Simplicial complexes are generalizations of graphs where relations can be between more or less than two entities. These relations are represented as simplices, which are points, lines, triangles, tetrahedra and higher-dimensional analogs each containing a number of vertices. A simplex consists of a number of hyperedges, which contain any number of nodes. A 0-edge is a 0-dimensional point, a node by itself, a 1-edge is a 1-dimensional line between 2 nodes, a 2-edge is a triangle of three nodes, and so on.
This visualization handles 0-, 1-, and 2-edges separately, representing them with circles, lines and triangles respectively. Larger hyperedges are shown by rendering all of their 2-faces with variants on the same color. An interactive force layout is applied using the 1-edges to achieve a visually appealing result which can be adjusted by the user if the network is unclear.