VertexList¶

Status: Stable

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

Description¶

VertexList[g]

gives the list of vertices of the graph g.

Examples (6)¶

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

Basic examples (4)¶

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

In[2]:= VertexList[Graph[{c->a, a->b}]]
Out[2]= {c, a, b}

In[3]:= VertexList[Graph[{}, {}]]
Out[3]= {}

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

Applications (2)¶

Vertices derived from the edges

In[5]:= VertexList[Graph[{1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4}]]
Out[5]= {1, 2, 3, 4}

Vertices may be any expressions

In[6]:= VertexList[PathGraph[{a, b, c}]]
Out[6]= {a, b, c}

Implementation notes¶

Algorithm. builtin_vertex_list is a thin reader: for a valid graph it returns a copy of the graph's vertex List — the first argument of the canonical Graph[List[verts], List[edges]] node — in canonical order, with no computation. For a non-graph argument it defers to the hypergraph reader hyp_vertex_list, which handles a Hypergraph[...] argument or returns unevaluated.

Data structures. None beyond the deep copy of the stored vertex list; the canonical graph already holds its vertices in the order VertexList reports.

Complexity / limits. O(V) for the copy. Always exactly one argument.

Protected. The query/representation heads (VertexList, EdgeList, VertexCount, EdgeCount, AdjacencyList, VertexDegree, VertexInDegree, VertexOutDegree, EdgeWeight) are all thin readers over the canonical form and return unevaluated on a non-graph argument.
Canonical order is the explicit vertex list, or first-appearance order when Graph[e] derived the vertices from the edges.

Attributes: Protected.

References¶

Source: src/graph/vertexlist.c
Specification: docs/spec/builtins/graphs.md
Tests: tests/test_graph.c
Tests: tests/test_graph_algos.c
Tests: tests/test_graph_ops.c
Tests: tests/test_hypergraph.c

Notes & additional examples¶

Notes¶

VertexList[g] returns the vertices of g in canonical order. When a graph is built from edges alone, the vertices are derived from the edge endpoints in order of first appearance.

Vertices are arbitrary expressions, not just integers; a path on symbols a, b, c lists them unchanged.