Structural Changes and Percolation Transition in Networks after Aging Processes

Abstract

In social networking services, users constantly change, and the network structure changes simultaneously. As the network structure changes, so does the word-of-mouth within it. To study how information transfer on the network changes with the aging of the network, we investigated the relation of the structure and the percolation in the aged networks. We first prepared the Bianconi-Barab\'{a}si model as the initial network and observed the time evolution of its properties by repeatedly deleting and adding nodes. We introduced two tunable parameters, the deleting parameter $\alpha$ and the adding parameter $\beta$, and observed the aging behavior for the various parameter sets. We found that the network did not reach its steady state depending on the parameters. We also found that when the network is stable, there is a parameter region where the degree distribution changes from power-law to exponential decay. We performed the percolation analyses and found that the behavior of the percolation probability changes simultaneously with changes in the network's structure. This study is expected to help control network structure in steady-state aged networks.