A triangle in a graph is a triangle graph subgraph, i.e., a 
(or equivalently, a 
)-subgraph.
There is a simple formula counting the number of triangles in an undirected
graph, namely
where 
denotes the matrix trace and 
is the graph's adjacency matrix
(Harary and Manvel 1972).
A graph with no triangles is said to be a triangle-free
graph.
See also
Graph Cycle,
Graph Tetrahedron,
Subgraph,
Triangle,
Triangle Graph,
Triangle-Free
Graph
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References
Harary, F. and Manvel, B. "On the Number of Cycles
in a Graph." Mat. Časopis Sloven. Akad. Vied 21, 55-63, 1971.
Cite this as:
Weisstein, Eric W. "Graph Triangle." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphTriangle.html
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