The paper proposes a random graph model, specifically a sparse random graph with given degree sequences, to study massive graphs. The model is characterized by two parameters: log-size and log-log growth rate, which capture universal characteristics of large graphs. The authors derive various properties of the graph from these parameters, such as the expected distribution of connected component sizes. They demonstrate the consistency of their model with real-world data from telecommunications, discussing threshold functions, giant components, and the evolution of random graphs in this model. The paper also compares the model's results with exact connectivity data for call graphs, showing that the model captures some structural properties of the Web and other real-world graphs. The authors conclude by highlighting the robustness of their model and the need for further research to understand the phase transition of giant components and the behavior of tiny components in realistic graphs.The paper proposes a random graph model, specifically a sparse random graph with given degree sequences, to study massive graphs. The model is characterized by two parameters: log-size and log-log growth rate, which capture universal characteristics of large graphs. The authors derive various properties of the graph from these parameters, such as the expected distribution of connected component sizes. They demonstrate the consistency of their model with real-world data from telecommunications, discussing threshold functions, giant components, and the evolution of random graphs in this model. The paper also compares the model's results with exact connectivity data for call graphs, showing that the model captures some structural properties of the Web and other real-world graphs. The authors conclude by highlighting the robustness of their model and the need for further research to understand the phase transition of giant components and the behavior of tiny components in realistic graphs.