论文标题
超图上的平均过程
An Averaging Processes on Hypergraphs
论文作者
论文摘要
考虑HyperGraph $ h $上的以下迭代过程。每个顶点$ v $具有初始顶点重量。在每个步骤中，我们按随机选择一个$ h $中的边缘$ f $，对于$ f $中的每个顶点$ v $，我们用$ f $中所有顶点的平均值代替了$ v $的权重。这是图形上的交互过程的概括，首先是Aldous和Lanoue提出的。在本文中，我们使用laplacian的特征值用于超图，以绑定迭代平均过程的收敛速率。
Consider the following iterated process on a hypergraph $H$. Each vertex $v$ has an initial vertex weight. At each step, we uniformly at random select an edge $F$ in $H$, and for each vertex $v$ in $F$ we replace the weight of $v$ by the average value of the vertex weights over all vertices in $F$. This is a generalization of an interactive process on graphs, first proposed by Aldous and Lanoue. In this paper, we use the eigenvalues of a Laplacian for hypergraphs to bound the rate of convergence for the iterated averaging process.
