A widespread methodology for modeling modern day information, which consists of high-dimensional digital measurements, is to use vine copulas; they can flexibly encode the underlying dependence structure of the data. Here we introduce a new algorithm to encode complete and truncated vines in a matrix, and as such, storing the information content of vines in a virtual environment. The conditional independence structure encoded by a vine can be represented in graph terms. We summarize these representations, and show equivalence between them. We show a new result, namely that when a perfect elimination ordering of a vine structure is given, then it can be uniquely represented with a matrix. Nápoles has shown a way to represent vines in a matrix, and we algorithmify this previous approach, while also showing a new method for constructing such a matrix, through cherry tree sequences, which can also store truncated vines. Moreover, this new algorithm can directly build truncated vines by storing each level separately - without building up the entire vine, which would be necessary in Nápoles' algorithm. We calculate the runtime of these algorithms. Lastly, we prove that these two matrix-building algorithms are equivalent if the same perfect elimination ordering is being used.