A statistical construction of power-law networks

We propose a new mechanism for generating networks 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, some of the existing models are merely formulaic and do not offer an explanation that can be interpreted naturally or intuitively, while the others require certain information that is not available in many real-world circumstances. 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. Further, as power-law networks with exponents in the same range are a crucial ingredient of efficient search algorithms in P2P networks, we believe our network construct may serve as a basis for new protocols that will enable P2P networks to efficiently establish a topology conducive to optimised search procedures.

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