  We generalize the concept of a cycle from graphs to simplicial
  complexes. We show that a simplicial cycle is either a sequence of
  facets connected in the shape of a circle, or is a cone over such a
  structure. We show that a simplicial tree is a connected cycle-free
  simplicial complex, and use this characterization to produce an
  algorithm that checks in polynomial time whether a simplicial
  complex is a tree. We also present an efficient algorithm for
  checking whether a simplicial complex is grafted, and therefore
  Cohen-Macaulay.
