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.     

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.     

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.     

Complex scale-free networks with tunable power-law exponent and clustering

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m$m$ “ambassador” nodes and l$l$ of each ambassador’s descendants where m$m$ and l$l$ are random variables selected from any choice of distributions _pl$p_l$ and _qm$q_m$. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m$m$ and the number of selected descendants from each ambassador is the constant l$l$, the power-law exponent is (2l+1)/l$(2l+1)/l$. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l$l$ and m$m$. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.     

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.     

The impact of connection density on scale-free distribution in random networks

Preferential attachment is considered as a fundamental mechanism that contributes to the scale-free characteristics of random networks, which include growth and non-growth networks. There exist some situations of non-growth random networks, particularly for very sparse or dense networks, where preferential attachments cannot consequentially result in true scale-free features, but only in scale-free-like appearances. This phenomenon implies that, a close relationship exists between the connection density p$p$ and the scaling. In this study, we propose a self-organized model with constant network size to study the phenomenon. We show analytically and numerically that there exists a certain critical point _pc$p_c$. Only when p=_pc$p=p_c$, the random network evolves into steady scale-free state. Otherwise, the network exhibits a steady scale-free-like state. The closer the p$p$ approximates _pc$p_c$, the closer the scale-free-like distribution approximates the true scale-free distribution. Our results show that, in random network lack of growth, a preferential scheme does not necessarily lead to a scale-free state, and a formation of scale-free is a consequence of two mechanisms: (i) a preferential scheme and (ii) appropriate connection density.     

Effective usage of shortest paths promotes transportation efficiency on scale-free networks

With rapid economic and social development, the problem of traffic congestion is getting more and more serious. Accordingly, network traffic models have attracted extensive attention. In this paper, we introduce a shortest-remaining-path-first queuing strategy into a network traffic model on Barabási–Albert scale-free networks under efficient routing protocol, where one packet’s delivery priority is related to its current distance to the destination. Compared with the traditional first-in-first-out queuing strategy, although the network capacity has no evident changes, some other indexes reflecting transportation efficiency are significantly improved in the congestion state. Extensive simulation results and discussions are carried out to explain the phenomena. Our work may be helpful for the designing of optimal networked-traffic systems.     

Dynamics of load entropy during cascading failure propagation in scale-free networks

In this Letter, we introduce the concept of load entropy, which can be an average measure of a network's heterogeneity in the load distribution. Then we investigate the dynamics of load entropy during failure propagation using a new cascading failures load model, which can represent the node removal mechanism in many real-life complex systems. Simulation results show that in the early stage of failure propagation the load entropy for a larger cascading failure increases more sharply than that for a smaller one, and consequently the cascading failure with a larger damage can be identified at the early stage of failure propagation according to the load entropy. Particularly, load entropy can be used as an index to be optimized in cascading failures control and defense in many real-life complex networks.     

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.     

Comparison of cascading failures in small-world and scale-free networks subject to vertex and edge attacks

Complex networks may undergo a global cascade of overload failures when a single highly loaded vertex or edge is intentionally attacked. Here we use the recent load model of cascading failures to investigate the performance of the small-world (SW) and scale-free (SF) networks subject to deliberate attacks on vertex and edge. Simulation results suggest that compared with the SW network, the SF network is more vulnerable to deliberate vertex attacks and more robust to deliberate edge attacks. In the SF network, deliberate vertex attacks can result in larger cascading failures than deliberate edge attacks; however, in the SW network the situation is opposite. Furthermore, with the increase of the rewiring probability the SW network becomes more and more robust to deliberate vertex and edge attacks.     

