On the effect of node sampling strategies on spectral Representation of graphs

Spectral graph theory has been an active research area, analyzing the structural properties of networks using the eigenvalues and eigenvectors of matrices, e.g., adjacency matrix and Laplacian matrix, that represent their structure. In this paper, we focus on a network representation called the spectral path, proposed by Jin et al. The spectral path is defined as a trajectory connecting low-order spectral moments — namely, the second-, third-, and fourth spectral moments — of subgraphs with different sizes. The spectral path is thought of as an embedding, and it can be useful for applications such as network classification. The aim of this paper is to explore the potential of the spectral path. More specifically, we try to answer the following research question: How does the sampling strategy affect the spectral path? Through experiments, we examine the effect of sampling strategies and demonstrate the effectiveness of combining multiple sampling strategies.