Three-option evolutionary minority game on small-world network

In this paper, we study the three-option evolutionary minority game with imitation on small-world networks. Numerical results show that the performance of the system depends on the ways of modifying the gene values as well as the points awarded to the agents belonging to the intermediate populated group. Better cooperation can be obtained through local communication within the agents.     

Scaling in small-world resistor networks

We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards–Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point resistance in the large system-size limit. We find that the small-world structure suppresses large network resistances: both the average resistance and its standard deviation approaches a finite value in the large system-size limit for any non-zero density of random links. We also consider a scenario where the link conductance decays as a power of the length of the random links, l⁻. In this case we find that the average effective system resistance diverges for any non-zero value of .     

Cascading failure in Watts-Strogatz small-world networks

In this paper, we study the cascading failure in Watts-Strogatz small-world networks. We find that this network model has a heterogeneous betweenness distribution, although its degree distribution is homogeneous. Further study shows that this small-world network is robust to random attack but fragile to intentional attack, in the cascading failure scenario. With comparison to standard random graph and scale-free networks, our result indicates that the robust yet fragile property in the cascading failure scenario is mainly related to heterogeneous betweenness, rather than the network degree distribution. Thus, it suggests that we have to be very careful when we use terms such as homogeneous network and heterogeneous network, unless the distribution we refer to is specified.     

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.     

On the structural properties of small-world networks with range-limited shortcut links

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter (r$r$) sets the length scale over which shortcuts are uniformly distributed. When r=0$r=0$ we have an ordered network, whereas r=1$r=1$ corresponds to the original Watts–Strogatz SWN model. These limited range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for r?1$r?1$, indicating that global shortcuts are not necessary for the small-world effect. For limited range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. We propose an expression for the average path length for limited range SWNs based on numerical simulations and analytical approximations.     

Memory-based evolutionary game on small-world network with tunable heterogeneity

Most papers about evolutionary games on graph assume agents have no memory. Yet, in the real world, interaction history can also affect an agent’s decision. So we introduce a memory-based agent model and investigate the Prisoner’s Dilemma game on a Heterogeneous Newman-Watts small-world network based on a Genetic Algorithm, focusing on heterogeneity’s role in the emergence of cooperative behaviors. In contrast with previous results, we find that a different heterogeneity parameter domain range imposes an entirely different impact on the cooperation fraction. In the parameter range corresponding to networks with extremely high heterogeneity, the decrease in heterogeneity greatly promotes the proportion of cooperation strategy, while in the remaining parameter range, which relates to relatively homogeneous networks, the variation of heterogeneity barely affects the cooperation fraction. Also our study provides a detailed insight into the microscopic factors that contribute to the performance of cooperation frequency.     

A study on small-world brain functional networks altered by postherpetic neuralgia

Understanding the effect of postherpetic neuralgia (PHN) pain on brain activity is important for clinical strategies. This is the first study, to our knowledge, to relate PHN pain to small-world properties of brain functional networks. Functional magnetic resonance imaging (fMRI) was used to construct functional brain networks of the subjects during the resting state. Sixteen patients with PHN pain and 16 (8 males, 8 females for both groups) age-matched controls were studied. The PHN patients exhibited decreased local efficiency along with non-significant changes of global efficiency in comparison with the healthy controls. Moreover, regional nodal efficiency was found to be significantly affected by PHN pain in the areas related to sense (postcentral gyrus, inferior parietal gyrus and thalamus), memory/affective processes (parahippocampal gyrus) and emotional activities (putamen). Significant correlation (p < 0.05) was also found between the nodal efficiency of putamen and pain intensity in PHN patients. Our results suggest that PHN modulates the local efficiency, and the small-world properties of brain networks may have potentials to objectively evaluate pain information in clinic.     

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.     

Continuous opinion model in small-world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al., the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance ?. In directed networks, if agent i is a neighbor of agent j,j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions 〈F〉 and their distribution as a function of ? and of the network structural disorder. In directed networks 〈F〉 exhibits a rich structure, being larger than in undirected networks for higher values of ?, and smaller for lower values of ?.     

