VertexCount

Status: Stable

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

Description

VertexCount[g]

gives the number of vertices in the graph g.

Examples (8)

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

Basic examples (5)

In[1]:= VertexCount[Graph[{1,2,3,4},{1->2,2->3,3->4,4->1}]]
Out[1]= 4

In[2]:= EdgeCount[Graph[{1,2,3,4},{1->2,2->3,3->4,4->1}]]
Out[2]= 4

In[3]:= VertexCount[Graph[{}, {}]]
Out[3]= 0

In[4]:= EdgeCount[Graph[{1,2,3},{}]]
Out[4]= 0

In[5]:= EdgeCount[x]
Out[5]= EdgeCount[x]

Applications (3)

K6 has six vertices

In[6]:= VertexCount[CompleteGraph[6]]
Out[6]= 6

In[7]:= VertexCount[CycleGraph[4]]
Out[7]= 4

Vertices may be arbitrary symbols

In[8]:= VertexCount[Graph[{a, b, c}, {a <-> b}]]
Out[8]= 3

Implementation notes

Algorithm. builtin_vertex_count returns the number of vertices of g as an integer — a thin reader over the canonical form Graph[List verts, List edges]: the answer is the argument count of the vertex list. When the argument is not a valid graph it falls through to hyp_vertex_count, which handles a Hypergraph (and otherwise returns NULL, leaving the expression unevaluated). The companion EdgeCount is the identical reader over the edge list.

Data structures. None — it reads g->data.function.args[0]->...arg_count after graph_is_valid confirms the shape and populates the memo. The result is a fresh Integer.

Complexity / limits. O(1) for a canonical graph (plus the one-time O(V + E) validation on first contact with the node). Returns NULL for a non-graph, non-hypergraph argument.

• Protected. Cardinalities read from the canonical form; unevaluated on a non-graph (see VertexList).

Attributes: Protected.

References

See also: EdgeCount, VertexList

• Source: src/graph/counts.c
• Specification: docs/spec/builtins/graphs.md
• Tests: tests/test_graph.c
• Tests: tests/test_graph_metrics.c
• Tests: tests/test_graph_ops.c
• Tests: tests/test_hypergraph.c

Notes & additional examples

Notes

VertexCount[g] is the number of vertices, read directly off the canonical graph form. Vertices can be any expressions, not just integers, and an isolated vertex (one with no incident edge) still counts.

The parallel reader for edges is EdgeCount.