A Parsimonious Statistical Protocol for Generating Power-Law Networks

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We propose a new mechanism for generating net- works with a wide variety of degree distributions. The idea is a modification of the well-studied preferential attachment scheme in which the degree of each node is used to determine its evolving connectivity. Modifications to this base protocol to include features other than connectivity have been considered in building the network. However, schemes based on preferential attachment in any form require substantial information on the entire network. We propose instead a protocol based only on a single statistical feature which results from the reasonable assumption that the effect of various attributes, which determine the ability of each node to attract other nodes, is multiplicative. This composite attribute or fitness is lognormally distributed and is used in forming the complex network. We show that, by varying the parameters of the lognormal distribution, we can recover both exponential and power-law degree distributions. The exponents for the power-law case are in the correct range seen in real- world networks such as the World Wide Web and the Internet. Further, as power-law networks with exponents in the same range are a crucial ingredient of efficient search algorithms in peer-to- peer networks, we believe our network construct may serve as a basis for new protocols that will enable peer-to-peer networks to efficiently establish a topology conducive to optimized search procedures. Index Terms—Power-law networks, growing random networks, lognormal distribution, peer-to-peer networks, search in power- law networks