Summary: Suppose \(V\) is a finite set and \(\mathcal{C}\) a collection of subsets of \(V\) that contains \(\empty\) and \(V\) and is closed under taking intersections. Then \(\mathcal{C}\) is called a convexity and the ordered pair \((V, \mathcal{C})\) is called an aligned space and the elements of \(\mathcal{C}\) are referred to as convex sets. For a set \(S\subseteq V\), the convex hull of \(S\) relative to \(\mathcal{C}\), denoted by \(\mathrm{CH}_{\mathcal{C}}(S)\), is the smallest convex set containing \(S\). A set \(S\) of vertices in a graph \(G\) with vertex set \(V\) is digitally convex if for every vertex \(v \in V\), \(N[v]\subseteq N[S]\) implies \(v \in S\). It is shown that every tree is uniquely determined by its digitally convex sets. These ideas can be used to show that every graph with girth at least 7 is uniquely determined by its digitally convex sets. Given the digitally convex sets of a graph it can be determined efficiently, as a function of the number of convex sets, if these are those of a tree.