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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 firstis a contribution in the study of complex networks. We propose preferentialattachment model with degree bound for the first time. In the normalpreferential 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 integerchosen according to the application. The second is in the security of wirelesssensor networks. We propose a new key predistribution scheme based on the abovemodel. The important features of this model are that the network is fullyconnected, it has fewer keys, has larger size of the giant component and loweraverage path length compared with traditional key predistribution schemes andcomparable resilience to random node attacks.  We argue that in many networks like key predistribution and Internet ofThings, having nodes of very high degree will be a bottle-neck incommunication. Thus, studying preferential attachment model with degree boundwill open up new directions in the study of complex networks, and will havemany applications in real world scenarios.

Preferential Attachment Model with Degree Bound and its Application to Key Predistribution in WSN