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Random Structures and Algorithms
Article . 2019 . Peer-reviewed
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Article . 2020
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Article . 2018
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Condensation in preferential attachment models with location‐based choice

Condensation in preferential attachment models with location-based choice
Authors: John Haslegrave; Jonathan H. Jordan; Mark Yarrow;

Condensation in preferential attachment models with location‐based choice

Abstract

We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model evolves in discrete time by selecting r vertices from the graph with replacement, with probabilities proportional to their degrees plus a constant α. A new vertex joins the network and attaches to one of these vertices according to a given probability associated to the ranking of their locations. We give conditions for the occurrence of condensation, showing the existence of phase transitions in α below which condensation occurs. The condensation in our model differs from that in preferential attachment models with fitness in that the condensation can occur at a random location, that it can be due to a persistent hub, and that there can be more than one point of condensation.

Country
United Kingdom
Keywords

preferential attachment, Preferential Attachment, Location, Applied Mathematics, Probability (math.PR), Random graphs (graph-theoretic aspects), Interacting random processes; statistical mechanics type models; percolation theory, Phase Transition, Mathematical Sciences, fitness, Random Graphs, phase transition, Fitness, FOS: Mathematics, Mathematics - Combinatorics, 05C82 (Primary) 05C80, 60J20, 90B15 (Secondary), Combinatorics (math.CO), QA, location, random graphs, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Top 10%
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bronze
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