StatGraph: an R package for complex network statistical analyses based on spectrum

The analysis of complex networks has traditionally relied on descriptive measures, such as centrality and clustering coefficients, as well as algorithms for detecting partitions and components. Additionally, a range of software packages has been designed for visualization and structural analysis. Although these approaches provide valuable information, they primarily focus on observable network features rather than their underlying generative mechanisms. We introduce statGraph , a nonparametric statistical framework for inferring properties of unobserved network generation mechanisms. At its core, statGraph leverages graph spectra, which intrinsically capture structural information and provide a robust basis for nonparametric inference. The package implements a range of methods, including graph entropy estimation, random graph parameter estimation, model selection procedures, statistical tests for comparing graphs, correlation analysis between sets of graphs, and graph clustering algorithms. By bridging graph theory and statistics via spectral analysis, statGraph provides a comprehensive toolkit for advancing the statistical analysis of complex networks.