In this paper, invulnerability and attack strategies are discussed for the undirected unweighted urban road networks and the directed weighted taxi networks of Beijing. Firstly, five new attack strategies, i.e., Initial All Degree (IAD), Initial All Strength (IAS), Recalculated Closeness (RC), Recalculated All Degree (RAD) and Recalculated All Strength (RAS) and five traditional attack strategies, i.e., Initial Degree (ID), Initial Betweenness (IB), Initial Closeness (IC), Recalculated Degree (RD) and Recalculated Betweenness (RB) are adopted to provoke the nodes failure. Secondly, we assess the impacts of these attack strategies using two invulnerability metrics, i.e., S (the relative size of the giant component) and E (the average network efficiency) through simulation experiments by MATLAB. Furthermore, we obtain some conclusions on the basis of the simulation results. Firstly, we discover that IB is more efficient than others for the undirected unweighted 5th ring Beijing road network based on S, and IB is more efficient than others at the beginning while ID is more efficient than IB at last based on E, while IAD causes a greater damage than IAS for the directed weighted 5th ring Beijing taxi network no matter with metrics S or E. Secondly, we find that dynamic attacks are more efficient than their corresponding static attacks, and RB is more destructive than others in all attack graphs while RAD is more destructive than RAS in all attack graphs. Moreover, we propose some suggestions to advance the reliability of the networks according to the simulation results. Additionally, we notice that the damage between ID (RD) and IAD (RAD) is similar due to the large proportion of two-way roads, and we realize that global measures should be employed to estimate the best attack strategy on the basis of that we find the best attack strategy changes with the nodes failure.

This Letter defines thirteen useful correlation measures for directed weighted complex network analysis. First, in-strength and out-strength are defined for each node in the directed weighted network. Then, one node-based strength-strength correlation measure and four arc-based strength-strength correlation measures are defined. In addition, considering that each node is associated with in-degree, out-degree, in-strength and out-strength, four node-based strength-degree correlation measures and four arc-based strength-degree correlation measures are defined. Finally, we use these measures to analyze the world trade network and the food web. The results demonstrate the effectiveness of the proposed measures for directed weighted networks.