Narrow Results

Recent work on the cascading failure of networks with dependence groups assumes that the number of nodes in each dependence group is equal. In this paper, we construct a model on interdependent networks with dependence groups against cascading failure. The size of dependence group is supposed to obey the Poisson Distribution and the Truncated Normal Distribution, respectively. By applying the tools of mean-field approximation and the generating function techniques, the cascading model is theoretically analyzed and the theoretical solutions are nearly consistent with the simulation values. Besides, we define three kinds of coupling preferences based on node degree, i.e. assortative coupling, disassortative coupling and random coupling. The connection between layers is no longer one-to-one correspondence of nodes, but fully connection of some groups. In addition, some factors affecting the network robustness are discussed and extensive simulations are realized on two-layer BA networks. The simulation results show that the coupling preference has influence on the network robustness and the network with dependence groups obeying the Truncated Normal Distribution performs better than the Poisson Distribution.

Air transportation networks play important roles in human mobility. In this paper, from the perspective of multilayer network mechanism, the dynamics of the Chinese air transportation network are extensively investigated. A multilayer-based passengers re-scheduling model is introduced, and a multilayer cooperation (MC) approach is proposed to improve the efficiency of network traffic under random failures. We use two metrics: the success rate and the extra transfer number, to evaluate the efficiency of re-scheduling. It is found that a higher success rate of passengers re-scheduling can be obtained by MC, and MC is stronger for resisting the instability of the capacity of links. Furthermore, the explosion of the number of extra transfer can be well restrained by MC. Our work will highlight a better understanding of the dynamics and robustness of the Chinese air transportation network.

Many realistic networked systems may face sustained attack over a sequence of time. In this paper, we propose a cascading failure model in coupled map lattices (CMLs) with sustained attack, where a number of crucial nodes will be attacked one by one at each time step. The effects of four attacking strategies: high-degree strategy (HDS), high-clustering coefficient strategy, high-closeness strategy and high-betweenness strategy are compared. This shows that the performance of HDS is better than that of other attacking strategies when the value of the outside attack is small. The effectiveness of HDS on Watts–Strogatz (WS) small-world networks and two real-world networks is extensively investigated. The results indicate that increasing the value of the rewiring probability of WS networks can make the network more robust to resist sustained attack. The sparser the network structure is, the faster the diffusion velocity of cascading failures is. A smaller coupling strength in CMLs can restrain the diffusion velocity of cascades. We also extend our CML-based model with sustained attack from one node strategy (ONS) to two nodes strategy (TNS) and compare the effect of ONS and TNS with different values of the outside attack. It is found that ONS outperforms TNS for small values of the outside attack, but TNS would be a better choice when the outside attack and the time step are all large. Our work will provide new insights into the problem of protecting complex networks against cascading failures with respect to malicious attack.

Cascading failure phenomena widely exist in real-life circumstances, such as the blackouts in power networks and the collapse in computer networks. In this paper, we construct a cascading failure model on the multilayer network, taking into account the number of invalid neighbors of nodes, the failure frequency of nodes, the effect between layers, and the percolation process. To minimize network losses caused by the cascading process, we propose a recovery strategy, i.e. repairing some certain clusters formed by ineffective nodes and links. The recovery strategy is discussed in detail, like whether to add links to the network, how many links are needed at least to add, how many layers are demanded to restore, and how to choose the values of $g$ and restorable threshold $\zeta$ to improve the network performance. Besides, we theoretically analyze the cascading failure model with recovery strategy by virtue of mean-field approximation and generating function techniques. The theoretical solutions are found to be consistent with experimental results simulated on the ER as well as BA networks. In addition, we also investigate the affecting factors of network robustness. The effects of failure threshold $\alpha$, base number $f$, and threshold $\phi$ between layers on network behaviors depend on the values of average degree $〈k〉$ and recovery proportion $\theta$. These results may provide particular reference significance for maintaining system security, adjusting the network performance, and enhancing network robustness.

In recent years, the frequent occurrence of extreme weather and national conflicts has highlighted the necessity of enhancing the robustness of the grain trade network. In this paper, we study the evolution of major trading countries, and the network robustness under random and different attack strategies. The results show that the heterogeneity of the Global Soybean Trade Network (GSTN) and trade connections among countries are increasing. The soybean trade network has strong resistance to random attacks, while subjected to targeted attacks, the stability of the network is significantly affected and damaged.

