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Degree Distribution of Competition-Induced Preferential Attachment Graphs | | N. Berger
; C. Borgs
; J. T. Chayes
; R. M. D’Souza
; R. D. Kleinberg
; | | Date: |
8 Feb 2005 | | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics; Probability; Networking and Internet Architecture | cond-mat.dis-nn cond-mat.stat-mech cs.NI math.PR | | Abstract: | We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is the first explanation of how preferential attachment can arise from a more basic underlying mechanism of local competition. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold. We also rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a ``fertility’’ parameter. We prove that the general model has a power-law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters. Limiting cases of the general model include the standard preferential attachment model without cutoff and the uniform attachment model. | | Source: | arXiv, cond-mat/0502205 | | Services: | Forum | Review | PDF | Favorites | |
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