  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 \textit{Fiedler} eigenvector computed using tensor
eigenvalue decomposition of hypergraph Laplacian. The \textit{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
