数据的离散性对特征向量中心性的影响
On the Effect of Data Dimensionality on Eigenvector Centrality
摘要：
图表（即，网络）已经成为表示和分析关系数据的整体工具。数据收集的进步导致了多关系数据集，这些数据集表现出更大的深度和范围。在某些情况下，可以使用超图对这些数据进行建模。然而，在实践中，分析师通常会减少数据的维度（无论是有意识的还是其他的），以适应传统的图模型。谱超图理论是近年来出现的研究一致超图的邻接超矩阵特征对的理论。我们展示了如何通过与上述超图相关联的超矩阵分析多关系数据，可以得出与将数据投影到其共生矩阵时不同的结论。特别地，我们提供了一个均匀超图的例子，其中最中心的顶点（à la eigencentrality）根据相关矩阵的阶而变化。据我们所知，这是第一个已知的超图表现出这种性质。
英文摘要：
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.
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