A connected graph G is spectrally non-redundant if the spectral radiuses of the connected induced subgraphs of G are all different. As observed by Fernandes, Júdice, and Trevisan (2017), for such graphs the number of connected induced subgraphs is equal to the number of complementarity eigenvalues. This note is an attempt at quantifying the so-called spectral redundancy phenomenon. Such a phenomenon occurs when there is a substantial amount of repetition among the spectral radiuses of the connected induced subgraphs.

中文翻译：

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连通诱导子图之间光谱半径的重复

一个连通图G ^是光谱非冗余如果的连接诱导子图的频谱半径ģ都是不同的。正如Fernandes，Júdice和Trevisan（2017）所观察到的那样，对于此类图，连接的诱导子图的数量等于互补特征值的数量。本文是对量化所谓的频谱冗余现象的尝试。当所连接的诱导子图的光谱半径之间存在大量重复时，会发生这种现象。