A graph, in the mathematical sense, is simply a set of nodes together with a set of edges connecting pairs of nodes. Kastalia treats its entire universe of discourse as one big graph: every stored unit of meaning is a node (Kastalia calls it a knot), and every stated relation between two units is a directed, labelled edge (a bound).

Unlike a tree, a graph permits any node to be reached from many different directions -- the same knot can simultaneously be the child of one category, a member of a group, the illustration of another knot, and the translation of yet another. This is precisely what lets Kastalia model real knowledge, which is rarely a strict hierarchy.