MetroSets: Visualizing Sets as Metro Maps

We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph
$\mathcal{H}=(V,\ \mathcal{S})$
, consisting of a set
$V$
of vertices and a set
$\mathcal{S}$
, which contains subsets of
$V$
called hyperedges. Our system then computes a metro map representation of
$\mathcal{H}$
, where each hyperedge
$E$
in
$\mathcal{S}$
corresponds to a metro line and each vertex corresponds to a metro station. Vertices that appear in two or more hyperedges are drawn as interchanges in the metro map, connecting the different sets. MetroSets is based on a modular 4-step pipeline which constructs and optimizes a path-based hypergraph support, which is then drawn and schematized using metro map layout algorithms. We propose and implement multiple algorithms for each step of the MetroSet pipeline and provide a functional prototype with easy-to-use preset configurations. Furthermore, using several real-world datasets, we perform an extensive quantitative evaluation of the impact of different pipeline stages on desirable properties of the generated maps, such as octolinearity, monotonicity, and edge uniformity.