论文标题
矩阵加权图中的扩展
Expansion in Matrix-Weighted Graphs
论文作者
论文摘要
矩阵加权图是一个无方向的图形，其中分配给每个边缘的$ k \ times k $阳性矩阵。对于此类图，具有Laplacian和邻接矩阵的天然概括。这些矩阵可用于定义和控制矩阵加权图的扩展。特别是，用于基质加权图的膨胀剂混合引理的类似物和cheeger型不平等的一半。矩阵加权扩展器图的一个新定义表明，矩阵加权图的家族的诱人可能性比 - 拉马尼亚膨胀更好。
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to define and control expansion for matrix-weighted graphs. In particular, an analogue of the expander mixing lemma and one half of a Cheeger-type inequality hold for matrix-weighted graphs. A new definition of a matrix-weighted expander graph suggests the tantalizing possibility of families of matrix-weighted graphs with better-than-Ramanujan expansion.
