# Girth (graph theory)

## Length of a shortest cycle contained in the graph / From Wikipedia, the free encyclopedia

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In graph theory, the **girth** of an undirected graph is the length of a shortest cycle contained in the graph.^{[1]} If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity.^{[2]}
For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A graph with girth four or more is triangle-free.