Enhancing Robustness and Immunization in geographical networks

Abstract

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, the strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain the explicit form of the percolation threshold $q_{c}$ for networks containing arbitrary order cycles. For 3-cycles, the dependence of $q_c$ on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with an analytical evidence.