Robustness Of Scale-free Networks Research Articles

Robustness of scale-free networks with dynamical behavior against multi-node perturbation

An issue which is increasingly attracting attention from scientists to engineers, is the robustness of networks which is the ability against perturbations. It is found that both the network topology and network dynamics affect the robustness of networks. In this article, we present the cascading failure model triggered by perturbing a fraction 1−p of nodes on SF networks with three dynamics: the biochemical(B), epidemic(E) and regulatory(R) dynamics. A mathematical method is developed to calculate the cascading failure size and the giant component to evaluate the robustness when a fraction 1−p of nodes is perturbed on SF dynamical networks. We perform extensive numerical simulations to test and verify this formula and find that the theoretical results are in good agreement with simulations. The results show that the network is more robust as the tolerance coefficient δ increases, and the size of network has little influence on the robustness, especially for B and R. Remarkably, the heterogeneity of networks is positive on the robustness. Moreover, the different characteristics that as the parameter B increases or the parameter R decreases the network with B is more robust, and as the parameter R increases or the parameter B decreases the network with E and R is more robust are found. These findings may be useful for engineers to improve the robustness of the network or design robust networks with dynamics.

Degree difference: a simple measure to characterize structural heterogeneity in complex networks

Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, ‘degree difference’ (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measures in network science. Typically, edges with different DD play different structural roles and the DD distribution is an important network signature. Notably, DD is the basic unit of assortativity. We provide an explanation as to why DD can characterize structural heterogeneity in mixing patterns unlike global assortativity and local node assortativity. By analyzing synthetic and real networks, we show that DD distribution can be used to distinguish between different types of networks including those networks that cannot be easily distinguished using degree sequence and global assortativity. Moreover, we show DD to be an indicator for topological robustness of scale-free networks. Overall, DD is a local measure that is simple to define, easy to evaluate, and that reveals structural properties of networks not readily seen from other measures.

Robustness of scale-free networks with various parameters against cascading failures

Many crucial real-world networks could be modeled as scale-free networks, which play an important role in the human society. Once these functional network systems suffer from cascading failures, they may lead to the malfunction of the rest part of networks. In recent years, the researches on cascading failures of scale-free networks have drawn great attention, and many studies focused on modeling the cascading phenomena and studying how to improve the robustness of networks against failures. However, the scale-free networks used in most existing studies are with fixed network parameters including scaling exponent and assortativity, which is segmentary for depicting the functionality of networked systems comprehensively. Therefore, in this paper, a series of generated scale-free networks with a certain range of parameters is adopted to evaluate the robustness against cascading failures. In addition, to make an accurate description of the ability of scale-free networks against cascading failures, we propose a link-based robustness index. The results show that influenced by the network structure, the enlargement of assortativity makes the networks weaker to resist node-based cascading failures, yet the impact on promoting link-based robustness is not clear enough. With higher scaling exponents, the tolerance of scale-free networks against link-based cascading failures decreases, however, it does not show obvious relation to node-based robustness.

Robustness of single and interdependent scale-free interaction networks with various parameters

Abstract The robustness of scale-free networks has attracted increasing attentions recently. It has been shown that scale-free networks are tolerant to random failures but fragile under malicious attacks. However, most existing studies focus on scale-free networks with fixed exponent (around 3) and assortativity (around 0), and the relationship between robustness and these parameters has not been studied systematically. Therefore, in this paper, we study the change of robustness along with different parameters, including scaling exponent and assortativity, of scale-free networks; moreover, the robustness of interdependent networks is also studied. In the experiments, synthetic single scale-free networks with varying scaling exponents are constructed and adjusted to fix assortativity. Several measures are adopted to estimate the robustness of networks under malicious and random attacks. Then, interdependent networks with varying parameters are constructed and their robustness against malicious attacks is studied. The results show that there is a positive correlation between robustness against node attacks and the scaling exponent as well as assortativity, and the positive correlation also exists in interdependent networks.

Optimal Design on Robustness of Scale-Free Networks Based on Degree Distribution

This paper uses 2-norm degree and coefficient of variation on degree to analyze the basic characteristics and to discuss the robustness of scale-free networks. And we design two optimal nonlinear mixed integer programming schemes to investigate the optimal robustness and analyze the characteristic parameters of different schemes. In this paper, we can obtain the optimal values of the corresponding parameters of optimal designs, and we find that coefficient of variation is a better measure than 2-norm degree and two-step degree to study the robustness of scale-free networks. Meanwhile, we discover that there is a tradeoff among the robustness, the degree, and the cost of scale-free networks, and we find that when average degree equals 6, this point is a tradeoff point between the robustness and cost of scale-free networks.

Cascading Dynamics of Heterogenous Scale-Free Networks with Recovery Mechanism

In network security, how to use efficient response methods against cascading failures of complex networks is very important. In this paper, concerned with the highest-load attack (HL) and random attack (RA) on one edge, we define five kinds of weighting strategies to assign the external resources for recovering the edges from cascading failures in heterogeneous scale-free (SF) networks. The influence of external resources, the tolerance parameter, and the different weighting strategies on SF networks against cascading failures is investigated carefully. We find that, under HL attack, the fourth kind of weighting method can more effectively improve the integral robustness of SF networks, simultaneously control the spreading velocity, and control the outburst of cascading failures in SF networks than other methods. Moreover, the third method is optimal if we only knew the local structure of SF networks and the uniform assignment is the worst. The simulations of the real-world autonomous system in, Internet have also supported our findings. The results are useful for using efficient response strategy against the emergent accidents and controlling the cascading failures in the real-world networks.

Robustness analysis of an unstructured overlay for media communication

The wide diffusion of network address translators (NATs) (and, in some respect, firewalls) may prevent some applications that require direct end-to-end connectivity (e.g. real-time media) from being able to connect to the remote party. Although the solutions currently adopted rely on centralised nodes as third party relays, the distributed connectivity service (DISCOS) architecture has been recently proposed and aims at distributing such functionalities across a peer-to-peer (P2P) overlay. The original study presented some performance characteristics of the overlay, but the ability to resist to both failures and attacks was not taken into consideration. This study illustrates the robustness feature of the DISCOS overlay and suggests some minor modifications to the original mechanisms, in order to improve the overall robustness. The key component of DISCOS is its dynamic scale-free topology. Hence, the study also extends the existing literature concerning the robustness of scale-free networks, which considers only static graphs.

Effect of Eliminating Edges on Robustness of Scale-Free Networks under Intentional Attack

We study the robustness of complex networks under edge elimination. We propose three different edge elimination strategies and investigate their effects on the robustness of scale-free networks under intentional attack. We show that deleting a proper fraction of edges connecting hub nodes and hub nodes can enhance the robustness of scale-free networks under intentional attack.