We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the $(m+1)$-uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We introduce some connectivity optimization problem into the hypergraph, and solve them with the algebraic connectivity. We introduce the Laplacian eigenmap algorithm to the hypergraph under our tensor product.

翻译：我们提出了一种与超图结构兼容的张量积结构。在该张量积下，我们定义了$(m+1)$-一致超图的代数连通度，并证明了其与顶点连通度的关系。我们将若干连通度优化问题引入超图，并利用代数连通度对其求解。我们还将拉普拉斯特征映射算法引入到我们所提出的张量积下的超图中。