A local-world node deleting evolving network model

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as pa decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient 〈C〉 decreases as generally node deleting increases. Finally, 〈C〉 trends up when the local-world size M increases, so as to kmax. Hence, the expanding local-world can compensate the infection of the node deleting.     

Properties of wealth distribution in multi-agent systems of a complex network

We present a simple model for examining the wealth distribution with agents playing evolutionary games (the Prisoners’ Dilemma and the Snowdrift Game) on complex networks. Pareto’s power law distribution of wealth (from 1897) is reproduced on a scale-free network, and the Gibbs or log-normal distribution for a low income population is reproduced on a random graph. The Pareto exponents of a scale-free network are in agreement with empirical observations. The Gini coefficient of an ER random graph shows a sudden increment with game parameters. We suggest that the social network of a high income group is scale-free, whereas it is more like a random graph for a low income group.     

Influence of network structure on rumor propagation

Rumor propagation in complex networks is studied analytically and numerically by using the SIR model. Analytically, a mean-field theory is worked out by considering the influence of network topological structure and the unequal footings of neighbors of an infected node in propagating the rumor. It is found that the final infected density of population with degree k   is ρ(k)=1−exp(−αk)$\rho (k)=1-\exp (-\alpha k)$, where α is a parameter related to network structure. The number of the total final infected nodes depends on the network topological structure and will decrease when the structure changes from random to scale-free network. Numerical simulations confirm the theoretical predictions.     

A class of improved algorithms for detecting communities in complex networks

Detecting communities in complex networks is of considerable importance for understanding both the structure and function of the networks. Here, we propose a class of improved algorithms for community detection, by combining the betweenness algorithm of Girvan and Newman with the edge weight defined by the edge-clustering coefficient. The improved algorithms are tested on some artificial and real-world networks, and the results show that they can detect communities of networks more effectively in both unweighted and weighted cases. In addition, the technique for improving the betweenness algorithm in this paper, thanks to its compatibility, can directly be applied to various detection algorithms.     

A robust matching model of capacity to defense cascading failure on complex networks

How to control the cascading failure has become a hot topic in recent years. In this paper, we propose a new matching model of capacity by developing a profit function to defense cascading failures on artificially created scale-free networks and the real network structure of the North American power grid. Results show that our matching model can enhance the network robustness efficiently, which is particularly important for the design of networks to deduce the damage triggered by the cascading failures.     

Spatial price dynamics: From complex network perspective

The spatial price problem means that if the supply price plus the transportation cost is less than the demand price, there exists a trade. Thus, after an amount of exchange, the demand price will decrease. This process is continuous until an equilibrium state is obtained. However, how the trade network structure affects this process has received little attention. In this paper, we give a evolving model to describe the levels of spatial price on different complex network structures. The simulation results show that the network with shorter path length is sensitive to the variation of prices.     

The effect of asymmetric payoff mechanism on evolutionary networked prisoner’s dilemma game

In social and biological systems, there are obvious individual divergence and asymmetric payoff phenomenon due to the strength, power and influence differences. In this paper, we introduce an asymmetric payoff mechanism to evolutionary Prisoner’s Dilemma Game (PDG) on scale-free networks. The co-effects of individual diversity and asymmetric payoff mechanism on the evolution of cooperation and the wealth distribution under different updating rules are investigated. Numerical results show that the cooperation is highly promoted when the hub nodes are favored in the payoff matrix, which seems to harm the interest of the majority. But the inequality of social wealth distribution grows with the unbalanced payoff rule. However, when the node difference is eliminated in the learning strategy, the asymmetric payoff rule will not affect the cooperation level. Our work may sharpen the understanding of the cooperative behavior and wealth inequality in the society.     

Detect overlapping and hierarchical community structure in networks

Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two properties of community structure separately. This paper proposes an algorithm (EAGLE) to detect both the overlapping and hierarchical properties of complex community structure together. This algorithm deals with the set of maximal cliques and adopts an agglomerative framework. The quality function of modularity is extended to evaluate the goodness of a cover. The examples of application to real world networks give excellent results.     

