graph theory The study of graphs, where a graph is an abstract mathematical system consisting of points (or nodes, vertices) and lines (or edges, arcs, segments), and the incidence function defined for lines which assigns to each one exactly one pair of points. If the pair of points is ordered, the line is directed; if the pair is unordered, the line is undirected. E. A. Wrigley (1973) wants to apply this kind of system to the elements of record linkage (cf. reachability, transitivity).