This paper presents three power-law relationships observed in the topology of the Internet. The power-laws describe the distribution of graph properties such as node outdegree, and they fit real data with high correlation coefficients (96% or higher). These power-laws hold for three snapshots of the Internet between November 1997 and December 1998, despite a 45% growth in the network size during that period. The power-laws are used to estimate important parameters such as the average neighborhood size and to generate realistic topologies for simulation purposes. The three power-laws identified are: 1. The rank exponent R: The outdegree of a node is proportional to the rank of the node to the power of a constant. 2. The outdegree exponent O: The frequency of an outdegree is proportional to the outdegree to the power of a constant. 3. The hop-plot exponent H: The number of pairs of nodes within h hops is proportional to the number of hops to the power of a constant. These power-laws provide a concise description of the skewed distributions of graph properties and can be used to estimate important parameters of the Internet. They also help in generating realistic topologies for simulation purposes. The power-laws are also used to estimate the effective diameter of the Internet, which is the number of hops required to reach a "sufficiently large" part of the network. The effective diameter is calculated using the hop-plot exponent and the number of nodes in the network. The power-laws are also used to analyze the performance of network protocols. They provide a more accurate estimate of the average neighborhood size compared to the commonly used average-outdegree estimate. The power-laws are also used to predict the evolution of the Internet, and they suggest that the Internet topology will likely continue to follow power-laws in the future. The power-laws are also used to distinguish between different families of graphs and to characterize the topology of the Internet.This paper presents three power-law relationships observed in the topology of the Internet. The power-laws describe the distribution of graph properties such as node outdegree, and they fit real data with high correlation coefficients (96% or higher). These power-laws hold for three snapshots of the Internet between November 1997 and December 1998, despite a 45% growth in the network size during that period. The power-laws are used to estimate important parameters such as the average neighborhood size and to generate realistic topologies for simulation purposes. The three power-laws identified are: 1. The rank exponent R: The outdegree of a node is proportional to the rank of the node to the power of a constant. 2. The outdegree exponent O: The frequency of an outdegree is proportional to the outdegree to the power of a constant. 3. The hop-plot exponent H: The number of pairs of nodes within h hops is proportional to the number of hops to the power of a constant. These power-laws provide a concise description of the skewed distributions of graph properties and can be used to estimate important parameters of the Internet. They also help in generating realistic topologies for simulation purposes. The power-laws are also used to estimate the effective diameter of the Internet, which is the number of hops required to reach a "sufficiently large" part of the network. The effective diameter is calculated using the hop-plot exponent and the number of nodes in the network. The power-laws are also used to analyze the performance of network protocols. They provide a more accurate estimate of the average neighborhood size compared to the commonly used average-outdegree estimate. The power-laws are also used to predict the evolution of the Internet, and they suggest that the Internet topology will likely continue to follow power-laws in the future. The power-laws are also used to distinguish between different families of graphs and to characterize the topology of the Internet.