Hybrid routing on scale-free networks

We propose a novel routing algorithm to optimize traffic performance on complex networks. It combines static structural properties and dynamic traffic conditions together and therefore can balance the traffic between hubs and peripheral nodes more effectively. Simulation results show that the network capacity can be enhanced considerably, and the average traveling time is also shortened sharply, compared with the other two recently-proposed routing algorithms. The effect of the timescale over which the routing information is updated is also investigated. Moreover, a counter-intuitive and beneficial phenomenon about the average traveling time emerges when the packet generation rate is relatively high.     

Optimal traffic networks topology: A complex networks perspective

We investigate and analyse an optimal traffic network structure for resisting traffic congestion with different volumes of traffic. For this aim, we introduce a cost function and user-equilibrium assignment (UE) which ensures the flow balance on traffic systems. Our finding is that an optimal network is strongly dependent on the total system flow. And the random network is most desirable when the system flow is small. But for the larger volume of traffic, the network with power-law degree distribution is the optimal one. Further study indicates, for scale-free networks, that the degree distribution exponent has large effects on the congestion of traffic network. Therefore, the volume of traffic and characteristic of network determine the optimal network structure so as to minimize the side-effect produced by traffic congestion.     

Effects of the cascading failures on scale-free traffic networks

In this paper, we consider the artificial scale-free traffic network with dynamic weights (cost) and focus on how the removal strategies (flow-based removal, betweenness-based removal and mix-based removal) affect the damage of cascading failures based on the user-equilibrium (UE) assignment, which ensures the balance of flow on the traffic network. Experiment simulation shows that different removal strategies can bring large dissimilarities of the efficiency and damage after the intentional removal of an edge. We show that the mix-based removal of a single edge might reduce the damage of cascading failures and delay the breakdown time, especially for larger reserve capacity coefficient α. This is particularly important for real-world networks with a highly hetereogeneous distribution of flow, i.e., traffic and transportation networks, logistics networks and electrical power grids.     

Deterministic weighted scale-free small-world networks

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the co-evolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. We provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution, degree correlations, average clustering coefficient and degree-cluster correlations as well as the diameter.     

A packet routing strategy using neural networks on scale-free networks

We propose a dynamic packet routing strategy by using neural networks on scale-free networks. In this strategy, in order to determine the nodes to which the packets should be transmitted, we use path lengths to the destinations of the packets, and adjust the connection weights of the neural networks attached to the nodes from local information and the path lengths. The performances of this strategy on scale-free networks which have the same degree distribution and different degree correlations are compared to one another. Our numerical simulations confirm that this routing strategy is more effective than the shortest path based strategy on scale-free networks with any degree correlations and that the performance of our strategy on assortative scale-free networks is better than that on disassortative and uncorrelated scale-free networks.     

Traffic dynamics in scale-free networks with tunable strength of community structure

In this paper we systematically investigate the impact of community structure on traffic dynamics in scale-free networks based on local routing strategy. A growth model is introduced to construct scale-free networks with tunable strength of community structure, and a packet routing strategy with a parameter α is used to deal with the navigation and transportation of packets simultaneously. Simulations show that the maximal network capacity stands at α=−1 in the case of identical vertex capacity and monotonously decreases with the strength of community structure which suggests that the networks with fuzzy community structure (i.e., community strength is weak) are more efficient in delivering packets than those with pronounced community structure. To explain these results, the distribution of packets of each vertex is carefully studied. Our results indicate that the moderate strength of community structure is more convenient for the information transfer of real complex systems.     

Routing in scale-free networks based on expanding betweenness centrality

In this paper, an improved routing strategy is proposed for enhancing the traffic capacity of scale-free networks. Instead of using the information of degree and betweenness centrality, the new algorithm is derived on the basis of the expanding betweenness centrality of nodes, which gives an estimate of the traffic handled by the vertex for a certain route set. Since the nodes with large betweenness centrality are more susceptible to traffic congestion, the traffic can be improved by redistributing traffic loads from nodes with large betweenness centrality to nodes with small betweenness centrality in the process of computing the collective routing table. Comparing with results of previous routing strategies, it is shown that the present improved routing performs more effectively.     

An imperfect competition on scale-free networks

We study an imperfect quantity competition on networks that represent rivalry relationships among firms. We show that the more heterogeneous the underlying network is, the more the output and the price are. The output and the price on scale-free networks are counter-intuitively the same as those in the monopoly regardless of the number of rival firms. We also show that any inverse demand function represented by a network has the corresponding utility function, which justifies the inverse demand function.     

一种有效提高无标度网络负载容量的管理策略

现有研究表明明显的社团结构会显著降低网络的传输性能. 本文基于网络邻接矩阵的特征谱定义了链路对网络社团特性的贡献度, 提出一种通过逻辑关闭或删除对网络社团特性贡献度大的链路以提高网络传输性能的拓扑管理策略, 即社团弱化控制策略(CWCS 策略). 在具有社团结构的无标度网络上分别进行了基于全局最短路径路由和局部路由的仿真实验, 并与关闭连接度大的节点之间链路的HDF 策略进行了比较. 仿真实验结果显示, 在全局最短路径路由策略下, CWCS策略能更有效地提高网络负载容量, 并且网络的平均传输时间增加的幅度变小. 在局部路由策略下, 当调控参数0<α<2, 对网络负载容量的提升优于HDF策略. 关键词： 复杂网络 社团特性 负载容量 拓扑管理     

A maximum algebraic connectivity increment edge-based strategy for capacity enhancement in scale-free networks

In this paper, we focus on how to improve transportation efficiency of scale-free networks via edge increments. Based on analyzing the correlation between algebraic connectivity, which is the second smallest eigenvalue of the graph Laplacian matrix, and traffic capacity, we propose an effective edge-addition strategy called maximum algebraic connectivity increment edge (MACIE). Existing approaches are based on topological structure parameters, such as path and degree of a network, which require expensive computation. Different from existing edge-addition strategies, MACIE enhances transport efficiency by maximizing algebraic connectivity, and thus has a shorter running time. Simulation results show that MACIE is efficient and performs better than the previous strategy of reduction structural hole (RSH).     

