Abstract:We consider a preferential attachment process in which a multigraph is built one node at a time. The number of edges added at stage t, emanating from the new node, is given by some prescribed function f (t), generalising a model considered by Kleinberg and Kleinberg in 2005 where f was presumed constant. We show that if f (t) is asymptotically bounded above and below by linear functions in t, then with probability 1 the infinite limit of the process will be isomorphic to the Rado multigraph. This structure is … Show more
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