A preferential attachment model with random initial degrees

Details A preferential attachment model with random initial degrees A preferential attachment model with random initial degrees

2007-05-29

arxiv.org/abs/0705.4151v1

Mathematics

Probability

Scientific paper

10.1007/s11512-007-0067-4

In this paper, a random graph process {G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let {W_t}_{t\geq 1} be an i.i.d. sequence. The graph process is defined so that, at each integer time t, a new vertex, with W_t edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on G(t-1), the probability that a given edge is connected to vertex i is proportional to d_i(t-1)+\delta, where d_i(t-1) is the degree of vertex i at time t-1, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent \tau=\min{\tau_{W}, \tau_{P}}, where \tau_{W} is the power-law exponent of the initial degrees {W_t}_{t\geq 1} and $\tau_{P} the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.

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