https://doi.org/10.1140/epjb/e2009-00211-7
Connectivity of growing networks with link constraints
1
College of
Physics and Electronic Information Engineering, Wenzhou
University, 325035, Wenzhou, P.R. China
2
National Laboratory of Infrared Physics,
Shanghai Institute of Technical Physics, Chinese Academy of
Sciences, 200083, Shanghai, P.R. China
Corresponding author: a kejianhong@yahoo.com.cn
Received:
2
February
2009
Published online:
23
June
2009
We propose a growing network model with link constraint, in which new nodes are continuously introduced into the system and immediately connected to preexisting nodes, and any arbitrary node cannot receive new links when it reaches a maximum number of links km. The connectivity of the network model is then investigated by means of the rate equation approach. For the connection kernel A(k)=kγ, the degree distribution nk takes a power law if γ≥1 and decays stretched exponentially if 0≤γ< 1. We also consider a network system with the connection kernel A(k)=kα(km-k)β. It is found that nk approaches a power law in the α> 1 case and has a stretched exponential decay in the 0≤α< 1 case, while it can take a power law with exponential truncation in the special α=β=1 case. Moreover, nk may have a U-type structure if α> β.
PACS: 89.75.Hc – Networks and genealogical trees / 05.20.Dd – Kinetic theory / 87.23.Ge – Dynamics of social systems / 05.10.Ln – Monte Carlo methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009