WeightedGraphQ

Status: Stable

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

Description

WeightedGraphQ[g]

gives True if g carries edge weights (EdgeWeight).

Examples (5)

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

Options (1)

In[1]:= {WeightedGraphQ[Graph[{1,2},{1<->2},EdgeWeight->{3}]], WeightedGraphQ[CycleGraph[3]], EdgeWeightedGraphQ[Graph[{1,2},{1<->2},EdgeWeight->{3}]], EdgeWeightedGraphQ[CycleGraph[3]], WeightedGraphQ[x]}
Out[1]= {True, False, True, False, False}

Applications (4)

Carries an EdgeWeight list

In[2]:= WeightedGraphQ[Graph[{1 -> 2, 2 -> 3}, EdgeWeight -> {5, 7}]]
Out[2]= True

An undirected weighted edge

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

A generator graph carries no weights

In[4]:= WeightedGraphQ[CompleteGraph[3]]
Out[4]= False

Unweighted, so False

In[5]:= WeightedGraphQ[CycleGraph[4]]
Out[5]= False

Implementation notes

Algorithm. builtin_weighted_graph_q returns True iff g is a valid graph that carries an EdgeWeight option list — the single test graph_is_valid(g) && graph_edge_weight_list(g) != NULL. A graph built with EdgeWeight -> {w1, ...} stores that list in the canonical 3-argument form; an unweighted graph has no such list and gives False. EdgeWeightedGraphQ is defined to call this same function, because Mathilda has no vertex weights and so the edge-weighted and weighted questions coincide.

Data structures. graph_edge_weight_list returns a borrowed pointer to the EdgeWeight List stored inside the canonical Graph[List verts, List edges, opts...] tree (per-edge options are read by key, not position — see graph.h). graph_is_valid is the memoized validator, so the validity half is O(1) after the first query. gops_truth builds the result symbol.

Complexity / limits. O(1) apart from the first validation pass. The test is purely presence-of-option: it does not inspect whether the stored weights are numeric or non-negative (that stricter check is graph_weights_usable, used by the shortest-path code). A non-graph argument gives False and never stays unevaluated.

• Protected. A non-graph argument gives False.

Attributes: Protected.

References

See also: EdgeWeightedGraphQ, EdgeWeight

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

Notes & additional examples

Notes

WeightedGraphQ[g] is True exactly when g is a valid graph built with an EdgeWeight option. It coincides with EdgeWeightedGraphQ — Mathilda has no vertex weights, so a graph is weighted iff its edges are. The test checks only for the presence of the weight list, not that the weights are numeric or usable by a shortest-path algorithm.

An unweighted graph (every accessor then treats each edge's weight as 1) gives False, as does any non-graph argument.