Watts-Strogatz Small-world Network Research Articles

The effect of incentive policies on the diffusion of construction and demolition waste recycling: A government perspective.

Construction and demolition (C&D) waste recycling plays a significant role in waste reduction and carbon reduction, which is critical for sustainable development. However, due to various limitations such as financial problems, C&D waste recycling industry is not well developed in developing countries. To address this problem, this study combines complex network theory and evolutionary game theory to analyse the diffusion of C&D waste recycling behaviour among enterprises under governmental incentive policies within a complex network context. The results demonstrate that the size of the network has limited effects on behaviour diffusion in Watts-Strogatz small-world network. Additionally, the study highlights the clear impact of governmental incentive probability, initial rate and connection degree on the diffusion path. By quantitatively investigating the effects of incentive tools, this study contributes to the knowledge of C&D waste management and provides valuable implications for stakeholders seeking to promote the diffusion of C&D waste recycling.

Modeling Misinformation Spread in a Bounded Confidence Model: A Simulation Study.

Misinformation has posed significant threats to all aspects of people's lives. One of the most active areas of research in misinformation examines how individuals are misinformed. In this paper, we study how and to what extent agents are misinformed in an extended bounded confidence model, which consists of three parts: (i) online selective neighbors whose opinions differ from their own but not by more than a certain confidence level; (ii) offline neighbors, in a Watts-Strogatz small-world network, whom an agent has to communicate with even though their opinions are far different from their own; and (iii) a Bayesian analysis. Furthermore, we introduce two types of epistemically irresponsible agents: agents who hide their honest opinions and focus on disseminating misinformation and agents who ignore the messages received and follow the crowd mindlessly. Simulations show that, in an environment with only online selective neighbors, the misinforming is more successful with broader confidence intervals. Having offline neighbors contributes to being cautious of misinformation, while employing a Bayesian analysis helps in discovering the truth. Moreover, the agents who are only willing to listen to the majority, regardless of the truth, unwittingly help to bring about the success of misinformation attempts, and they themselves are, of course, misled to a greater extent.

A Two-Phase Feature Selection Method for Identifying Influential Spreaders of Disease Epidemics in Complex Networks.

Network epidemiology plays a fundamental role in understanding the relationship between network structure and epidemic dynamics, among which identifying influential spreaders is especially important. Most previous studies aim to propose a centrality measure based on network topology to reflect the influence of spreaders, which manifest limited universality. Machine learning enhances the identification of influential spreaders by combining multiple centralities. However, several centrality measures utilized in machine learning methods, such as closeness centrality, exhibit high computational complexity when confronted with large network sizes. Here, we propose a two-phase feature selection method for identifying influential spreaders with a reduced feature dimension. Depending on the definition of influential spreaders, we obtain the optimal feature combination for different synthetic networks. Our results demonstrate that when the datasets are mildly or moderately imbalanced, for Barabasi-Albert (BA) scale-free networks, the centralities' combination with the two-hop neighborhood is fundamental, and for Erdős-Rényi (ER) random graphs, the centralities' combination with the degree centrality is essential. Meanwhile, for Watts-Strogatz (WS) small world networks, feature selection is unnecessary. We also conduct experiments on real-world networks, and the features selected display a high similarity with synthetic networks. Our method provides a new path for identifying superspreaders for the control of epidemics.

Topology identification for stochastic multi-layer networks via graph-theoretic method

The topological structures of multi-layer networks have an important influence on their dynamical properties, but in most cases the topological structures of networks are unknown. Hence, this paper pays attention to investigating topology identification problems for multi-layer networks with stochastic perturbations. Both intra-layer coupling and inter-layer coupling are incorporated into the research model. Based on the graph-theoretic method and Lyapunov function, topology identification criteria for stochastic multi-layer networks are obtained by designing a suitable adaptive controller. Furthermore, to estimate the time of identification, the finite-time identification criteria are obtained by finite-time control technique. Finally, double-layer Watts–Strogatz small-world networks are presented for numerical simulations to illustrate the correctness of theoretical results.

Event-Triggered Distributed Average Tracking Control for Lipschitz-Type Nonlinear Multiagent Systems.

This article investigates the event-triggered distributed average tracking (ETDAT) control problems for the Lipschitz-type nonlinear multiagent systems with bounded time-varying reference signals. By using the state-dependent gain design approach and event-triggered mechanism, two types of ETDAT algorithms called: 1) static and 2) adaptive-gain ETDAT algorithms are developed. It is the first time to introduce the event-triggered strategy into DAT control algorithms and investigate the ETDAT problem for multiagent systems with Lipschitz nonlinearities, which is more practical in real physical systems and can better meet the needs of practical engineering applications. Besides, the adaptive-gain ETDAT algorithms do not need any global information of the network topology and are fully distributed. Finally, a simulation example of the Watts-Strogatz small-world network is presented to illustrate the effectiveness of the adaptive-gain ETDAT algorithms.

