Dynamics In Scale-free Networks Research Articles

Conflict Dynamics in Scale-Free Networks with Degree Correlations and Hierarchical Structure.

We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor's state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions leads to a lower separation. Moreover, positive assortative mixing leads to greater divergence between the states, while negative assortative mixing reduces this dispersion. We also find that hierarchical scale-free networks have both similarities and differences when compared with scale-free networks. Hierarchical scale-free networks, like scale-free networks, show the least divergence for an equal mix of cooperative and competitive interactions between actors. On the other hand, hierarchical scale-free networks, unlike scale-free networks, show much greater divergence when dominated by cooperative rather than competitive actors, and while the formation of a rich club (adding links between hubs) with cooperative interactions leads to greater divergence, the divergence is much less when they are fully competitive. Our findings highlight the importance of the topology where the interaction dynamics take place, and the fact that a balanced presence of cooperators and competitors makes the system more cohesive, compared to the case where one strategy dominates.

Simple epidemic network model for highly heterogeneous populations

Network models for disease transmission and dynamics are popular because they are among the simplest agent-based models. Highly heterogeneous populations (in the number of contacts) may be modeled by networks with long-tailed degree distributions for which the variance is much greater than the mean degree. An example is given by scale-free networks where the degree distribution follows a power law. In these type of networks there is not a typical degree. Some nodes may have low representation in the population but are key to drive disease transmission. Coarse graining may be used to simplify these complex networks. In this work we present a simple model consisting in of a network where nodes have only two possible degrees, a low degree close to the mean degree and a high degree about ten times the mean degree. We show that in spite of this extreme simplification, main features of disease dynamics in scale-free networks are well captured by our model.

Synaptic Failure Differentially Affects Pattern Formation in Heterogenous Networks.

The communication of neurons is primarily maintained by synapses, which play a crucial role in the functioning of the nervous system. Therefore, synaptic failure may critically impair information processing in the brain and may underlie many neurodegenerative diseases. A number of studies have suggested that synaptic failure may preferentially target neurons with high connectivity (i.e., network hubs). As a result, the activity of these highly connected neurons can be significantly affected. It has been speculated that anesthetics regulate conscious state by affecting synaptic transmission at these network hubs and subsequently reducing overall coherence in the network activity. In addition, hubs in cortical networks are shown to be more vulnerable to amyloid deposition because of their higher activity within the network, causing decrease in coherence patterns and eventually Alzheimer’s disease (AD). Here, we investigate how synaptic failure can affect spatio-temporal dynamics of scale free networks, having a power law scaling of number of connections per neuron – a relatively few neurons (hubs) with a lot of emanating or incoming connections and many cells with low connectivity. We studied two types of synaptic failure: activity-independent and targeted, activity-dependent synaptic failure. We defined scale-free network structures based on the dominating direction of the connections at the hub neurons: incoming and outgoing. We found that the two structures have significantly different dynamical properties. We show that synaptic failure may not only lead to the loss of coherence but unintuitively also can facilitate its emergence. We show that this is because activity-dependent synaptic failure homogenizes the activity levels in the network creating a dynamical substrate for the observed coherence increase. Obtained results may lead to better understanding of changes in large-scale pattern formation during progression of neuro-degenerative diseases targeting synaptic transmission.

Metric clusters in evolutionary games on scale-free networks

The evolution of cooperation in social dilemmas in structured populations has been studied extensively in recent years. Whereas many theoretical studies have found that a heterogeneous network of contacts favors cooperation, the impact of spatial effects in scale-free networks is still not well understood. In addition to being heterogeneous, real contact networks exhibit a high mean local clustering coefficient, which implies the existence of an underlying metric space. Here we show that evolutionary dynamics in scale-free networks self-organize into spatial patterns in the underlying metric space. The resulting metric clusters of cooperators are able to survive in social dilemmas as their spatial organization shields them from surrounding defectors, similar to spatial selection in Euclidean space. We show that under certain conditions these metric clusters are more efficient than the most connected nodes at sustaining cooperation and that heterogeneity does not always favor—but can even hinder—cooperation in social dilemmas.

