Link prediction in graphs is studied by modeling the dyadic interactions among two nodes. The relationships can be more complex than simple dyadic interactions and could require the user to model super-dyadic associations among nodes. Such interactions can be modeled using a hypergraph, which is a generalization of a graph where a hyperedge can connect more than two nodes. In this work, we consider the problem of hyperedge prediction in a k-uniform hypergraph. We utilize the tensor-based representation of hypergraphs and propose a novel interpretation of the tensor eigenvectors. This is further used to propose a hyperedge prediction algorithm. The proposed algorithm utilizes the Fiedler eigenvector computed using tensor eigenvalue decomposition of hypergraph Laplacian. The Fiedler eigenvector is used to evaluate the construction cost of new hyperedges, which is further utilized to determine the most probable hyperedges to be constructed. The functioning and efficacy of the proposed method are illustrated using some example hypergraphs and a few real datasets. The code for the proposed method is available on https://github.com/d-maurya/hypred_tensorEVD.

通过对两个节点之间的二元交互进行建模来研究图中的链接预测。这些关系可能比简单的二元交互更复杂，并且可能需要用户对节点之间的超二元关联进行建模。这种交互可以使用超图进行建模，超图是超边可以连接两个以上节点的图的泛化。在这项工作中，我们考虑了k均匀超图中的超边预测问题。我们利用超图的基于张量的表示，并提出了张量特征向量的新解释。这进一步用于提出超边缘预测算法。所提出的算法利用了使用超图拉普拉斯算子的张量特征值分解计算的Fiedler特征向量。这Fiedler特征向量用于评估新超边的构建成本，进一步用于确定最有可能构建的超边。使用一些示例超图和一些真实数据集说明了所提出方法的功能和功效。所提议方法的代码可在 https://github.com/d-maurya/hypred_tensorEVD 上获得。