Naming game on small-world networks with geographical effects

The naming game model characterizes the main evolutionary features of languages or more generally of communication systems. Very recently, the combination of complex networks and the naming game has received much attention and the influences of various topological properties on the corresponding dynamical behavior have been widely studied. In this paper, we investigate the naming game on small-world geographical networks. The small-world geographical networks are constructed by randomly adding links to two-dimensional regular lattices, and it is found that the convergence time is a nonmonotonic function of the geographical distance of randomly added shortcuts. This phenomenon indicates that, although a long geographical distance of the added shortcuts favors consensus achievement, too long a geographical distance of the added shortcuts inhibits the convergence process, making it even slower than the moderates.     

Long-duration transcutaneous electric acupoint stimulation alters small-world brain functional networks

Acupuncture, which is recognized as an alternative and complementary treatment in Western medicine, has long shown efficiencies in chronic pain relief, drug addiction treatment, stroke rehabilitation and other clinical practices. The neural mechanism underlying acupuncture, however, is still unclear. Many studies have focused on the sustained effects of acupuncture on healthy subjects, yet there are very few on the topological organization of functional networks in the whole brain in response to long-duration acupuncture (longer than 20 min). This paper presents a novel study on the effects of long-duration transcutaneous electric acupoint stimulation (TEAS) on the small-world properties of brain functional networks. Functional magnetic resonance imaging was used to construct brain functional networks of 18 healthy subjects (9 males and 9 females) during the resting state. All subjects received both TEAS and minimal TEAS (MTEAS) and were scanned before and after each stimulation. An altered functional network was found with lower local efficiency and no significant change in global efficiency for healthy subjects after TEAS, while no significant difference was observed after MTEAS. The experiments also showed that the nodal efficiencies in several paralimbic/limbic regions were altered by TEAS, and those in middle frontal gyrus and other regions by MTEAS. To remove the psychological effects and the baseline, we compared the difference between diffTEAS (difference between after and before TEAS) and diffMTEAS (difference between after and before MTEAS). The results showed that the local efficiency was decreased and that the nodal efficiencies in frontal gyrus, orbitofrontal cortex, anterior cingulate gyrus and hippocampus gyrus were changed. Based on those observations, we conclude that long-duration TEAS may modulate the short-range connections of brain functional networks and also the limbic system.     

The evolutionary public goods game on scale-free networks with heterogeneous investment

The public goods game (PGG) is generally considered as a suitable paradigm to explain ubiquitous cooperative behavior. In this study, we investigated the evolutionary PGG on scale-free networks and studied the effect of individual heterogeneity by setting the cooperator x an investment value correlated to its degree as I_x=N⋅k_x^β/∑_jk_j^β, where k_x is the degree of x, j runs over all players and β is a tunable parameter. It is shown that the cooperation level is remarkably promoted by negative values of β whereas it is highly depressed by positive values of β. Moreover, the effect of environmental noise has also been investigated. Our result may sharpen the understanding of cooperation induced by the individual diversity.     

Random pseudofractal networks with competition

In this paper, we present a simple rule which assigns fitness to each edge to generate random pseudofractal networks (RPNs). This RPN model is both scale-free and small-world. We obtain the theoretical results that the power-law exponent is γ=2+1/(1+α) for the tunable parameter α>-1, and that the degree distribution is of an exponential form for others. Analytical results also show that an RPN has a large clustering coefficient and can process hierarchical structure as C(k)∼k^-1 that is in accordance with many real networks. And we prove that the mean distance L(N) scales slower logarithmically with network size N. In particular, we explain the effect of nodes with degree 2 on the clustering coefficient. These results agree with numerical simulations very well.     

Effect of imitation in evolutionary minority game on small-world networks

The system performance in an evolutionary minority game with imitation on small-world networks is studied. Numerical results show that system performance positively correlates with the clustering coefficients. The domain structure of the agents’ strategies can be used to give a qualitative explanation for it. We also find that the time series of the reduced variance σ²/N could have a phasic evolution from a metastable state (two crowds are formed but the distribution of their probabilities does not peak at p≈0 and p≈1) to a steadystate (the two crowds evolve into a crowd and an anticrowd with the distribution of their probabilities peaking at p≈0 and p≈1).     

