论文标题
关于数据维度对特征向量中心性的影响
On the Effect of Data Dimensionality on Eigenvector Centrality
论文作者
论文摘要
图（即网络）已成为表示和分析关系数据的组成工具。数据收集的进步导致了具有更大深度和范围的多关系数据集。在某些情况下，可以使用HyperGraph对这些数据进行建模。但是，在实践中，分析师通常会降低数据的维度（无论是有意识还是其他）以适应传统的图形模型。近年来，光谱超图理论已经出现了，研究了均匀超图的邻接超矩阵的特征。我们展示了通过与上述超图关联的超质量分析多脉络数据的分析如何导致结论与数据投影到其共发生矩阵时的结论不同。特别是，我们提供了一个均匀的超图的示例，其中最中心的顶点（特征性）会根据相关矩阵的顺序而变化。据我们所知，这是展示此属性的第一个已知的超图。
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this data can be modeled using a hypergraph. However, in practice analysts typically reduce the dimensionality of the data (whether consciously or otherwise) to accommodate a traditional graph model. In recent years spectral hypergraph theory has emerged to study the eigenpairs of the adjacency hypermatrix of a uniform hypergraph. We show how analyzing multi-relational data, via a hypermatrix associated to the aforementioned hypergraph, can lead to conclusions different from those when the data is projected down to its co-occurrence matrix. In particular, we provide an example of a uniform hypergraph where the most central vertex (à la eigencentrality) changes depending on the order of the associated matrix. To the best of our knowledge this is the first known hypergraph to exhibit this property.
