TY - JOUR
T1 - Connectivity transitions in networks with super-linear preferential attachment
AU - Oliveira, Roberto
AU - Spencer, Joel
N1 - Publisher Copyright:
© A K Peters, Ltd.
PY - 2005/1/1
Y1 - 2005/1/1
N2 - We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the pth power of the in-degree of b. We restrict to the super-linear case p > 1. When (Formula presented), the structure of the final countable tree is determined. There is a finite tree T with distinguished v (which has a limiting distribution) on which is “glued” a specific infinite tree; v has an infinite number of children, an infinite number of which have k − 1 children, and there are only a finite number of nodes (possibly only v) with k or more children. Our basic technique is to embed the discrete process in a continuous time process using exponential random variables, a technique that has previously been employed in the study of balls-in-bins processes with feedback.
AB - We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the pth power of the in-degree of b. We restrict to the super-linear case p > 1. When (Formula presented), the structure of the final countable tree is determined. There is a finite tree T with distinguished v (which has a limiting distribution) on which is “glued” a specific infinite tree; v has an infinite number of children, an infinite number of which have k − 1 children, and there are only a finite number of nodes (possibly only v) with k or more children. Our basic technique is to embed the discrete process in a continuous time process using exponential random variables, a technique that has previously been employed in the study of balls-in-bins processes with feedback.
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U2 - 10.1080/15427951.2005.10129101
DO - 10.1080/15427951.2005.10129101
M3 - Article
AN - SCOPUS:50249104858
SN - 1542-7951
VL - 2
SP - 121
EP - 163
JO - Internet Mathematics
JF - Internet Mathematics
IS - 2
ER -