Word diversity can accelerate consensus in naming game

In this paper,we introduce word diversity that reflects the inhomogeneity of words in a communication into the naming game.Diversity is realized by assigning a weight factor to each word.The weight is determined by three different distributions(uniform,exponential,and power-law distributions).During the communication,the probability that a word is selected from speaker’s memory depends on the introduced word diversity.Interestingly,we find that the word diversity following three different distributions can remarkably promote the final convergency,which is of high importance in the self-organized system.In particular,for all the ranges of amplitude of distribution,the powerlaw distribution enables the fastest consensus,while uniform distribution gives the slowest consensus.We provide an explanation of this effect based on both the number of different names and the number of total names,and find that a wide spread of names induced by the segregation of words is the main promotion factor.Other quantities,including the evolution of the averaging success rate of negotiation and the scaling behavior of consensus time,are also studied.These results are helpful for better understanding the dynamics of the naming game with word diversity.     

Coevolution with weights of names in structured language games

We propose a coevolutionary version to investigate the naming game, a model recently introduced to describe how shared vocabulary can emerge and persist spontaneously in communication systems. We base our model on the fact that more popular names have more opportunities to be selected by agents and then spread in the population. A name’s popularity is concerned with its communication frequency, characterized by its weight coevolving with the name. A tunable parameter governs the influence of name weight. We implement this modified version on both scale-free networks and small-world networks, in which interactions proceed between paired agents by means of the reverse naming game. It is found that there exists an optimal value of the parameter that induces the fastest convergence of the population. This illustration indicates that a moderately strong influence of evolving name weight favors the rapid achievement of final consensus, but very strong influences inhibit the convergence process. The rank-distribution of the final accumulated weights of names qualitatively explains this nontrivial phenomenon. Investigations of some pertinent quantities are also provided, including the time evolution of the number of different names and the success rate, as well as the total memory of agents for different parameter values, which are helpful for better understanding the coevolutionary dynamics. Finally, we explore the scaling behavior in the convergence time and conclude a smaller scaling parameter compared to the previous naming game models.     

Effects of friend-making resources/costs and remembering on acquaintance networks

We consider two overlooked yet important factors that affect acquaintance network evolution and formation—friend-making resources and remembering—and propose a bottom-up, network-oriented simulation model based on three rules representing human social interactions. Our proposed model reproduces many topological features of real-world acquaintance networks, including a small-world phenomenon and a sharply peaked connectivity distribution feature that mixes power-law and exponential distribution types. We believe that this is an improvement over fieldwork sampling methods that fail to capture acquaintance network node connectivity distributions. Our model may produce valuable results for sociologists working with social opinion formation and epidemiologists studying epidemic dynamics.     

Fast convergence in language games induced by majority rule

We propose a simple model to investigate the evolutionary dynamics of a naming game on well-mixed populations. We assume that each individual has an inherent propensity to maintain his own word about an object whereas other individuals would affect his decision when they communicate. On the one hand, individuals learn the word of another one with a probability pertaining to their propensities. On the other hand, the focal individual would adopt the word held by the majority in a randomly selected group. We have numerically explored how dynamical behavior evolves as a result of combination of these two competing update patterns. A parameter governs the time scale ratio at which the two update patterns separately progress. We find that an increasing tendency to adopt the word held by the majority results in a rapid extinction of most words, thus more easily induces the system to a global consensus. Large initial probabilities denoting propensity are found to be unfavorable for the achievement of the consensus. Interestingly, simulation results indicate that the convergence time is negligibly affected by the number of initial distinct words when this number exceeds a certain value. Results from our model may offer an insight into better understanding the intricate dynamics of naming games.     

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.     

Evolutionary minority game on complex networks

In this work we investigate the dynamics of networked evolutionary minority game (NEMG) wherein each agent is allowed to evolve its strategy according to the information obtained from its neighbors in the network. We investigate four kinds of networks, including star network, regular network, random network and scale-free network. Simulation results indicate that the dynamics of the system depends crucially on the structure of the underlying network. The strategy distribution in a star network is sensitive to the precise value of the mutation magnitude L, in contrast to the strategy distribution in regular, random and scale-free networks, which is easily affected by the value of the prize-to-fine ratio R. Under a simple evolutionary scheme, the networked system with suitable parameters evolves to a high level of global coordination among its agents. In particular, the performance of the system is correlated to the clustering property of the network, where larger clustering coefficient leads to better performance.