Time-invariant Preferential Attachment in Complex Networks[go to overview]
Real networks rarely grow uniformly in time. However, this aspect is not considered in the original Barabasi-Albert model and is mostly overlooked by its kin. The linear growth of the network results in the early mover advantage. We show empirical evidences that in real networks degree growth of nodes is, on the contrary, often time-invariant, i.e., node degree grows with time, on average, in the same way regardless of the node's time of appearance. While different growth forms of the network can be considered, we show that the exponential growth is not only approximately fulfilled in many real systems but also the key to the time-invariant degree growth of nodes. The decay of node relevance (nodes with aging fitness) is necessary to recover realistic degree growth curves that are slower than exponential, e.g., power functions. Finally, we introduce a novel mathematical formalism of the preferential attachment models, where the exponential growth of the network emerges as a solution of an eigenvalue problem.
01.08.19 - 10:15