We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set of connected triples, making unique reconstruction of the original graph from the triples impossible. We identify some families of graphs (including triangle-free graphs) for which all graphs have a different set of connected triples. We also give algorithms that reconstruct a graph from a set of triples, and for testing if this reconstruction is unique. Finally, we study a possible extension of the model in which the subsets of size $k$ that induce a connected graph are given for larger (fixed) values of $k$.

翻译：我们提出了一种新的图不确定模型：输入不包含图的所有边，而是给定所有构成连通子图的三元组顶点。一般情况下，不同的（带标签）图可能具有相同的连通三元组集合，这使得从三元组唯一重构原始图变得不可能。我们识别了某些图族（包括无三角形图），在这些图族中所有图都具有不同的连通三元组集合。我们还给出了从三元组集合重构图的算法，以及检验该重构是否唯一的算法。最后，我们研究了该模型的一种可能扩展，其中给定诱导连通图的 $k$ 元子集（对于更大的固定 $k$ 值）。