SimpleGraphQ
SimpleGraphQ[g]
yields True if the graph g is a simple graph and False otherwise.
Examples
open all close allBasic Examples (2)
Scope (5)
SimpleGraphQ works with undirected graphs:
SimpleGraphQ[[image]]SimpleGraphQ[[image]]SimpleGraphQ[[image]]SimpleGraphQ[[image]]SimpleGraphQ works with large graphs:
GridGraph[{10, 10, 10, 10}];SimpleGraphQ[%]//TimingProperties & Relations (8)
A graph with self-loops is not simple:
Graph[{12, 23, 31, 11}]{SimpleGraphQ[%], LoopFreeGraphQ[%]}A simple graph can have a cycle:
GridGraph[{2, 3}]{SimpleGraphQ[%], AcyclicGraphQ[%]}A simple graph can be bipartite:
CompleteGraph[{2, 3}]{SimpleGraphQ[%], BipartiteGraphQ[%]}A PathGraph is always simple:
g = GridGraph[{1, 5}]PathGraphQ[g]SimpleGraphQ [g]The adjacency matrix of a simple graph has zeros on the diagonal:
g = CycleGraph[4]SimpleGraphQ[g]Diagonal[AdjacencyMatrix[g]]//NormalThe incidence matrix of a simple graph has entries -1, 0, or 1:
g = Graph[{12, 23, 31}, EdgeStyle -> Arrowheads[Small]]IncidenceMatrix[g]//MatrixFormAll vertices of a simple graph have maximum degree less than the number of vertices:
g = WheelGraph[6]SimpleGraphQ[g]Max[VertexDegree[g]] < VertexCount[g]A nontrivial simple graph must have at least one pair of vertices with the same degree:
g = GridGraph[{2, 3}]SimpleGraphQ[g]VertexDegree[g]Possible Issues (2)
A simple graph can have two edges between the same vertices but with opposite direction:
SimpleGraphQ[[image]]SimpleGraphQ gives False for non-explicit graphs:
SimpleGraphQ[CompleteGraph[n]]Text
Wolfram Research (2010), SimpleGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SimpleGraphQ.html.
CMS
Wolfram Language. 2010. "SimpleGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SimpleGraphQ.html.
APA
Wolfram Language. (2010). SimpleGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SimpleGraphQ.html