# Cactus graph

## Mathematical tree of cycles / From Wikipedia, the free encyclopedia

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In graph theory, a **cactus** (sometimes called a **cactus tree**) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently, it is a connected graph in which every edge belongs to at most one simple cycle, or (for nontrivial cacti) in which every block (maximal subgraph without a cut-vertex) is an edge or a cycle.

Mathematical tree of cycles