We propose a new paradigm for describing complex networks in terms of the spectrum of the adjacency matrix and its submatrices. We show that a variety of basic node information, such as degree, clique, and subgraph centrality, can be calculated analytically. Moreover, we find that energy of spectrum series can uncover randomness and complexity of network structure. Interestingly, it presents an universal linear growth pattern with the growth of networks. Furthermore, the spectrum series of synthetic and real networks present clearly self-similarity characteristics for which the associated scaling exponents remain constant. Our work reveals that spectrum series representation will provide an alternative perspective for studying and understanding structure and function of complex networks rather than connectivity.

我们提出了一种新的范式，用于根据邻接矩阵及其子矩阵的频谱描述复杂的网络。我们展示了各种基本节点信息，例如度，集团，以及子图的中心度，可以通过分析来计算。此外，我们发现频谱序列的能量可以揭示网络结构的随机性和复杂性。有趣的是，随着网络的增长，它呈现出一种普遍的线性增长模式。此外，合成网络和真实网络的频谱系列明显呈现出自相似特性，相关的缩放指数对其保持恒定。我们的工作表明，频谱序列表示将为研究和理解复杂网络的结构和功能（而不是连通性）提供一个替代的视角。