Evolving Networks and Birth-and-Death Processes

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of non-homogeneous birth-and-death processes, and, with which, we capture the process by which the network connectivity evolves. We develop an effective algorithm to compute the network degree distribution accurately. Comparing analytical and numerical results with simulation, we identify some interesting network properties and verify the effectiveness of our method.