Graph Drawing by Force-directed Placement

A graph G = (V,E) is a set V of vertices and a set E of edges, in which an edge joins a pair of vertices. 1 Normally, graphs are depicted with their vertices as points in a plane and their edges as line or curve segments connecting those points. There are different styles of representation, suited to different types of graphs or different purposes of presentation. We concentrate on the most general class of graphs: undirected graphs, drawn with straight edges. In this paper, we introduce an algorithm that attempts to produce aesthetically-pleasing, two-dimensional pictures of graphs by doing simplified simulations of physical systems. We are concerned with drawing undirected graphs according to some generally accepted aesthetic criteria: 2