论文标题
公共交通网络中的高级仪器
Spectra of hyperstars on public transportation networks
论文作者
论文摘要
本文的目的是引入一个模型来研究公共交通网络中广泛存在的结构。我们表明，通过超图，可以描述这些结构并研究其光谱之间的关系。为此，我们将$（m，k）$ - 星形的结构扩展到超图：$（m，k）$ - 超图中的高级巨星。同样，通过在超边权重的情况下给出适当的条件，我们证明了可计算值和多重性的矩阵特征值的存在，其中所考虑的矩阵是laplacian，邻接和过渡矩阵。通过单独考虑通用超图和均匀的超图的情况，我们证明具有$（m，k）$ - hyperstar对超图的两种顶点设置是可行的，可以使相同的特征值保持相同的特征值。最后，将一些有用的特征向量属性得出了具有合适矩阵的产品，我们将这些结果与在超图上的Fiedler光谱分区相关联。
The purpose of this paper is to introduce a model to study structures which are widely present in public transportation networks. We show that, through hypergraphs, one can describe these structures and investigate the relation between their spectra. To this aim, we extend the structure of $(m,k)$-stars on graphs to hypergraphs: the $(m,k)$-hyperstars on hypergraphs. Also, by giving suitable conditions on the hyperedge weights we prove the existence of matrix eigenvalues of computable values and multiplicities, where the matrices considered are Laplacian, adjacency and transition matrices. By considering separately the case of generic hypergraphs and uniform hypergraphs, we prove that two kinds of vertex set reductions on hypergraphs with $(m,k)$-hyperstar are feasible, keeping the same eigenvalues with reduced multiplicity. Finally, some useful eigenvectors properties are derived up to a product with a suitable matrix, and we relate these results to Fiedler spectral partitioning on the hypergraph.
