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2004
Springer

A Geometric Preferential Attachment Model of Networks

12 years 5 months ago
A Geometric Preferential Attachment Model of Networks
We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. The vertices of Gn are n sequentially generated points x1, x2, . . . , xn chosen uniformly at random from the unit sphere in R3 . After generating xt, we randomly connect it to m points from those points in x1, x2, . . . , xt−1 which are within distance r. Neighbors are chosen with probability proportional to their current degree and a parameter α biasses the choice towards self loops. We show that if m is sufficiently large, if r ≥ ln n/n1/2−β for some constant β, and if α > 2, then whp at time n the number of vertices of degree
Abraham Flaxman, Alan M. Frieze, Juan Vera
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Where WAW
Authors Abraham Flaxman, Alan M. Frieze, Juan Vera
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