Enhancing the robustness of scale-free networks

Error tolerance and attack vulnerability are two common and important properties of complex networks, which are usually used to evaluate the robustness of a network. Recently, much work has been devoted to determining the network design with optimal robustness. However, little attention has been paid to the problem of how to improve the robustness of existing networks. In this paper, we present a new parameter α, called enforcing parameter, to guide the process of enhancing the robustness of scale-free networks by gradually adding new links. Intuitively, α < 0 means the nodes with lower degrees are selected preferentially while the nodes with higher degrees will be more probably selected when α > 0. It is shown both theoretically and experimentally that when α < 0 the attack survivability of the network can be enforced apparently. Then we propose new strategies to enhance the network robustness. Through extensive experiments and comparisons, we conclude that establishing new links between nodes with low degrees can drastically enforce the attack survivability of scale-free networks while having little impact on the error tolerance. PACS numbers: 89.75.Fb, 89.20.Hh, 89.75.-k, 89.75.Hc      N j i ij d N N E 1 , 1 1 ) 1 ( 1 , (1) where N is the size of the network and dij is the length of the shortest path between i and j. The error tolerance of the network can be measured by the entropy, which is computed based on the degree distribution of the network [11, 12]. During the malicious attacks or random failures, fc is always used to characterize the critical fraction of the least nodes that need to be removed until the network is collapsed [13, 14]. fc rand and fc targ were used as responses to random failures and malicious attacks respectively in [13]. In particular, fc rand can be easily computed by the following formula [15] 1 1 1 2       