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- W4300007235 abstract "We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power -a, for some a in (0,1). Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a power law degree distribution with exponent 1+1/a whenever vertices are ranked according to their degree, their age, or a randomly chosen fitness value. We also investigate the case where the ranking is based on the initial rank of each vertex; the rank of existing vertices only changes to accommodate the new vertex. Here, we obtain a sharp threshold for power law behaviour. Only if initial ranks are biased towards lower ranks, or chosen uniformly at random, we obtain a power law degree distribution with exponent 1+1/a. This indicates that the power law degree distribution often observed in nature can be explained by a rank-based attachment scheme, based on a ranking scheme that can be derived from a number of different factors; the exponent of the power law can be seen as a measure of the strength of the attachment." @default.
- W4300007235 created "2022-10-03" @default.
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- W4300007235 date "2009-08-24" @default.
- W4300007235 modified "2023-09-25" @default.
- W4300007235 title "Rank-based attachment leads to power law graphs" @default.
- W4300007235 doi "https://doi.org/10.48550/arxiv.0908.3436" @default.
- W4300007235 hasPublicationYear "2009" @default.
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