Collection of graphs including optimal twin-width contraction sequences

This dataset was prepared to carry out the research discussed in "A Learning Framework for Twin-Width and Related Problems" [O'Conner et al. / INOC 2026]. Solved Twin-Width Instances - Number of graphs: 115307- Number of optimal solutions: 295154 This repository contains small undirected but connected graphs that can be used as instances for twin-width computations.Each graph is stored in a `graph.gr` file in the [Pace 2023 file format](https://pacechallenge.org/2023/io/) in its own directory. We use the following folder structure: {graph-model}/n{number of nodes}/m{number of edges}/{hash}/graph.grwhere `{graph-model}` indicates the origin of the instance, and the `{hash}` is some digest or identifier of the graph with no particular meaning other than to support multiple graphs of the same size. We consider the following network models:- `gnp` are Gilbert graphs of various density- `netrep` contains small instances of [networkrepository.com](https://networkrepository.com/).- `planar` is a selection of planar connected components from [networkrepository.com](https://networkrepository.com/), processed as `netrep`.- `rhg25` and `rhg30` are random hyperbolic graphs with degree powerlaw exponents of 2.5 and 3.0 respectively- `rgg` are two dimensional random geometric (Euclidean) graphs with various connection radii If the original instance is directed, we replace each directed edge with a bi-directed edge pair, and remove multi-edges.- `rook` contains rook graphs where `{hash}` represents the model parameters For each model, we generate a graph and consider only a largest connected component. Hence all graphs are connected. Each graph may be accompanied by contraction sequences in the format`[compl_]{solver}_tww{tww found}.cs` in the [Pace 2023 file format](https://pacechallenge.org/2023/io/).Files with the `compl_` prefix contain contraction sequences that were computed on the complement of `graph.gr`; they are also checked to solve the original `graph.gr`.Observe that there may be meta information stored in the comments (indicated by a line starting with `c`) of contraction sequences. For example:```c {"tag": "rank1", "tww": 0, "res": {"utime": 0.10846399999999999, "stime": 0.015493999999999999, "maxrss": 21220}}```where `tag` indicates the solver, `tww` the twin width implied by the sequence and `res`the resources required by the solver: `utime` is user time in seconds, `stime` is system time in seconds, `maxrss` is maximum resident set size in kilobytes. Solver names are arbitrary strings. We use `rank{X}` where `X` corresponds to the final rank reported by PACE, i.e.- `rank1` is the winner `Hydra Prime`- `rank2` is `GUTHMi`- `rank5` is `Soapen`