In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, this type of data arises for structures that are richer than graphs, because they involve the interactions of larger sets; for example, the core nodes might be a set of individuals under surveillance, where we observe the attendees of meetings involving at least one of the core individuals. We model such scenarios using hypergraphs, and we study the problem of core recovery: if we observe the hypergraph but not the labels of core and fringe nodes, can we recover the ‘planted’ set of core nodes in the hypergraph? We provide a theoretical framework for analyzing the recovery of such a set of core nodes and use our theory to develop a practical and scalable algorithm for core recovery. The crux of our analysis and algorithm is that the core nodes are a hitting set of the hypergraph, meaning that every hyperedge has at least one node in the set of core nodes. We demonstrate the efficacy of our algorithm on a number of real-world datasets, outperforming competitive baselines derived from network centrality and core-periphery measures.

在各种应用领域，网络数据是通过测量涉及某些特定核心节点集的交互来收集的。这导致网络数据集包含核心节点以及可能更大的一组边缘节点，这些边缘节点都至少与核心节点有一个交互。在许多环境中，这种类型的数据出现在比图更丰富的结构中，因为它们涉及更大集合的交互；例如，核心节点可能是一组受监视的个人，我们在其中观察涉及至少一个核心个人的会议的与会者。我们使用超图对此类场景进行建模，我们研究核心恢复问题：如果我们观察超图而不是核心和边缘节点的标签，我们是否可以恢复超图中“种植”的核心节点集？我们为分析这样一组核心节点的恢复提供了一个理论框架，并使用我们的理论开发了一种实用且可扩展的核心恢复算法。我们的分析和算法的关键是核心节点是超图的命中集，这意味着每个超边在核心节点集中至少有一个节点。我们证明了我们的算法在许多真实世界数据集上的有效性，优于源自网络中心性和核心外围措施的竞争基线。