Optimization of the robustness of multimodal networks

Toshihiro Tanizawa, Gerald Paul, Shlomo Havlin, H. Eugene Stanley
2006 Physical Review E  
We investigate the robustness against both random and targeted node removal of networks in which P͑k͒, the distribution of nodes with degree k, is a multimodal distribution, Dirac's delta function ␦͑x͒. We refer to this type of network as a scale-free multimodal network. For m = 2, the network is a bimodal network; in the limit m approaches infinity, the network models a scale-free network. We calculate and optimize the robustness for given values of the number of modes m, the total number of
more » ... des N, and the average degree ͗k͘, using analytical formulas for the random and targeted node removal thresholds for network collapse. We find, when N 1, that ͑i͒ the robustness against random and targeted node removal for this multimodal network is controlled by a single combination of variables, N 1/͑m−1͒ , ͑ii͒ the robustness of the multimodal network against targeted node removal decreases rapidly when the number of modes becomes larger than a critical value that is of the order of ln N, and ͑iii͒ the values of exponent opt that characterizes the scale-free degree distribution of the multimodal network that maximize the robustness against both random and targeted node removal fall between 2.5 and 3.
doi:10.1103/physreve.74.016125 pmid:16907169 fatcat:pi5vii3w6fgfhatitorpn3wzim