A preferential attachment model with random initial degrees

A preferential attachment model with random initial degrees

Deijfen, M.
Van den Esker, H.
Van der Hofstad, R.
Hooghiemstra, G.

Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics

2008-03-21

In this paper, a random graph process {G(t)} (ta parts per thousand yen1) is studied and its degree sequence is analyzed. Let {W (t) } (ta parts per thousand yen1) 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 of vertex t 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) } (ta parts per thousand yen1) and tau(P) the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze.

http://resolver.tudelft.nl/uuid:3db39217-05ae-4357-adcb-13e6a28960c8

https://doi.org/10.1007/s11512-007-0067-4

Springer

1871-2487

Arkiv för Matematik, 47 (1), 2009

Institutional Repository

journal article

(c) 2008 Deijfen, M.; Van den Esker, H.; Van der Hofstad, R.; Hooghiemstra, G.