Measuring microscopic evolution processes of complex networks based on empirical data

Aiming at understanding the microscopic mechanism of complex systems in real world, we perform the measurement that characterizes the evolution properties on two empirical data sets. In the Autonomous Systems Internet data, the network size keeps growing although the system suffers a high rate of node deletion (r = 0.4) and link deletion (q = 0.81). However, the average degree keeps almost unchanged during the whole time range. At each time step the external links attached to a new node are about c = 1.1 and the internal links added between existing nodes are approximately m = 8. For the Scientific Collaboration data, it is a cumulated result of all the authors from 1893 up to the considered year. There is no deletion of nodes and links, r = q = 0. The external and internal links at each time step are c = 1.04 and m = 0, correspondingly. The exponents of degree distribution p (k) similar to k(-gamma) of these two empirical datasets gamma(data) are in good agreement with that obtained theoretically gamma(theory.) The results indicate that these evolution quantities may provide an insight into capturing the microscopic dynamical processes that govern the network topology.