A Force-Directed Algorithm for Drawing Directed Graphs Symmetrically

Abstract

Symmetry is one of the most important aesthetic criteria on graph drawing. It is quite necessary to measure the extent to which the drawings can be considered symmetric. For this purpose, a symmetric metric based on vertex coordinate calculation is proposed in this paper. It is proven theoretically and experimentally that the proposed metric is robust to contraction, expansion, and rotation of drawings. This robustness conforms to human perception of symmetry. Star-subgraphs and cycles are two common structures in digraphs. Both of them have inherent symmetry which should be displayed in drawings. For this purpose, a force-directed algorithm named FDS is proposed which can draw star-subgraphs and cycles as symmetrically as possible. FDS algorithm draws cycles as circles whose positions are fixed to provide a scaffolding for overall layout, renders non-leaf vertices by a standard force-directed layout, and places leaf vertices on concentric circles via a deterministic strategy. A series of experiments are carried out to test FDS algorithm. The results show that FDS algorithm draws digraphs more symmetrically than the existing state-of-the-art algorithms and performs efficiency comparable to O(nlog⁡n) YFHu algorithm.

Avaliação de um sistema de analítica visual para recuperação de informação em coleções de documentos

“…Em seguida o modelo, descrito pela Equação 2.4, tenta minimizar a "energia" de todos os nós do grafo de forma iterativa, aproximando-se cada vez mais de um estado global de equilíbrio. A força referente a cada nó do grafo é descrita pela Equação 2.5 de forma que: Γ(i) representa o conjunto de nós vizinhos ao nó i; X constitui o conjunto de nós; K e C denotam parâmetros para adaptar as forças de atração e repulsão (CABRAL, 2020;GOU, 2018;HU, 2005).…”