EmptyGraphQ¶

Status: Stable

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

Description¶

EmptyGraphQ[g]

gives True if g is a graph with no edges (it may have vertices), and False otherwise.

Examples (6)¶

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

Basic examples (4)¶

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

In[2]:= EmptyGraphQ[Graph[{},{}]]
Out[2]= True

In[3]:= EmptyGraphQ[PathGraph[2]]
Out[3]= False

In[4]:= EmptyGraphQ[5]
Out[4]= False

Applications (2)¶

Isolated vertices, no edges

In[5]:= EmptyGraphQ[Graph[{1, 2, 3}, {}]]
Out[5]= True

Has edges

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

Implementation notes¶

Algorithm. builtin_empty_graph_q is a direct structural predicate: it returns True iff its argument is a valid graph whose edge list is empty. The vertex count is irrelevant, so a graph of isolated vertices counts as empty. No adjacency is built; it reads the length of the edge List (the graph's second argument) after validation.

Data structures. None beyond the validated-graph node — the edge-list length comes straight from the expression, and validation itself is served from the per-node memo.

Complexity / limits. O(1) after the graph's one-time validation. Exactly one argument. A non-graph argument returns False (it is a predicate), never unevaluated.

Protected. Any number of vertices, including none. False for a non-graph (see UndirectedGraphQ).

Attributes: Protected.

References¶

See also: UndirectedGraphQ

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

Notes & additional examples¶

Notes¶

A graph is empty when it has no edges, whatever its vertices — a set of isolated vertices is an empty graph. The predicate is about edges only; VertexCount can be any value.

Like the other ...Q predicates it returns False for a non-graph argument rather than staying unevaluated.