关于一般超图中的邻接和e-邻接:一个新的e-邻接张量

Q2 Mathematics
X. Ouvrard , J.M. Le Goff , S. Marchand-Maillet
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引用次数: 6

摘要

在图中,邻接的概念是明确定义的:它是顶点之间的成对关系。超图中的邻接性必须整合超边的多半径性:需要通过引入两个新概念来正确定义邻接性的概念:k-邻接性- k个顶点在同一个超边上-和e-邻接性-给定超边的顶点是e邻接的。为了构建一个新的e-邻接张量,可以根据超图均匀化来解释,我们设计了两个过程:第一个是超图均匀化过程(HUP),第二个是多项式均匀化过程(PHP)。PHP允许构造e邻接张量,而HUP确保PHP保持可解释性。这个张量是对称的,可以用超边的数量来充分描述;它的顺序是超图的范围,而额外的维度允许捕获额外的超图结构信息,包括每个超边的k邻接的最大级别。讨论了光谱分析的一些结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Adjacency and e-Adjacency in General Hypergraphs: Towards a New e-Adjacency Tensor

In graphs, the concept of adjacency is clearly defined: it is a pairwise relationship between vertices. Adjacency in hypergraphs has to integrate hyperedge multi-adicity: the concept of adjacency needs to be defined properly by introducing two new concepts: k-adjacency – k vertices are in the same hyperedge – and e-adjacency – vertices of a given hyperedge are e-adjacent. In order to build a new e-adjacency tensor that is interpretable in terms of hypergraph uniformisation, we designed two processes: the first is a hypergraph uniformisation process (HUP) and the second is a polynomial homogeneisation process (PHP). The PHP allows the construction of the e-adjacency tensor while the HUP ensures that the PHP keeps interpretability. This tensor is symmetric and can be fully described by the number of hyperedges; its order is the range of the hypergraph, while extra dimensions allow to capture additional hypergraph structural information including the maximum level of k-adjacency of each hyperedge. Some results on spectral analysis are discussed.

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来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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