A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.

Spatial graphs, where nodes carry geographic location information, are vital for modeling complex relationships in domains such as location-based social networks, transportation systems, and knowledge graphs. However, it is challenging to visualize large spatial graphs while simultaneously showing edge connections and vertex spatial fidelity, especially when the location of each vertex is imprecise. We present a distributed geospatial force-directed framework that visualizes spatial graphs where location can be represented as a point, multi-point, linestring, or polygon. It integrates three models for anchoring forces: centroidal, inside-out, and closest-point. The algorithm is formulated as relational operations and runs end-to-end on Apache Spark/SparkSQL, achieving near-linear scaling. Experiments on train networks, author-publication graphs, and location-based social networks show clearer layouts that balance edge lengths and spatial fidelity while reducing crossings.

Force-directed algorithms are among the most flexible methods for calculating layouts of simple undirected graphs. Also known as spring embedders, such algorithms calculate the layout of a graph using only information contained within the structure of the graph itself, rather than relying on domain-specific knowledge. Graphs drawn with these algorithms tend to be aesthetically pleasing, exhibit symmetries, and tend to produce crossing-free layouts for planar graphs. In this survey we consider several classical algorithms, starting from Tutte's 1963 barycentric method, and including recent scalable multiscale methods for large and dynamic graphs.