Angle Optimization of Graphs Embedded in the Plane

TL;DR

This paper introduces a spring-embedding method for optimizing angles in graph drawings with edge length constraints, maximizing the minimum angle to improve visual clarity.

Contribution

It presents an analytical solution for vertices of degree up to three and a numerical approach for higher degrees in angle optimization of graph embeddings.

Findings

Analytical solution for vertices with degree ≤ 3

Numerical method for higher degree vertices

Implemented algorithm produces improved graph drawings

Abstract

In this paper we study problems of drawing graphs in the plane using edge length constraints and angle optimization. Specifically we consider the problem of maximizing the minimum angle, the MMA problem. We solve the MMA problem using a spring-embedding approach where two forces are applied to the vertices of the graph: a force optimizing edge lengths and a force optimizing angles. We solve analytically the problem of computing an optimal displacement of a graph vertex optimizing the angles between edges incident to it if the degree of the vertex is at most three. We also apply a numerical approach for computing the forces applied to vertices of higher degree. We implemented our algorithm in Java and present drawings of some graphs.