The network infrastructures, such as the power grids and Internet, are expanding in size due to the increasing needs of our society. This brings about the problem of expanding networks with a guarantee of robustness against network disturbances that may cause catastrophic consequences. In this paper, we study the optimal network expansion in terms of network robustness against cascading failures. Specifically, we consider the network expansion as a Markovian decision process and further propose a reinforcement learning based network expansion method. Simulation results in model networks and real-world networks demonstrate that our expansion method can greatly improve network robustness. Our work provides some insights for the optimal expansion of network infrastructures.

The urban rail network system plays a significant role in the urban transportation system and urban economic development. Further study of the urban rail network properties can provide additional guidance to related scholars and designers. This study explored urban rail network properties worldwide, including assessments of their static and dynamic network topologic characteristics. Statically, this study analyzed various related network topological indicators for all of these urban rail networks. We found that, with increasing network size, the average degree slightly increases while the complexity and connectivity decrease. Using the Kolmogorov–Smirnov goodness-of-fit, the scale of the degree interval of these cities is [3.5 12.2]. Approximately 90% of these cities have network efficiency values less than 0.12, and 78% of these cities have lower assortativity coefficients. Focusing on the sustainable growth of rail networks, this study tested some specific networks to further deliberate their network expansion ability, network growth, and network robustness properties. The network expansion capability of small networks is relatively poor, while that of large networks is relatively strong. A simulation of network growth suggests that the connection of nodes with the maximum path length will seriously affect the efficiency and characteristics of the network. The robustness of the network indicates that adopting the maximum nodal degree elimination strategy will affect the function of the network. The results provide essential reference information for the rational planning, structural optimization, safe operation and sustainable growth of rail transit networks.

Identifying critical nodes in complex networks has gained increasing attention in recent years. However, how to design an algorithm that has low computational complexity but can accurately identify important network nodes is still a challenge. Considering the role of structural holes in shaping communication channels, this paper presents an effective method based on local characteristics to identify critical nodes that play important roles in maintaining network connectivity. Our method considers the connections of a node as well as the connectivity of the neighborhood of the node. Through numerical simulations on various real-world networks, we have demonstrated that the proposed approach outperforms some other well-known heuristic algorithms in identifying vital nodes and leads to faster network collapse in target destruction.

Network resilience is vital for the survival of networks, and scale-free networks are fragile when confronted with targeted attacks. We survey network robustness to targeted attacks from the viewpoint of network clients by designing a unique mechanism based on the undeniable roles of network clients in real-world networks. Especially, the mechanism here is designed on the actual phenomenon that the vital nodes in a network may be totally different for clients with different demands. Concretely, node client-demand centrality is proposed to quantify the contributions of nodes to network clients and we show that it is a proper index to assign an order to network nodes according to node importance for network clients. Great discrepancy of node importance order for clients with different demands is found in scale-free networks with four different kinds of link weight distribution, which suggests that the destructiveness of fatal attacks on networks can be greatly reduced by adjusting the demands of network clients.

As a decisive parameter of network robustness and network economy, the capacity of network edges can directly affect the operation stability and the construction cost of the network. This paper proposes a multilevel load–capacity optimal relationship (MLCOR) model that can substantially improve the network economy on the premise of network safety. The model is verified in artificially created networks including free-scale networks, small-world networks, and in the real network structure of the Shanghai Metro network as well. By numerical simulation, it is revealed that under the premise of ensuring the stability of the network from the destruction caused by initial internal or external damage on edge, the MLCOR model can effectively reduce the cost of the entire network compared to the other two linear load–capacity models regardless of what extent of the destruction that the network edges suffer initially. It is also proved that there exists an optimal tunable parameter and the corresponding optimal network cost for any BA and NW network topology, which can provide the reference for setting reasonable capacities for network edges in a real network at the stage of network planning and construction, promoting security and stability of network operation.

The topological structures and robustness of the protein-protein interaction networks (PINs) is studied via random graph theory. Several global topological parameters are used to characterize PINs for seven species. Good evidence by correlation analysis support the fact that the seven PINs are well approximated by scale-free networks. It is also found that two of the species' PINs are well described by the hierarchical models. In particular, it is determined that the E. coli and the yeast PINs are well represented by the stochastic and deterministic hierarchical network models respectively. These results suggest that the hierarchical network model is a better description for certain species' PINs. Furthermore, it is demonstrated that PINs are robust with respective to failure, attack, random rewiring and edge deletion perturbations.