Efficacy of local attack strategies on the Beijing road complex weighted network

Understanding the complex network response to nodes failure is important to protect them and guarantee their functioning. Most existing studies considered binary networks where the intensity (weight) of the links is not accounted for. However, in real world networks the intensity of the links widely differ so that a realistic description of complex networks is only possible if the heterogeneity present in edge weights is taken into account. Further, the vast majority of the existing studies investigates the efficacy of the attack strategies when all the nodes are removed. Despite it is important to study the network behavior in such a circumstance, real-world networks are more likely to experience local failures involving a small amount of nodes with a decrease in the system functioning not causing an overall collapse. This is the case of crossroad closing in complex road networks. For this reason it is interesting to investigate the networks response focusing to small node removals. In this paper we analyze the response of the real-world road networks of Beijing, the capital of China, to the removal of 1 and 2 nodes and accounting the weighted structure of the network. We use both classic binary node properties and network functioning measurement, introduced a weighted rank for node importance (node strength or page rank), and used a measurement for network functioning that accounts for the weight of the links (weighted efficiency). We find that the weighted node attack strategy Str (i.e. strength attack), which removes nodes according to their strength, is the most efficient to blemish the system when evaluating the damage with a weighted efficiency. Differently, betweenness attack strategy Bet, which removes nodes according to their centrality is the most efficient when using the binary efficiency to compute the network damage. These results indicate that adopting weighted or binary efficiency to measure networks functioning changed the efficacy of the attack strategies to damage the system. Last, we found a non-negligible fraction of random removals to be more efficient than the attack strategies; given that the main goal of the attack strategies is to individuate important nodes in the system, i.e. nodes which removal triggers highest damage, our results would indicate how in order to find the most important nodes may be more efficient to simulate an higher number of random nodes removal.