Spatiotemporal Characteristic of Epidemic Spreading in Mobile Individuals

We numerical simulate the propagation behaviour and people distribution trait of epidemic spreading in mobile individuals by using cellular automaton method. The simulation results show that there exists a critical value of infected rate fluctuating amplitude, above which the epidemic can spread in whole population. Moreover, with the value of infected rate fluctuating amplitude increasing, the spatial distribution of infected population exhibits the spontaneous formation of irregular spiral waves and convergence phenomena, at the same time, the density of different populations will oscillate automatically with time. What is more, the traits of dynamic grow clearly and stably when the time and the value of infected rate fluctuating amplitude increasing. It is also found that the maximal proportion of infected individuals is independent of the value of fluctuating amplitude rate, but increases linearly with the population density.     

A unified model for Sierpinski networks with scale-free scaling and small-world effect

In this paper, we propose an evolving Sierpinski gasket, based on which we establish a model of evolutionary Sierpinski networks (ESNs) that unifies deterministic Sierpinski network [Z.Z. Zhang, S.G. Zhou, T. Zou, L.C. Chen, J.H. Guan, Eur. Phys. J. B 60 (2007) 259] and random Sierpinski network [Z.Z. Zhang, S.G. Zhou, Z. Su, T. Zou, J.H. Guan, Eur. Phys. J. B 65 (2008) 141] to the same framework. We suggest an iterative algorithm generating the ESNs. On the basis of the algorithm, some relevant properties of presented networks are calculated or predicted analytically. Analytical solution shows that the networks under consideration follow a power-law degree distribution, with the distribution exponent continuously tuned in a wide range. The obtained accurate expression of clustering coefficient, together with the prediction of average path length reveals that the ESNs possess small-world effect. All our theoretical results are successfully contrasted by numerical simulations. Moreover, the evolutionary prisoner’s dilemma game is also studied on some limitations of the ESNs, i.e., deterministic Sierpinski network and random Sierpinski network.     

A limited resource model of fault-tolerant capability against cascading failure of complex network

We propose a novel capacity model for complex networks against cascading failure. In this model, vertices with both higher loads and larger degrees should be paid more extra capacities, i.e. the allocation of extra capacity on vertex i will be proportional to k_i ^γ , where k_i is the degree of vertex i and γ > 0 is a free parameter. We have applied this model on Barabási-Albert network as well as two real transportation networks, and found that under the same amount of available resource, this model can achieve better network robustness than previous models.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

Evolutionary ultimatum game on complex networks under incomplete information

This paper studies the evolutionary ultimatum game on networks when agents have incomplete information about the strategies of their neighborhood agents. Our model assumes that agents may initially display low fairness behavior, and therefore, may have to learn and develop their own strategies in this unknown environment. The Genetic Algorithm Learning Classifier System (GALCS) is used in the model as the agent strategy learning rule. Aside from the Watts-Strogatz (WS) small-world network and its variations, the present paper also extends the spatial ultimatum game to the Barabási-Albert (BA) scale-free network. Simulation results show that the fairness level achieved is lower than in situations where agents have complete information about other agents’ strategies. The research results display that fairness behavior will always emerge regardless of the distribution of the initial strategies. If the strategies are randomly distributed on the network, then the long-term agent fairness levels achieved are very close given unchanged learning parameters. Neighborhood size also has little effect on the fairness level attained. The simulation results also imply that WS small-world and BA scale-free networks have different effects on the spatial ultimatum game. In ultimatum game on networks with incomplete information, the WS small-world network and its variations favor the emergence of fairness behavior slightly more than the BA network where agents are heterogeneously structured.     

Other-regarding preference and the evolutionary prisoner’s dilemma on complex networks

