  In this paper, we propose a growing random complex network model, which we
call context dependent preferential attachment model (CDPAM), when the
preference of a new node to get attached to old nodes is determined by the
local and global property of the old nodes. We consider that local and global
properties of a node as the degree and relative average degree of the node
respectively. We prove that the degree distribution of complex networks
generated by CDPAM follow power law with exponent lies in the interval [2, 3]
and the expected diameter grows logarithmically with the size of new nodes
added in the initial small network. Numerical results show that the expected
diameter stabilizes when alike weights to the local and global properties are
assigned by the new nodes. Computing various measures including clustering
coefficient, assortativity, number of triangles, algebraic connectivity,
spectral radius, we show that the proposed model replicates properties of real
networks better than BA model for all these measures when alike weights are
given to local and global property. Finally, we observe that the BA model is a
limiting case of CDPAM when new nodes tend to give large weight to the local
property compared to the weight given to the global property during link
formation.
