On Power-Law Relationships of the Internet Topology
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چکیده
Describing graphs: Exponents vs. Averages. Power-laws provide a new way to describe topological properties. Average values falsely imply a uniform distribution, and they can be misleading. For example, 85% of the AS-nodes in December 1998 had an outdegree less than the average outdegree! Protocol performance: Formulas based on power-laws provide estimates for the effective diameter, the average neighbourhood size, and the number of edges of a graph. This way, one can fine-tune and analyze the performance and the complexity of several Internet protocols. Graph Generation and Selection: Power-laws can be used to characterize graph topologies. This way, the power-laws can be used as a composite “qualifying exam” for the realism of a graph. Predictions and Extrapolations: Power-laws offer guidelines for answering “what-if” questions. One can predict useful parameters of the Internet under different hypotheses and assumptions.
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