Force-Directed Graph Drawing

Years and Authors of Summarized Original Work

• 1963; Tutte

• 1984; Eades

Problem Definition

Given a connected undirected graph, the problem is to determine a straight-line layout such that the structure of the graph is represented in a readable and unbiased way. Part of the problem is the definition of readable and unbiased.

Formally, we are given a simple, undirected graph G = (V, E) with vertex set V and edge set $E \subseteq \binom{V }{2}$. Let n =  | V | be the number of vertices and m =  | E | the number of edges. The neighbors of a vertex v are defined as N(v) = { u : { u, v} ∈ E}, and $\deg (v) = \vert N(v)\vert$ is its degree. We assume that G is connected, for otherwise the connected components can be treated separately.

A (two-dimensional) layout for G is a vector p = (p _v )_v ∈ V of vertex positions $p_{v} =\langle x_{y},y_{v}\rangle \in \mathbb{R}^{2}$. Since edges are drawn as line segments, the drawing is completely determined by these vertex positions. All approaches...