Skip to content

HypergraphVertexAdd

Status: Stable

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

Description

HypergraphVertexAdd[h, v]

adds the vertex v to h; HypergraphVertexAdd[h, {v1, ...}] adds several. Existing vertices are left alone.

Examples (8)

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

Basic examples (5)

In[1]:= InputForm[HypergraphVertexAdd[Hypergraph[{{1,2,3},{3,4},{4,5,6},{7}}], {1, 8, 9}]]
Out[1]= Hypergraph[{1, 2, 3, 4, 5, 6, 7, 8, 9}, {{1, 2, 3}, {3, 4}, {4, 5, 6}, {7}}]

In[2]:= InputForm[HypergraphVertexAdd[Hypergraph[{{1,2}}], {{a,b}}]]
Out[2]= Hypergraph[{1, 2, {a, b}}, {{1, 2}}]

In[3]:= InputForm[HypergraphVertexDelete[Hypergraph[{{1,2,3},{3,4},{4,5,6},{7}}], 3]]
Out[3]= Hypergraph[{1, 2, 4, 5, 6, 7}, {{4, 5, 6}, {7}}]

In[4]:= InputForm[HypergraphVertexDelete[Hypergraph[{{1,2,3},{3,4},{4,5,6},{7}}], {1, 7}]]
Out[4]= Hypergraph[{2, 3, 4, 5, 6}, {{3, 4}, {4, 5, 6}}]

In[5]:= HypergraphVertexDelete[Hypergraph[{{1,2,3},{3,4},{4,5,6},{7}}], 99]
Out[5]= HypergraphVertexDelete[Hypergraph[<7 vertices, 4 hyperedges>], 99]

Applications (3)

A single new vertex

In[6]:= InputForm[HypergraphVertexAdd[Hypergraph[{{1, 2}}], 3]]
Out[6]= Hypergraph[{1, 2, 3}, {{1, 2}}]

Several at once

In[7]:= InputForm[HypergraphVertexAdd[Hypergraph[{{1, 2}}], {3, 4}]]
Out[7]= Hypergraph[{1, 2, 3, 4}, {{1, 2}}]

An existing vertex is left alone

In[8]:= InputForm[HypergraphVertexAdd[Hypergraph[{{1, 2}}], 2]]
Out[8]= Hypergraph[{1, 2}, {{1, 2}}]

Implementation notes

Algorithm. builtin_hypergraph_vertex_add appends vertices to h, leaving the hyperedges untouched. edit_items interprets the second argument: for the Vertex heads any List is a list of vertices (so a List-valued vertex must be wrapped as {{...}}), otherwise it is a single vertex. Each candidate not already in the memo's vertex index ā€” and not a duplicate among the candidates, screened by a throwaway GraphVIdx extra ā€” is appended in order after the existing vertices. A vertex already present is silently skipped. The result is a fresh Hypergraph[{...}, edges].

Data structures. The memo's vertex GraphVIdx (membership test) and a temporary GraphVIdx extra (de-duplicating the new candidates); the vertex and (shared) edge Lists are rebuilt with mk_hyp/mk_list. Because the memo holds an immutable reference, the original object is never mutated.

Complexity / limits. O(n + k) for k candidates. Only the vertex set grows; to add hyperedges use HypergraphEdgeAdd.

  • In the Vertex heads any List is a list of vertices; wrap a List-valued vertex as {{...}}.
  • HypergraphVertexDelete is unevaluated if a named vertex is absent.
  • Mutators unshare a memoized hypergraph node before editing, so the original object is never changed.

Attributes: Protected.

References

See also: HypergraphVertexDelete, VertexDelete

Notes & additional examples

Notes

HypergraphVertexAdd[h, v] appends the vertex v, and HypergraphVertexAdd[h, {v1, ...}] appends several; the hyperedges are untouched, so this introduces isolated vertices. A vertex already present is silently skipped, and the new vertices keep their given order after the existing ones.

In the Vertex heads any List second argument is read as a list of vertices, so to add a single List-valued vertex wrap it as {{...}}. Because a memoized hypergraph is held immutably, the edit builds a fresh object and never changes the original. To add hyperedges instead, use HypergraphEdgeAdd.