Growing network: Models following nonlinear preferential attachment rule

V.N. Zadorozhnyi and E.B. Yudin

Physica A: Statistical Mechanics and its Applications, 2015, vol. 428, issue C, 111-132

Abstract: We investigate the preferential attachment graphs proceeding from the following two assumptions. The first one: the probability that a new vertex connects to a vertex i is proportional to an arbitrary nonnegative function f of a vertex degree k. The second assumption: a new vertex can have a random number of edges. We derive formulas for any f to determine the vertex degree distribution {Qk} in generated graphs. The inverse problem is solved: we have obtained formulas, that allow from a given distribution {Qk} to determine f (the problem of a model calibration). The formulas allowing for any f to calculate the joint distribution of vertex degrees at the ends of randomly selected edge are also obtained. Some other results are presented in the paper.

Keywords: Networks; Random graphs; Nonlinear preferential attachment rule; Structural properties (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:428:y:2015:i:c:p:111-132

DOI: 10.1016/j.physa.2015.01.052

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