A Spectral Representation of Networks: The Path of Subgraphs
A Spectral Representation of Networks: The Path of Subgraphs
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DOI：
10.1145/3534678.3539433
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
Shengmin Jin;Hao Tian;Jiayu Li;R. Zafarani
中科院分区：
文献类型：
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作者：
Shengmin Jin;Hao Tian;Jiayu Li;R. Zafarani
网络表示学习在网络研究中发挥了至关重要的作用。研究图的一种方法是关注其谱，即其相关矩阵的特征值分布。谱图理论的最新进展表明，网络的谱矩可用于捕获网络结构和各种图属性。然而，有时不同结构或大小的网络可以具有相同或相似的谱矩，更不用说共谱图的存在了。为了解决这些问题，我们提出了一种依赖于子图的光谱信息的 3D 网络表示：光谱路径，连接网络的光谱矩及其不同大小的子图的光谱矩的路径。我们证明了谱路径是可解释的，并且可以捕获网络及其子图之间的关系，为此我们提供了理论基础。我们证明了光谱路径在网络可视化和网络识别等应用中的有效性。
Network representation learning has played a critical role in studying networks. One way to study a graph is to focus on its spectrum, i.e., the eigenvalue distribution of its associated matrices. Recent advancements in spectral graph theory show that spectral moments of a network can be used to capture the network structure and various graph properties. However, sometimes networks with different structures or sizes can have the same or similar spectral moments, not to mention the existence of the cospectral graphs. To address such problems, we propose a 3D network representation that relies on the spectral information of subgraphs: the Spectral Path, a path connecting the spectral moments of the network and those of its subgraphs of different sizes. We show that the spectral path is interpretable and can capture relationship between a network and its subgraphs, for which we present a theoretical foundation. We demonstrate the effectiveness of the spectral path in applications such as network visualization and network identification.