Robustness on interdependent networks with a multiple-to-multiple dependent relationship

Coupled spreading between information and epidemics on multiplex networks with simplicial complexes

The way of information diffusion among individuals can be quite complicated, and it is not only limited to one type of communication, but also impacted by multiple channels. Meanwhile, it is easier for an agent to accept an idea once the proportion of their friends who take it goes beyond a specific threshold. Furthermore, in social networks, some higher-order structures, such as simplicial complexes and hypergraph, can describe more abundant and realistic phenomena. Therefore, based on the classical multiplex network model coupling the infectious disease with its relevant information, we propose a novel epidemic model, in which the lower layer represents the physical contact network depicting the epidemic dissemination, while the upper layer stands for the online social network picturing the diffusion of information. In particular, the upper layer is generated by random simplicial complexes, among which the herd-like threshold model is adopted to characterize the information diffusion, and the unaware-aware-unaware model is also considered simultaneously. Using the microscopic Markov chain approach, we analyze the epidemic threshold of the proposed epidemic model and further check the results with numerous Monte Carlo simulations. It is discovered that the threshold model based on the random simplicial complexes network may still cause abrupt transitions on the epidemic threshold. It is also found that simplicial complexes may greatly influence the epidemic size at a steady state.

Network resilience of non-hub nodes failure under memory and non-memory based attacks with limited information

Previous studies on network robustness mainly concentrated on hub node failures with fully known network structure information. However, hub nodes are often well protected and not accessible to damage or malfunction in a real-world networked system. In addition, one can only gain insight into limited network connectivity knowledge due to large-scale properties and dynamic changes of the network itself. In particular, two different aggression patterns are present in a network attack: memory based attack, in which failed nodes are not attacked again, or non-memory based attack; that is, nodes can be repeatedly attacked. Inspired by these motivations, we propose an attack pattern with and without memory based on randomly choosing n non-hub nodes with known connectivity information. We use a network system with the Poisson and power-law degree distribution to study the network robustness after applying two failure strategies of non-hub nodes. Additionally, the critical threshold 1 - _p and the size of the giant component S are determined for a network configuration model with an arbitrary degree distribution. The results indicate that the system undergoes a continuous second-order phase transition subject to the above attack strategies. We find that 1 - _p gradually tends to be stable after increasing rapidly with n. Moreover, the failure of non-hub nodes with a higher degree is more destructive to the network system and makes it more vulnerable. Furthermore, from comparing the attack strategies with and without memory, the results highlight that the system shows better robustness under a non-memory based attack relative to memory based attacks for n > 1. Attacks with memory can block the system's connectivity more efficiently, which has potential applications in real-world systems. Our model sheds light on network resilience under memory and non-memory based attacks with limited information attacks and provides valuable insights into designing robust real-world systems.

Improving robustness in interdependent networks under intentional attacks by optimizing intra-link allocation

The interdependent network is particularly vulnerable to attacks on high degree nodes; therefore, the improvement of its robustness under intentional attacks has become an important topic. In this paper, we put forward a new metric to quantify the robustness of interdependent networks against intentional attacks and develop an improved simulated annealing algorithm (ISAA) to maximize this metric by optimizing the allocation of intra-links in subnetworks. Based on the comparison between the ISAA and existing algorithms, it is found that the algorithm presented in this paper is more effective to enhance the robustness of an interdependent scale-free network (ISFN). By applying the ISAA to ISFNs with different coupling preferences, there is a key finding that the robustness of the optimized ISFN is significantly stronger than that of the original ISFN. In particular, for cases of disassortative and random couplings, no sudden collapse occurs in optimized ISFNs. According to the analysis of the degree and the clustering coefficient, we find that the subnetwork of the optimized ISFN exhibits an onion-like structure. In addition, the ISFN whose robustness is enhanced to resist the attacks on high degree nodes is still robust to the intentional attacks concerning the betweenness and PageRank.

A Security Scheme Based on Intranal-Adding Links for Integrated Industrial Cyber-Physical Systems

With the advent of the Internet of Everything era, the Industrial Internet is increasingly showing mutual integration and development. Its core framework, the industrial CPS (Cyber-Physical Systems), has received more and more attention and in-depth research in recent years. These complex industrial CPS systems are usually composed of multiple interdependent sub-networks (such as physical networks and control networks, etc.). Minor faults or failure behaviors between sub-networks may cause serious cascading failure effects of the entire system. In this paper, we will propose a security scheme based on intranal-adding links in the face of the integrated and converged industrial CPS system environment. Firstly, by calculating the size of the largest connected component in the entire system, we can compare and analyze industrial CPS systems’ security performance under random attacks. Secondly, we compare and analyze the risk of cascading failure between integrated industrial CPS systems under different intranal-adding link strategies. Finally, the simulation results verify the system security strategy’s effectiveness under different strategies and show a relatively better exchange strategy to enhance the system’s security. In addition, this paper’s research work can help us design how to further optimize the interdependent industrial CPS system’s topology to cope with the integrated and converged industrial CPS system environment.

Percolation on coupled networks with multiple effective dependency links

The ubiquitous coupled relationship between network systems has become an essential paradigm to depict complex systems. A remarkable property in the coupled complex systems is that a functional node should have multiple external support associations in addition to maintaining the connectivity of the local network. In this paper, we develop a theoretical framework to study the structural robustness of the coupled network with multiple useful dependency links. It is defined that a functional node has the broadest connectivity within the internal network and requires at least M support link of the other network to function. In this model, we present exact analytical expressions for the process of cascading failures, the fraction of functional nodes in the stable state, and provide a calculation method of the critical threshold. The results indicate that the system undergoes an abrupt phase transition behavior after initial failure. Moreover, the minimum inner and inter-connectivity density to maintain system survival is graphically presented at different multiple effective dependency links. Furthermore, we find that the system needs more internal connection densities to avoid collapse when it requires more effective support links. These findings allow us to reveal the details of a more realistic coupled complex system and develop efficient approaches for designing resilient infrastructure.

Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks

In the real Internet of Everything scenario, many large-scale information systems can be converted into interdependent sensor networks, such as smart grids, smart medical systems, and industrial Internet systems. These complex systems usually have multiple interdependent sensor networks. Small faults or failure behaviors between networks may cause serious cascading failure effects of the entire system. Therefore, in this paper, we will focus on the security of interdependent sensor networks. Firstly, by calculating the size of the largest functional component in the entire network, the impact of random attacks on the security of interdependent sensor networks is analyzed. Secondly, it compares and analyzes the impact of cascading failures between interdependent sensor networks under different switching edge strategies. Finally, the simulation results verify the effect of the security of the system under different strategies, and give a better exchange strategy to enhance the security of the system. In addition, the research work in this article can help design how to further optimize the topology of interdependent sensor networks by reducing the impact of cascading failures.

An asymmetric interdependent networks model for cyber-physical systems

Cyber-physical systems (CPSs) are integrations of information technology and physical systems, which are more and more significant in society. As a typical example of CPSs, smart grids integrate many advanced devices and information technologies to form a safer and more efficient power system. However, interconnection with the cyber network makes the system more complex, so that the robustness assessment of CPSs becomes more difficult. This paper proposes a new CPS model from a complex network perspective. We try to consider the real dynamics of cyber and physical parts and the asymmetric interdependency between them. Simulation results show that coupling with the communication network makes better robustness of power system. But since the influences between the power and communication networks are asymmetric, the system parameters play an important role to determine the robustness of the whole system.