Research on Network Similarity Comparison Method Based on Higher-Order Information

Quantifying structural similarity between complex networks presents a fundamental and formidable challenge in network science, which plays a crucial role in various fields, such as bioinformatics, social science, and economics, and serves as an effective method for network classification, temporal network evolution and network generated model evaluation, etc. Traditional network comparison methods often rely on simplistic structural properties such as node degree and network distance. However, these methods only consider the local or global aspect of a network, leading to inaccuracies in network similarity assessments. In this paper, we introduce a network similarity comparison method based on the high-order structure. This innovative approach takes into account both the global and local structures of a network, resulting in a more comprehensive and accurate quantification of the network difference. Specifically, we construct distributions of higher-order clustering coeffcients and distance between nodes within a network. The JensenShannon divergence, based on these two distributions, is used to quantitatively measure the similarity between two networks, offering a more refined and robust measure of network similarity. To validate the effectiveness of our proposed method, we conducted a series of comprehensive experiments on both artificial and real-world networks, spanning various domains and applications. By meticulously fine-tuning the parameters associated with three distinct artificial network generation models, we systematically compared the performance of our method under a wide range of parameter settings within the same network. In addition, we generated four different network models with varying levels of randomization, creating a diverse set of test cases to evaluate the method's robustness and adaptability. In artificial networks, our study rigorously compared our proposed method with other baseline techniques, consistently demonstrating its superior accuracy and stability through experimental results; In real networks, we selected datasets from diverse domains and confirmed the reliability of our method by conducting extensive similarity assessments between real networks and their perturbed reconstructed counterparts. Furthermore, in real networks, the rigorous comparison between our method and null models underscored its robustness and stability across a broad spectrum of scenarios and applications. Finally, a meticulous sensitivity analysis of the parameters revealed that our method exhibited remarkable performance consistency across networks of different types, scales, and complexities.