论文标题
在某些HyperGraphs的一般操作员上
On Some General Operators of Hypergraphs
论文作者
论文摘要
在这里，我们介绍了连接运算符，即扩散操作员，一般拉普拉斯运算符和一般的邻接操作员，用于HyperGraphs。这些操作员是一些与超图相关的连通性矩阵显然不同的常规概念的概括。实际上，我们在这里介绍了一个统一的框架，用于研究与超图相关的连接算子的不同变化。计算了与某些类别超图相关联的一般连接运算符的特征值和相应的特征空间。从我们新介绍的运营商的角度研究了诸如超图，动力网络和疾病传播之类的应用。我们还得出了弱连接性数量，顶点程度，最大切割，两部分宽度和等法超图的光谱界限。
Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some conventional notions of apparently different connectivity matrices associated with hypergraphs. In fact, we introduce here a unified framework for studying different variations of the connectivity operators associated with hypergraphs at the same time. Eigenvalues and corresponding eigenspaces of the general connectivity operators associated with some classes of hypergraphs are computed. Applications such as random walks on hypergraphs, dynamical networks, and disease transmission on hypergraphs are studied from the perspective of our newly introduced operators. We also derive spectral bounds for the weak connectivity number, degree of vertices, maximum cut, bipartition width, and isoperimetric constant of hypergraphs.
