On the growth of a superlinear preferential attachment scheme

2017/04/19 by Sethuraman, Sunder, Venkataramani, Shankar C. · 1 citation
#37H10 #60G20 #Combinatorics (math.CO) #FOS: Mathematics #O5C20 #Probability (math.PR)

paper · doi:10.48550/arxiv.1704.05568

Abstract

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known that the graph evolution condenses, that is a.s. in the limit graph there will be a single random node with infinite degree, while all others have finite degree. In this note, we establish a.s. law of large numbers type limits and fluctuation results, as n\uparrow∞, for the counts of the number of nodes with degree k≥ 1 at time n≥ 1. These limits rigorously verify and extend a physical picture of Krapivisky, Redner and Leyvraz (2000) on how the condensation arises with respect to the degree distribution.

Cited by

• Self-Reinforced Preferential Attachment

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