The Sugiyama algorithm, also known as the layered algorithm or hierarchical algorithm, is an established algorithm to produce crossing-minimal drawings of graphs. It does not, however, consider an initial order of the vertices and edges. We show how ordering real vertices, dummy vertices, and edge ports before crossing minimization may preserve the initial order given by the graph without compromising, on average, the quality of the drawing regarding edge crossings. Even for solutions in which the initial graph order produces more crossings than necessary or the vertex and edge order is conflicting, the proposed approach can produce better crossing-minimal drawings than the traditional approach