Prevailing models of the evolutionary prisoner’s game on networks always assume that agents are pursuing their own profit maximization. But the results from experimental games show that many agents have other-regarding preference. In this paper, we study the emergence of cooperation from the prisoner’s dilemma game on complex networks while some agents exhibit other-regarding preference such as inequality aversion, envious and guilty emotions. Contrary to common ideas, the simulation results show that the existence of inequality aversion agents does not promote cooperation emergence on a BA (Barabási and Albert) scale-free network in most situations. If the defection attraction is big and agents exhibit strong preference for inequality aversion, the frequency of cooperators will be lower than in situations where no inequality aversion agents exist. In some cases, the existence of the inequality agents will even induce the frequency of cooperators to zero, a feature which is not observed in previous research on the prisoner’s dilemma game when the underlying interaction topology is a BA scale-free network. This means that if an agent cares about equality too much, it will be difficult for cooperation to emerge and the frequency of cooperators will be low on BA networks. The research on the effect of envy or guilty emotions on the emergence of cooperation in the prisoner’s dilemma game on BA networks obtains similar results, though some differences exist. However, simulation results on a WS (Watts and Strogatz) small-world network display another scenario. If agents care about the inequality of agents very much, the WS network favors cooperation emergence in the prisoners’ dilemma game when other-regarding agents exist. If the agent weight on other-regarding is lowered, the cooperation frequencies emerging on a WS network are not much different from those in situations without other-regarding agents, although the frequency of cooperators is lower than those of the situation without other-regarding preference agents sometimes. All the simulation results imply that inequality aversion and its variations can have important effects on cooperation emergence in the prisoner’s dilemma game, and different network topologies have different effects on cooperation emergence in the prisoner’s dilemma game played on complex networks.     

Heterogeneity of Some Cooperation/Competition Properties

We show that the heterogeneity index, which was proposed by Hu and Wang [Physica A 387 （2008） 3769], can be used to describe the disparity of the cooperation sharing or competition gain distributions, which is very important for understanding the dynamics of a cooperation/competition system. An analytical relation between the distribution parameters and the heterogeneity index is derived, which is in good agreement with the empirical results. Our theoretical and empirical analyses also show that the relation between the distribution parameters can be analytically derived from the so-called Zhang-Chang model [Physica A 360 （2006） 599; 383 （2007） 687）. This strongly recommends a possibility to create a general dynamic cooperation/competition model.     

Message Spreading and Forget--Remember Mechanism on a Scale-Free Network

We study message spreading on a scale-free network, by introducing a novel forget-remember mechanism. Message, a general term which can refer to email, news, rumor or disease, etc, can be forgotten and remembered by its holder. The way the message is forgotten and remembered is governed by the forget and remember function, F and R, respectively. Both F and R are functions of history time t concerning individual's previous states, namely being active (with message) or inactive (without message). Our systematicsimulations show at the low transmission rate whether or not the spreading can be efficient is primarily determined by the corresponding parameters for F and R.     

Network effects in a human capital based economic growth model

We revisit a recently introduced agent model [ACS, 11, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents’ social network, both on an agent’s decision to pursue education and on the output of new ideas. Regular and random networks are considered. The results are compared with the predictions of a mean field (representative agent) model.     

A new weighting method in network-based recommendation

In this paper, we propose a influence-based approach to investigate network-based recommendation systems. Different from the previous mass diffusion approach, we give a new expression of initial resource distribution and take into account the influence of resources associated with the receiver nodes. According to ranking score and two measures about the degree of personalization, we demonstrate that our method can outperform the previous methods greatly. It’s found that there exists an optimal initial resource distribution that leads to the best algorithmic accuracy and personalization strength. The optimal initial resource distribution indicates that we should increase the initial resource located on popular objects, rather than decrease them.     

Entropy and HUHPM approach for complex networks

The general formulas of the network for the power exponents of the degree distribution and the entropy are presented based on an open Liouville equation for the driven network. The proposed harmonious unifying hybrid preferential models (HUHPM) have been studied using the obtained formalism, in which the simulating results are quite consistent with the theoretical results.     

Influence of different initial distributions on robust cooperation in scale-free networks: A comparative study

We study the evolutionary Prisoner's dilemma game on scale-free networks, focusing on the influence of different initial distributions for cooperators and defectors on the evolution of cooperation. To address this issue, we consider three types of initial distributions for defectors: uniform distribution at random, occupying the most connected nodes, and occupying the lowest-degree nodes, respectively. It is shown that initial configurations for defectors can crucially influence the cooperation level and the evolution speed of cooperation. Interestingly, the situation where defectors initially occupy the lowest-degree vertices can exhibit the most robust cooperation, compared with two other distributions. That is, the cooperation level is least affected by the initial percentage of defectors. Moreover, in this situation, the whole system evolves fastest to the prevalent cooperation. Besides, we obtain the critical values of initial frequency of defectors above which the extinction of cooperators occurs for the respective initial distributions. Our results might be helpful in explaining the maintenance of high cooperation in scale-free networks.