EdgeList¶

Status: Stable

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

Description¶

EdgeList[g]

gives the list of edges of the graph g.

Examples (7)¶

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

Basic examples (4)¶

In[1]:= EdgeList[Graph[{1,2,3},{1->2, 2<->3}]]
Out[1]= {1 -> 2, 2 <-> 3}

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

In[3]:= EdgeList[Graph[{1,2},{}]]
Out[3]= {}

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

Applications (3)¶

Undirected edges, in canonical order

In[5]:= EdgeList[CompleteGraph[3]]
Out[5]= {1 <-> 2, 1 <-> 3, 2 <-> 3}

Directed edges keep their arrows

In[6]:= EdgeList[Graph[{1 -> 2, 2 -> 3}]]
Out[6]= {1 -> 2, 2 -> 3}

The count is the list length

In[7]:= EdgeCount[CycleGraph[4]] == Length[EdgeList[CycleGraph[4]]]
Out[7]= True

Implementation notes¶

Algorithm. builtin_edge_list validates g and returns a deep copy of the graph's canonical edge sublist args[1], preserving stored order. Each element is already in the canonical two-argument DirectedEdge[u, v] / UndirectedEdge[u, v] form the constructor normalises edge sugar (u -> v, u <-> v) into, so EdgeList is the inverse of the edge half of Graph[...]. When the argument is not a valid graph the call is forwarded to hyp_edge_list (which returns the hyperedges of a Hypergraph) and otherwise yields NULL.

Data structures. The result is expr_copy(g->data.function.args[1]) — an independent List of edge nodes, so the caller can mutate or consume it without disturbing the graph. No adjacency structure is consulted.

Complexity / limits. O(E) for the copy, after an O(1) memo-hit (or O(V + E) first-time) validation. One-argument only; other arities return NULL.

Protected. A thin reader over the canonical form; unevaluated on a non-graph (see VertexList).
Edges print in operator form (1 -> 2, 2 <-> 3), but are DirectedEdge/UndirectedEdge internally.

Attributes: Protected.

References¶

See also: VertexList

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

Notes & additional examples¶

Notes¶

EdgeList[g] returns the graph's edges in the canonical two-argument form: UndirectedEdge[u, v] (printed u <-> v) and DirectedEdge[u, v] (printed u -> v). Edge sugar given to the constructor is already normalised to these heads, so EdgeList round-trips the edge half of Graph[...].

A Hypergraph argument returns its hyperedges; any other non-graph argument leaves the call unevaluated.