无标度复杂网络负载传输优化策略

提出了一种能够显著提高无标度复杂网络负载传输性能的优化路由策略.实现了负载在核心节点与边缘节点间的合理分配.分析表明该策略使得网络的负载处理能力正比于网络规模的平方,而与单个节点的度值无关.实验结果显示优化路由策略在保持了最短路由策略小世界效应的同时,成倍地提升了网络的负载传输能力,且随着网络平均节点度的增加其优势越趋显著.此外,与有效路由策略的比较进一步验证了优化路由策略的优异性能. 关键词： 优化路由策略 复杂网络 负载传输 网络阻塞     

Noisy scale-free networks

The impact of observational noise on the analysis of scale-free networks is studied. Various noise sources are modeled as random link removal, random link exchange and random link addition. Emphasis is on the resulting modifications for the node-degree distribution and for a functional ranking based on betweenness centrality. The implications for estimated gene-expressed networks for childhood acute lymphoblastic leukemia are discussed.     

Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

Preferential spreading on scale-free networks

Based on a classical contact model, the spreading dynamics on scale-free networks is investigated by taking into account exponential preferentiality in both sending out and accepting processes. In order to reveal the macroscopic and microscopic dynamic features of the networks, the total infection density ρ and the infection distribution ρ(k), respectively, are discussed under various preferential characters. It is found that no matter what preferential accepting strategy is taken, priority given to small degree nodes in the sending out process increases the total infection density ρ. To generate maximum total infection density, the unbiased preferential accepting strategy is the most effective one. On a microscopic scale, a small growth of the infection distribution ρ(k) for small degree classes can lead to a considerable increase of ρ. Our investigation, from both macroscopic and microscopic perspectives, consistently reveals the important role the small degree nodes play in the spreading dynamics on scale-free networks.     

Efficient and robust routing on scale-free networks

Information routing is one of the most important problems in large communication networks. In this paper we propose a novel routing strategy in which the optimal paths between all pairs of nodes are chosen according to a cost function that incorporates degrees of nodes in paths. Results on large scale-free networks demonstrate that our routing strategy is more efficient than the shortest path algorithm and the efficient routing strategy proposed by Yan et al. [Phys. Rev. E 73, 046108 (2006)]. Furthermore our routing strategy has strong robustness against cascading failure attacks on networks.     

Boolean game on scale-free networks

Inspired by the local minority game, we propose a network Boolean game and investigate its dynamical properties on scale-free networks. The system can self-organize to a stable state with better performance than the random choice game, although only the local information is available to each agent. By introducing the heterogeneity of local interactions, we find that the system will achieve the best performance when each agent's interaction frequency is linearly correlated with its information capacity. Generally, the agents with more information gain more than those with less information, while in the optimal case, each agent almost has the same average profit. In addition, we investigate the role of irrational factor and find an interesting symmetrical behavior.     

Percolation on bipartite scale-free networks

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual-contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with a probability proportional to (kq)^−α, where α is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.     

Incremental routing strategy on scale-free networks

The most important function of a network is for transporting traffic. Due to the low traffic capacity of network systems under the global shortest path routing, plenty of heuristic routing strategies are emerging. In this paper, we propose a heuristic routing strategy called the incremental routing algorithm to improve the traffic capacity of complex networks. We divide the routing process into N$N$(the network size) steps and, at each step, we heuristically calculate all the routes for one source node considering both the dynamic efficient betweenness centrality and node degree information. We do extensive simulations on scale-free networks to confirm the effectiveness of the proposed incremental routing strategy. The simulation results show that the traffic capacity has been enhanced by a substantial factor at the expense of a slight lengthening in the average path.     

Deterministic scale-free small-world networks of arbitrary order

In many real-life networks, both the scale-free distribution of degree and small-world behavior are important features. There are many random or deterministic models of networks to simulate these features separately. However, there are few models that combine the scale-free effect and small-world behavior, especially in terms of deterministic versions. What is more, all the existing deterministic algorithms running in the iterative mode generate networks with only several discrete numbers of nodes. This contradicts the purpose of creating a deterministic network model on which we can simulate some dynamical processes as widely as possible. According to these facts, this paper proposes a deterministic network generation algorithm, which can not only generate deterministic networks following a scale-free distribution of degree and small-world behavior, but also produce networks with arbitrary number of nodes. Our scheme is based on a complete binary tree, and each newly generated leaf node is further linked to its full brother and one of its direct ancestors. Analytical computation and simulation results show that the average degree of such a proposed network is less than 5, the average clustering coefficient is high (larger than 0.5, even for a network of size 2 million) and the average shortest path length increases much more slowly than logarithmic growth for the majority of small-world network models.