EXACT SOLUTIONS FOR AVERAGE TRAPPING TIME OF RANDOM WALKS ON WEIGHTED SCALE-FREE NETWORKS

In this paper, we present two deterministic weighted scale-free networks controlled by a weight parameter [Formula: see text]. One is fractal network, the other one is non-fractal network, while they have the same weight distribution when the parameter [Formula: see text] is identical. Based on their special network structure, we study random walks on network with a trap located at a fixed node. For each network, we calculate exact solutions for average trapping time (ATT). Analyzing and comparing the obtained solutions, we find that their ATT all grow asymptotically as a power-law function of network order (number of nodes) with the exponent [Formula: see text] dependent on the weight parameter, but their exponent [Formula: see text] are obviously different, one is an increasing function of [Formula: see text], while the other is opposite. Collectively, all the obtained results show that the efficiency of trapping on weighted Scale-free networks has close relation to the weight distribution, but there is no stable positive or negative correlation between the weight distribution and the trapping time on different networks. We hope these results given in this paper could help us get deeper understanding about the weight distribution on the property and dynamics of scale-free networks.

QUEUE RESOURCE REALLOCATION STRATEGY FOR TRAFFIC SYSTEMS IN SCALE-FREE NETWORK

In real communication systems, each node has a finite queue length to store packets due to physical constraints. In this paper, we propose a queue resource allocation strategy for traffic dynamics in scale-free networks. With a finite resource of queue, the allocation of queue length on node i is based on Bi, where Biis the generalized betweenness centrality of node i. The overall traffic capacity of a network system can be evaluated by the critical packet generating rate (Rc). Through the use of the proposed queue allocation scheme for the shortest path protocol and efficient routing protocol, our strategy performs better than the uniform queue length allocation strategy, which is demonstrated by a larger value of the critical generating rate. We also give a method to estimate the network traffic capacity theoretically.

Revealing the process of edge-based-attack cascading failures

In this paper, concerned with the highest-load attack (HL) and random attack (RA) on one edge or one node, we model the cascading dynamics in scale-free networks (SF), WS small-world networks (WS) and ER random networks (ER). How long the cascade propagation in networks will persist and what features the avalanche edges or nodes at each time step will show in cascading failures are questions investigated. We find that, under both HL and RA attack, the persistent time of cascade propagation in SF networks is always longer than in ER and WS networks (except p=0.1). Under HL attack, there exists a threshold αc of tolerance parameter α making the cascading propagation in SF and WS networks longest-running. Moreover, under HL attack, the avalanche edges and nodes in WS and ER networks always reach a peak over a period of time, while the SF network shows similar characteristics only in some field of α. However, under RA attack, in the case of big α, most of the avalanche edges and nodes in SF, WS and ER networks always occur at the beginning of the cascading failures. Furthermore, under node-targeted attack, SF shows to be more vulnerable than under edge-targeted attack and most of avalanche nodes occur at the beginning of failures. The results remind us to grasp the rhythm of controlling disasters according to the features of cascading failures in different 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.

Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics

We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 − p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.

Study on queue resource allocation in scale-free networks

In this article,information traffic dynamics in scale-free networks with limited queue resource is investigated firstly. It is found that the network transits from a free flow state to full congestion state with the increase in the packet generation rate. Then,a queue resource allocation model based on node degree is proposed. The core of this model is to make the queue length of node i proportional to kβi (ki being the degree of node i and β being an allocation parameter). Simulations show that the capacity of the scale-free network is maximal when β is about 1.25 for the shortest path algorithm used to transfer information. Furthermore,the optimal value of allocation parameter β is irrelevant to the network size and the amount of queue resource.

Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node i is proportional to k i ϕ , where k i is the degree of node i and ϕ is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter ϕ leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal ϕ .

Traffic dynamics in scale-free networks with limited buffers and decongestion strategy

We studied the information traffic in Barabási–Albert scale-free networks wherein each node has a finite queue length to store the packets. It is found that in the case of the shortest path routing strategy, the networks undergo a first-order phase transition, i.e. from a free flow state to a full congestion state, with increasing packet generation rate. We also incorporate the random effect (namely random selection of a neighbor to deliver packets) as well as a control method (namely the packet-dropping strategy of the congested nodes after some delay time T) into the routing protocol to test the traffic capacity of the heterogeneous networks. It is shown that there exists an optimal value of T for the networks to achieve the best handling ability, and the presence of an appropriate random effect also contributes to the performance of the networks.