Load balanced diffusive capture process on homophilic scale-free networks

Diffusive capture processes are known to be an effective method for information search on complex networks. The biased N$N$ lions–lamb model provides quick search time by attracting random walkers to high degree nodes, where most capture events take place. The price of the efficiency is extreme traffic concentration on top hubs. We propose traffic load balancing provided by type specific biased random walks. For that we introduce a multi-type scale-free graph generation model, which embeds homophily structure into the network by utilizing type dependent random walks. We show analytically and with simulations that by augmenting the biased random walk method with a simple type homophily rule, we can alleviate the traffic concentration on high degree nodes by spreading the load proportionally between hubs with different types of our generated multi-type scale-free topologies.     

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.     

Traffic of packets with non-homogeneously selected destinations in scale-free network

In this paper, we study the information traffic flow in communication networks with scale-free topology. We consider the situation arising when packets are delivered to non-homogeneously selected destinations. It is found that the network capacity R_c increases with the increase of 〈k〉 (average degree of destination nodes) under local routing strategy. In contrast, R_c is essentially independent of 〈k〉 under shortest path strategy. Based on this finding, an integrated routing strategy that can enhance network capacity is proposed by combining the two strategies.     

Emergency response to disaster-struck scale-free network with redundant systems

Disasters cause tremendous damage every year. In this paper, we have specifically studied emergency response to disaster-struck scale-free networks when some nodes in the network have redundant systems. If one node collapses, its redundant system will substitute it to work for a period of time. In the first part, according to the network structure, several redundant strategies have been formulated, and then our studies focused on their effectiveness by means of simulation. Results show that the strategy based on total degrees is the most effective one. However, many nodes still collapse in the end if redundant systems do not have sufficient capability, so emergency responses are necessary. Several emergent strategies controlling the distribution of external resources have been proposed in the second part. The effectiveness of those emergent strategies are then studied from three aspects, such as the effect of strategies on spreading processes, minimum sufficient quantities of external resources and determination of the most appropriate emergent strategy. In addition, the effects of redundant intensity on these aspects have been discussed as well.     

The networks from medical knowledge and clinical practice have small-world,scale-free,and hierarchical features

Here, we constructed and analyzed a network (henceforth, “medical knowledge network”) derived from a commonly used medical text. We show that this medical knowledge network has small-world, scale-free, and hierarchical features. We then constructed a network from data from a hospital information system that reflected actual clinical practice and found that this network also had small-world, scale-free, and hierarchical features. Moreover, we found that both the diagnosis frequency distribution of the hospital network and the diagnosis degree distribution of the medical knowledge network obeyed a similar power law. These findings suggest that the structure of clinical practice may emerge from the mutual influence of medical knowledge and clinical practice, and that the analysis of a medical knowledge network may facilitate the investigation of the characteristics of medical practice.     

Effects of consumption strategy on wealth distribution on scale-free networks

We investigate wealth distribution on scale-free networks with different consumption strategies. We indicate that nonlinear consumption function can lead to exponential wealth distribution with a power law tail in accordance with empirical data. In addition, we suggest that anti-degree preference and consumption promotion can make distribution more equal. This provides an effective and practical way to optimize the equality of wealth distribution.     

Weighted scale-free networks with variable power-law exponents

We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model.     

Onset of power-law scaling behavior in idiotypic random and scale-free networks

We numerically study the dynamics of model immune networks with random and scale-free topologies. We observe that a memory state is reached when the antigen is attached to the most connected sites of the network, whereas a percolation state may occur when the antigen attaches to the less connected sites. For increasing values of the connectivity of the antibody directly binded to the antigen, its population converges exponentially to the asymptotic value of the memory state. On the other hand, the next-nearest populations evolve slowly as power-laws towards the virgin-like state.     

A stochastic SIR epidemic on scale-free network with community structure

The scale-free degree distribution and community structure are two significant properties shared by numerous complex networks. In this paper, we investigate the impact of these properties on a stochastic SIR epidemic which incorporates the stochastic nature of epidemic spreading. A two-type branching process is employed to approximate the early stage of epidemic spreading. The basic reproduction number _R0$R_0$ is obtained. And the influences of scale-free property and community structure on _R0$R_0$ are analyzed by numerical simulations.     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.