Kronecker graphs are a generative model for networks that can produce graphs with properties observed in real networks, such as heavy-tailed degree distributions, small diameters, and densification over time. The model uses the Kronecker product of matrices to generate graphs recursively, allowing for efficient computation and analysis. The paper introduces KRONFIT, a fast algorithm for fitting Kronecker graphs to real networks, which can accurately model network properties using only four parameters. Kronecker graphs are mathematically tractable and can be used for network analysis, simulations, and data anonymization. The model is shown to match real-world network patterns, including small-world properties and temporal evolution. The paper also discusses the properties of Kronecker graphs, including their degree distributions, eigenvalues, and connectivity, and presents a stochastic version of the model that avoids "staircase effects" in degree and spectral properties. The model is applied to various real and synthetic networks, demonstrating its effectiveness in capturing network structure and behavior.Kronecker graphs are a generative model for networks that can produce graphs with properties observed in real networks, such as heavy-tailed degree distributions, small diameters, and densification over time. The model uses the Kronecker product of matrices to generate graphs recursively, allowing for efficient computation and analysis. The paper introduces KRONFIT, a fast algorithm for fitting Kronecker graphs to real networks, which can accurately model network properties using only four parameters. Kronecker graphs are mathematically tractable and can be used for network analysis, simulations, and data anonymization. The model is shown to match real-world network patterns, including small-world properties and temporal evolution. The paper also discusses the properties of Kronecker graphs, including their degree distributions, eigenvalues, and connectivity, and presents a stochastic version of the model that avoids "staircase effects" in degree and spectral properties. The model is applied to various real and synthetic networks, demonstrating its effectiveness in capturing network structure and behavior.