2D illustration of an alpha complex based representation of a molecule and the empty space within.(a) Union of disks (balls in 3D represent atoms) where the contribution from each disk is equal to its intersection with the corresponding Voronoi cell. (b) The weighted Delaunay triangulation of the disks and the convex hull (green). (c) Alpha complex at α=0, shown in red, is a subcomplex of the weighted Delaunay triangulation. (d) A cavity is a connected component of the complement of the alpha complex. A cavity with atleast one opening is a pocket (blue), while buried cavities are referred to as voids (green). (e) The empty space represented by the cavity triangles. (f) A channel is a simply connected subset of simplices of a pocket each of whose triangles has at most two neighbors and at least one boundary edge is a mouth edge. Here a pore (pink), a channel with two openings, is shown represented as a subset of the complement of the alpha complex. (g) A channel from the boundary to an interior point. (h) Underlying empty space of the channel. (i) Simplices of the complement of the alpha complex that represent the channel. (j) A path representation of the channel in which nodes are located at the centers of the orthogonal circle corresponding to each triangle and arcs connect nodes that correspond to neighbouring triangles.