Vine copulas can efficiently model a large portion of probability distributions. This paper focuses on a more thorough understanding of their structures. We are building on well-known existing constructions to represent vine copulas with graphs as well as matrices. The graph representations include the regular, cherry and chordal graph sequence structures, which we show equivalence between. Importantly we also show that when a perfect elimination ordering of a vine structure is given, then it can always be uniquely represented with a matrix. O. M. N\'apoles has shown a way to represent them in a matrix, and we algorithmify this previous approach, while also showing a new method for constructing such a matrix, through cherry tree sequences. Lastly, we prove that these two matrix-building algorithms are equivalent if the same perfect elimination ordering is being used.

翻译：葡萄干瓜可以有效地模拟大部分的概率分布。 本文侧重于更透彻地了解它们的结构。 我们正在以众所周知的现有结构为基础, 以图表和矩阵来代表葡萄干椰子。 图表的表示方式包括常规结构、 樱桃结构、 和圆柱形图序列结构, 我们显示了这些结构之间的等同性 。 重要的是, 我们还要表明, 当给出了完全消除松树结构的顺序时, 它总是可以用一个矩阵来代表。 O. M. N\'apoles 已经展示了一种在矩阵中代表它们的方法, 我们用算法来解释先前的方法, 同时展示了一种通过樱桃树序列构建这种矩阵的新方法 。 最后, 我们证明, 如果使用同样的完全消除命令, 这两种矩阵构建的算法是等同的 。