Context dependent preferential attachment model for complex networks

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 to 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 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.