Pauls Scott D, Remondini Daniel
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066127. doi: 10.1103/PhysRevE.85.066127. Epub 2012 Jun 20.
We introduce a family of new centralities, the k-spectral centralities. k-spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.
我们引入了一类新的中心性，即k-谱中心性。k-谱中心性是一种关于与图相关联的图拉普拉斯算子变形的重要性度量。由于这种联系，k-谱中心性在频谱确定的信息方面有多种解释。我们在几个例子的背景下探讨这种中心性。对于稀疏无加权网络，1-谱中心性的行为与其他标准中心性类似，但对于密集加权网络，它们表现出不同的性质。总之，k-谱中心性提供了一种与其他已知度量不同的、用于衡量（单个网络元素以及整个子网）相关性的新颖且有用的度量方法。
