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HypergraphPlot

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

HypergraphPlot[h, opts]

gives a Graphics object drawing the hypergraph h (or a list of hyperedges): vertices placed by the stress layout of the star expansion, each hyperedge of 3 or more vertices a translucent rounded hull in its own palette colour, one of 2 a stadium and one of 1 a circle around its vertex, vertex disks on top. Options: VertexLabels, VertexCoordinates, VertexStyle and GraphLayout as in GraphPlot; others pass through to Graphics.

Examples (8)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (4)

In[1]:= Head[HypergraphPlot[Hypergraph[{{1,2,3},{3,4},{4,5,6},{7}}]]]
Out[1]= Graphics

In[2]:= Count[HypergraphPlot[Hypergraph[{{1,2,3},{3,4},{4,5,6},{7}}]], _Polygon, Infinity]
Out[2]= 4

In[3]:= HypergraphPlot[Hypergraph[{{1,2,3}}]] === HypergraphPlot[Hypergraph[{{1,2,3}}]]
Out[3]= True

In[4]:= HypergraphPlot[5]
Out[4]= HypergraphPlot[5]

Options (1)

In[5]:= Count[HypergraphPlot[{{1, 2, 3}, {3, 4}}, VertexLabels -> "Name"], _Text, Infinity]
Out[5]= 4

Applications (3)

The result is a Graphics object

In[6]:= Head[HypergraphPlot[Hypergraph[{{1, 2, 3}, {3, 4}}]]]
Out[6]= Graphics

One filled hull per hyperedge

In[7]:= Count[HypergraphPlot[Hypergraph[{{1, 2, 3}, {3, 4}, {7}}]], _Polygon, Infinity]
Out[7]= 3

Deterministic, like GraphPlot

In[8]:= HypergraphPlot[Hypergraph[{{1, 2}}]] === HypergraphPlot[Hypergraph[{{1, 2}}]]
Out[8]= True

Implementation notes

Algorithm. builtin_hypergraph_plot returns a Graphics[...] object, deterministically (like GraphPlot). Vertices are placed by the stress layout (glayout.c) of the star expansion ā€” one extra node per hyperedge of two or more vertices joined to its members ā€” so a hyperedge's members cluster around a common centre; GraphLayout selects another embedding and VertexCoordinates overrides any subset. Each hyperedge is drawn as the convex hull of its members (Andrew's monotone chain, convex_hull) inflated by a margin with rounded corners (the Minkowski sum with a disk, sampled every 15Ā°, rounded_hull): a translucent (Opacity 0.22) filled Polygon plus a darker outline in one colour of ColorData[97], cycled by hyperedge index. Size 2 becomes a stadium, size 1 a circle. Shapes are drawn largest-first (by inflated area) and a hyperedge sharing a vertex with smaller ones gets a wider margin (level), so nested hyperedges read as concentric outlines. Vertex disks and labels (direction-avoiding) go on top.

Data structures. The HypView distinct sets; the star-expansion edge arrays eu/ev and the layout coordinate buffer xy; per-hyperedge pts/hull point buffers and an HOrder draw-order table; the shared graphics-primitive builder GDPrims. The option plumbing (VertexLabels, VertexStyle, VertexCoordinates, GraphLayout) reuses GraphPlot's helpers.

Complexity / limits. Dominated by the stress layout; hull and inflation are O(k log k) per hyperedge. A non-hypergraph (and a non-List, non-rule option) leaves the call unevaluated. Mathematica has no built-in hypergraph drawing; the Function Repository's HypergraphPlot is the model.

  • Protected. Implemented in src/graph/hyp_plot.c; Mathematica has no built-in hypergraph drawing (the Function Repository's HypergraphPlot is the model). Deterministic, like GraphPlot.
  • Layout: the vertices are placed by the stress layout of the star expansion (one extra node per hyperedge of two or more vertices, joined to its members), so the members of a hyperedge sit around a common centre and hyperedges sharing vertices are drawn side by side. GraphLayout picks another embedding of the star expansion; VertexCoordinates overrides any subset.
  • Hyperedges: each is the convex hull of its (distinct) members, inflated by a margin with rounded corners (sampled every 15 degrees), drawn as a translucent (Opacity[0.22]) filled Polygon with a darker outline, in its own colour of the ColorData[97] palette (cycled by hyperedge index). A hyperedge of size 2 is therefore a stadium (a thick translucent line with round caps) and one of size 1 a circle around its vertex; an empty one is not drawn. Larger shapes are drawn first so smaller ones stay visible; a hyperedge sharing a vertex with smaller ones gets a wider margin, so nested and repeated hyperedges show as concentric outlines.
  • Vertices are dark disks drawn on top; labels avoid the directions of the vertex's hyperedges.
  • Unevaluated on a non-hypergraph.

Attributes: Protected.

References

See also: GraphPlot

Notes & additional examples

Notes

HypergraphPlot[h] returns a Graphics[...] object. Vertices are placed by the stress layout of the star expansion, so a hyperedge's members cluster around a shared centre and hyperedges that share vertices are drawn side by side. Each hyperedge is the convex hull of its members, inflated with rounded corners and drawn as a translucent filled Polygon with a darker outline, one palette colour per hyperedge; a hyperedge of two vertices becomes a stadium and one of a single vertex a circle. Larger shapes are drawn first and overlapping hyperedges get widening margins, so nested ones read as concentric outlines.

The examples above query the result (Head, Count, equality) rather than displaying it, so they are safe to run headless; evaluating HypergraphPlot[h] directly renders the picture. Options VertexLabels, VertexCoordinates, VertexStyle and GraphLayout behave as in GraphPlot; others pass through to Graphics. Output is deterministic. HypergraphPlot[{e1, e2, ...}] draws a bare list of hyperedges.