2012/08/24 by Jonathan Jordan, Jordan, Jonathan · 1 citation
Business, Management and Accounting · Psychology · Social Sciences · #05C82 #Business Strategy and Innovation #Evolutionary Game Theory and Cooperation #Evolutionary Psychology and Human Behavior #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1208.4938
openalex publication_date 2012/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that of the preferential attachment with multiplicative fitness models investigated by Borgs et al. When the metric space is finite, the degree distribution at each point of the space converges to a degree distribution which is an asymptotic power law whose index depends on the chosen point. For infinite metric spaces, we can show that for vertices in a Borel subset of S of positive measure the degree distribution converges to a distribution whose tail is close to that of a power law whose index again depends on the set.