论文标题
$λ$ - 核心距离分区
$λ$-Core Distance Partitions
论文作者
论文摘要
图形的$λ$ - 核顶点对应于该图的通用邻接矩阵$ \ mathbf {u} $的某些特征向量的非零条目。我们根据$λ$ -Core顶点集及其社区定义了顶点集$ V $的分区，以距离$ r $ $，并给出许多结果，将图形的结构与本分区相关联。对于此类分区，我们还为图表的信息内容定义了一个熵度量，与$ \ Mathbf {u} $的每个独特的特征值$λ$有关，并讨论其属性和潜在的应用程序。
The $λ$-core vertices of a graph correspond to the non-zero entries of some eigenvector of $λ$ for a universal adjacency matrix $\mathbf{U}$ of the graph. We define a partition of the vertex set $V$ based on the $λ$-core vertex set and its neighbourhoods at a distance $r$, and give a number of results relating the structure of the graph to this partition. For such partitions, we also define an entropic measure for the information content of a graph, related to every distinct eigenvalue $λ$ of $\mathbf{U}$, and discuss its properties and potential applications.
