  Preferential attachment models have been widely studied in complex networks,
because they can explain the formation of many networks like social networks,
citation networks, power grids, and biological networks, to name a few.
Motivated by the application of key predistribution in wireless sensor networks
(WSN), we initiate the study of preferential attachment with degree bound.
  Our paper has two important contributions to two different areas. The first
is a contribution in the study of complex networks. We propose preferential
attachment model with degree bound for the first time. In the normal
preferential attachment model, the degree distribution follows a power law,
with many nodes of low degree and a few nodes of high degree. In our scheme,
the nodes can have a maximum degree $d_{\max}$, where $d_{\max}$ is an integer
chosen according to the application. The second is in the security of wireless
sensor networks. We propose a new key predistribution scheme based on the above
model. The important features of this model are that the network is fully
connected, it has fewer keys, has larger size of the giant component and lower
average path length compared with traditional key predistribution schemes and
comparable resilience to random node attacks.
  We argue that in many networks like key predistribution and Internet of
Things, having nodes of very high degree will be a bottle-neck in
communication. Thus, studying preferential attachment model with degree bound
will open up new directions in the study of complex networks, and will have
many applications in real world scenarios.
