Forceangrep

Forceangrep is a term used in graph drawing and data visualization to describe a family of layout algorithms that integrate traditional force-directed placement with angular constraints and repulsive penalties to manage edge angles. The name is commonly interpreted as force-angle-repulsion, signaling a combined emphasis on edge springs, inter-node repulsion, and the enforcement of angular separation at node junctions.

In typical formulations, the layout energy E consists of three components: an attractive spring term for connected nodes, a repulsive term for all node pairs, and an angular penalty that discourages small angles between consecutive edges around each node. The angular term helps preserve readability by promoting more uniform edge directions and reducing visual ambiguity in dense regions.

The algorithm proceeds by initializing node positions and then iteratively moving nodes along the negative gradient of E until convergence or a fixed number of iterations. Practical implementations often employ multi-resolution or adaptive step-size schemes. Naively, each iteration runs in O(n^2) time for n nodes, but acceleration techniques such as Barnes–Hut or fast multipole methods can reduce the practical cost for larger graphs.

Applications of forceangrep include social and information networks, biological interaction networks, and software architecture diagrams where maintaining legibility in the presence of high-degree nodes is important. Variants differ in how strictly angular constraints are enforced and how the energy terms are weighted, reflecting trade-offs between layout stability, aesthetics, and computation time.

See also: force-directed layout, angular resolution, graph drawing, network visualization.