Representing graphs and maps
Motivated by graph drawing problems, we can formulate a theory of graph representations precisely, admitting various generalizations. Each vertex is represented as a point in Euclidean space and each edge as a line segment spanned by the representations of its end-vertices. A typical problem in this area is finding an optimal graph representation that minimizes a given energy function. For some parameters this problem admits an exact solution while other parameters require iterative methods. Representations of graphs are then extended to representations of maps and other incidence geometries.