is beneficial to three aspects of recommendations: (a) expressive power - expression and subsequent use of several significantly different, existing but also novel recommendation approaches is reduced to parameterizing a unique model; (b) usability - by capturing part of the recommendation mechanisms in the underlying path algebra semantics, specification of recommendation approaches becomes easier and less tedious; (c) processing speed - implementing recommender systems on top of graph engines opens up the door for several optimizations that speed up execution. We demonstrate the above benefits by expressing several categories of recommendation approaches in the path algebra model and benchmarking some of them in a recommender system implemented on top of Neo4J, a widely used graph system.