Iterative decomposition of Barabasi–Albert scale-free networks

We study a decomposition process where all nodes with a targeted degree are removed from the network. Each removal step results in changes in the degrees of the remaining nodes, and other nodes may attain the targeted degree. The processes continue iteratively until no more nodes with the targeted degree are present in the decomposed network. The network model used in our study is the well known Barabasi–Albert network, that is built with an iterative growth based on preferential attachment. Our results show an exponential decay of the number of nodes removed at each step. The total number of nodes removed in the whole process depends on the targeted degree and decay with a power law controlled by the same exponent as the degree distribution of the network.