EdgeIndex

Status: Stable

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

Description

EdgeIndex[g, e]

gives the position of the edge e in EdgeList[g] (an undirected edge matches either orientation; u->v and u\<->v sugar are accepted); EdgeIndex[g, {e1, ...}] gives a list of positions.

Examples (9)

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

Basic examples (6)

In[1]:= VertexIndex[Graph[{a<->b, b<->c}], b]
Out[1]= 2

In[2]:= VertexIndex[Graph[{a<->b, b<->c}], {c, a}]
Out[2]= {3, 1}

In[3]:= EdgeIndex[CycleGraph[4], 3<->2]
Out[3]= 2

In[4]:= EdgeIndex[CycleGraph[4], 3->4]
Out[4]= 3

In[5]:= EdgeIndex[CycleGraph[4], {1<->2, 4<->1}]
Out[5]= {1, 4}

In[6]:= EdgeIndex[Graph[{1->2}], 2->1]
Out[6]= EdgeIndex[Graph[<2 vertices, 1 edge>], 2 -> 1]

Applications (3)

Position of this edge in EdgeList

In[7]:= EdgeIndex[CycleGraph[4], 2 <-> 3]
Out[7]= 2

K3 lists {1<->2, 1<->3, 2<->3}

In[8]:= EdgeIndex[CompleteGraph[3], 1 <-> 3]
Out[8]= 2

A list of edges gives a list of positions

In[9]:= EdgeIndex[CycleGraph[5], {1 <-> 2, 3 <-> 4}]
Out[9]= {1, 3}

Implementation notes

Algorithm. builtin_edge_index gives the 1-based position of an edge in EdgeList[g]. A single edge argument — written u -> v, u <-> v, or an explicit DirectedEdge/UndirectedEdge — is resolved to its EdgeList position; an undirected edge matches either orientation. EdgeIndex[g, {e1, ...}] maps the resolver over a list and returns the list of positions. Any edge not present (or a mixed-up orientation for a directed edge) leaves the call unevaluated.

Data structures. It opens a GopsView over the graph (the shared borrowed view of vertices, integer endpoint arrays eu[]/ev[], and direction flags), parses each query edge to endpoint positions with gops_parse_edge, and resolves them through the subsystem's resolve_edges helper, which indexes g's edges so each lookup is a hash probe rather than a scan.

Complexity / limits. O(V + E) to build the view and edge index, then O(1) per queried edge. The companion VertexIndex does the same for vertices. Returns NULL (unevaluated) if any queried edge is absent.

• Protected. A non-graph first argument, or a vertex/edge not in the graph, is left unevaluated.
• EdgeIndex matches u -> v against an undirected edge of an undirected graph, as Mathematica does; an undirected edge matches either orientation.

Attributes: Protected.

References

See also: VertexIndex

• Source: src/graph/gops_edit.c
• Specification: docs/spec/builtins/graphs.md
• Tests: tests/test_graph_ops.c

Notes & additional examples

Notes

EdgeIndex[g, e] is the inverse of indexing EdgeList[g]: it reports where e sits in the edge list, counting from 1. An undirected edge matches in either orientation, and the sugar u -> v / u <-> v is accepted alongside explicit DirectedEdge / UndirectedEdge.

An edge that is not in the graph leaves the expression unevaluated rather than returning 0 or a Missing wrapper.