A graph crossing is a point, other than a common endpoint, where the arcs representing two distinct edges in a graph drawing of a graph cross rather than merely touch. In a good drawing of a graph, no three edges cross at one point, adjacent edges do not cross, and any two edges cross at most once (Schaefer 2018, p. 4).
Crossings are counted between pairs of edges, so if several edges cross pairwise at one point, each pair contributes a crossing (Schaefer 2018, p. 4). The graph crossing number minimizes the number of graph crossings over all graph drawings of a given graph in the plane. Restricting the drawings to straight edges instead gives the rectilinear crossing number.
