  In this paper we introduce the notion of a $d$-dimensional cycle which is a
homological generalization of the idea of a graph cycle to higher dimensions.
We examine both the combinatorial and homological properties of this structure
and use these results to describe the relationship between the combinatorial
structure of a simplicial complex and its simplicial homology. In particular,
we show that over any field of characteristic 2 the existence of non-zero
$d$-dimensional homology corresponds exactly to the presence of a
$d$-dimensional cycle in the simplicial complex. We also show that
$d$-dimensional cycles which are orientable give rise to non-zero simplicical
homology over any field.
