Large-Scale Connectivity vs. Spreading Efficiency: Spectral Analysis on Explosive Percolation

Some of the results of a spectral analysis of the process of explosive percolation on complex networks (Chung et al., Europhys Lett 101:66003, 2013) are presented here. More specifically, we explore how the maximum eigenvalues of the adjacency matrix of a network, which governs the spreading efficiency, evolves as the density of network connections are increased. We find that for networks with connectivity that grow in an explosive way, information spreading and mass transport are carried out inefficiently. When we looked into the conventional explosive percolation models, the sudden emergency of large connectivity comes with relatively lowered efficiency of spreading. Nevertheless, the spreading efficiency of the explosive models can be improved by introducing heterogeneous structures into the networks.