Improving robustness of complex networks by a new capacity allocation strategy

The robustness of infrastructure networks has attracted great attention in recent years. Scholars have studied the robustness of complex networks against cascading failures from different aspects. In this paper, a new capacity allocation strategy is proposed to reduce cascading failures and improve network robustness without changing the network structure.Compared with the typical strategy proposed in Motter–Lai(ML) model, the new strategy can reduce the scale of cascading failure. The new strategy applied in scale-free network is more efficient. In addition, to reasonably evaluate the two strategies, we introduce contribution rate of unit capacity to network robustness as evaluation index. Results show that our new strategy works well, and it is more advantageous in the rational utilization of capacity in scale-free networks.Furthermore, we were surprised to find that the efficient utilization of capacity costs declined as costs rose above a certain threshold, which indicates that it is not wise to restrain cascading failures by increasing capacity costs indefinitely.     

Sandpile Dynamics Driven by Degree on Scale-Free Networks

We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld （BTW） model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation.     

Robustness of Complex Networks under Attack and Repair

To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to the
understanding of robustness of complex networks with reparability.     

Effects of average degree of network on an order-disorder transition in opinion dynamics

We have investigated the influence of the average degree k of network on the location of an order-disorder transition in opinion dynamics.For this purpose,a variant of majority rule (VMR) model is applied to Watts-Strogatz (WS) small-world networks and Barabá si-Albert (BA) scale-free networks which may describe some non-trivial properties of social systems.Using Monte Carlo simulations,we find that the order-disorder transition point of the VMR model is greatly affected by the average degree k of the networks;a larger value of k results in a more ordered state of the system.Comparing WS networks with BA networks,we find WS networks have better orderliness than BA networks when the average degree k is small.With the increase of k,BA networks have a more ordered state.By implementing finite-size scaling analysis,we also obtain critical exponents β/ν,γ/ν and 1/ν for several values of average degree k.Our results may be helpful to understand structural effects on order-disorder phase transition in the context of the majority rule model.     

Tolerance of edge cascades with coupled map lattices methods

This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods.The whole work focuses on investigating some indices including the number of failed edges,dynamic edge tolerance capacity and the perturbation of edge.In general,it assumes that the perturbation is attributed to the normal distribution in adopted simulations.By investigating the effiectiveness of edge tolerance in scale-free and random networks,it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks.These results indicate that the cascading failure process can be effiectively controlled by increasing the tolerance parameter λ.Moreover,the simulations also show that,larger variance of perturbation can easily trigger the cascading failures than the smaller one.This study may be useful for evaluating efficiency of whole traffic systems,and for alleviating cascading failure in such systems.     

Row–column visibility graph approach to two-dimensional landscapes

A new concept, called the row–column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough(e.g., H >0.5), the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H < 0.5 is destroyed completely. Hence, the row–column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes.     

A realistic model for complex networks with local interaction, self-organization and order

In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution with an exponent in a range of 3-to-5 is given. Moreover, this model could also reproduce the exponential distribution that is discovered in some real networks. Finally, the analytical result of the model is given and the simulation shows the validity of our result,     

Robustness of Cooperation on Highly Clustered Scale-Free Networks

We study the effect of mutation on the evolutionary prisoner＇s dilemma in highly clustered scale-free networks. It is found that cooperation is more sensitive and vulnerable to strategy mutation in more highly clustered networks. For small mutation rates, high clustering coefficient promotes cooperation. For medium mutation rates, high clustering coefficient inhibits the emergence of cooperation. For large mutation rates, cooperation is insensitive to clustering property. We provide explanations for the effects of clustering on cooperation with varied mutation rates.     

Breakdown of an Inhomogeneous Scale—Free Network Under Intentional Attack

Using a recently introduced network model with node and connection diversity,we study the breakdown of different scale-free networks under intentional attacks.Our simulation results show that inhomogeneous networks are more sensitive to intentional attack than the homnogeneous ones and that the centralization of the networks is an important variable,reflecting,the characteristics of the network under intentional attack,Using a recently introduced method we can theoretically develop the critical point of the inhomogeneous networks.     

Modelling the spread of sexually transmitted diseases on scale-free networks

In this paper a new model for the spread of sexually transmitted diseases (STDs) is presented. The dynamic behaviors of the model on a heterogenous scale-free (SF) network are considered, where the absence of a threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained. Three immunization strategies, uniform immunization, proportional immunization and targeted immunization, are applied in this model. Analytical and simulated results are given to show that the proportional immunization strategy in the model is effective on SF networks.