A new method to optimize the force-directed placement for 3D large graph drawing

Abstract

This paper describes a novel force-directed placement approach for 3D drawing of large graphs. The main idea behind our approach consists in optimizing the layout by equitably distributing vertices in the space. We consider the largest sphere inscribed in the 3D space and the vertices are then assigned random initial positions that are improved by force-directed placement. In order to ensure the effectiveness of the algorithm, we propose a new energy function minimization which uses the conjugated gradient of Fletcher-Reeves [1, 2]. Our algorithm is not only addressed to general undirected graphs but also it produces good layout of large trees. This work is motivated by our need to offer 3D visualization tools for large computing networks but this first phase will be focused on the graph representation.