Reconstruction of complex network from time series data based on graph attention network and Gumbel Softmax

It is a challenging practical problem to infer the network structure from measurable time series data. Recently, with the rapid development of graph deep learning, Zhang et al. [Appl. Netw. Sci. 4, 110 (2019)] applied graph neural network to the field of network reconstruction and proposed Gumbel Graph Network. In this paper, a graph deep learning network reconstruction method based on graph attention network and Gumbel Softmax (GAT-GS) is proposed, which can realize high accuracy network reconstruction and node state prediction of discrete and continuous systems. The GAT-GS model is designed based on the dynamic equation of nodes. It consists of two parts: a network structure learner to reconstruct a more real rather than functionally connected networks, based on Gumbel Softmax sampling to generate network structures; and a node state learner using graph attention networks to learn the state evolution of nodes, with the introduction of Laplacian matrix and adjacency matrix for better adaptation to diffusion coupling and unidirectional coupling systems. This model is trained to dynamically adjust the network adjacency matrix and attention coefficients to obtain the network structure and predict the node state. Experimental results show that the GAT-GS model has high reconstruction accuracy, strong robustness and high universality. It can be applied to various kinds of dynamic systems, including Coupled Map Lattice model and Lorenz system, can deal with time series data from regular to complete chaos, can reconstruct various kinds of complex networks, including regular network, Barabási–Albert network and Watts–Strogatz small world network, and it can also reconstruct networks from small scale to large scale with higher computational efficiency.

A new centrality measure based on neighbor loop structure for network dismantling

Nearly all real-world networks are complex networks and usually are in danger of collapse. Therefore, it is crucial to exploit and understand the mechanisms of network attacks and provide better protection for network functionalities. Network dismantling aims to find the smallest set of nodes such that after their removal the network is broken into connected components of sub-extensive size. To overcome the limitations and drawbacks of existing network dismantling methods, this paper focuses on network dismantling problem and proposes a neighbor-loop structure based centrality metric, NL, which achieves a balance between computational efficiency and evaluation accuracy. In addition, we design a novel method combining NL-based nodes-removing, greedy tree-breaking and reinsertion. Moreover, we compare five baseline methods with our algorithm on ten widely used real-world networks and three types of model networks including Erdös-Rényi random networks, Watts-Strogatz small-world networks and Barabási-Albert scale-free networks with different network generation parameters. Experimental results demonstrate that our proposed method outperforms most peer methods by obtaining a minimal set of targeted attack nodes. Furthermore, the insights gained from this study may be of assistance to future practical research into real-world networks.

It is a small world, or is it? A look into two decades of tourism system

By adopting network science and Leiper (1979)’s tourism system conceptualization and by utilizing the UNWTO’s outbound tourism database, a portray of Global Tourism System (GTS) was constructed for the years between 1995 and 2018. GTS was then studied by using the measures of degree distribution, shortest geodesic distance, transitivity, and modularity analysis. Our results showed that GTS is a dense system (≈30%) which becomes denser with an average increase of 0.8% per year. Also while the system is on track to becoming resilient to economic crises, it is becoming vulnerable to other perturbations such as health crises. Furthermore, although GTS’s degree centrality is on the rise, its degree centralization is on a continuous decline. This continuous decline coupled with GTS’s disassortative nature are the indications of system’s decentralization. The findings of this study support the proposed hypothesis that GTS is best represented with Watts–Strogatz small-world network model. Nevertheless, the system’s in-degree and out-degree centrality measures follow two separate evolution regimes. From an out-degree perspective, we witness GTS’s transformation from a broad-scale small-world network to a single-scale one, while from an in-degree perspective, the system strictly follows a broad-scale small-world network. This means that although the small-world network is the best fitting model to GTS, the degree-preserved rewiring process is widely violated and therefore should be considered when modeling GTS. The disassortative nature of GTS and the lack of degree-preserved rewiring process have resulted in an obscure modularity structure which in turn generates a dynamic alternating pattern. Therefore, while, GTS demonstrates a static behavior with a fixed number of modules at all times, it has a dynamic destination membership in modules and destinations’ memberships constantly shift between modules.

Spike-timing-dependent plasticity enhances chaotic resonance in small-world network

Weak signals can be detected by a nonlinear system with an appropriate chaotic current input, known as the chaotic resonance (CR). Based on Watts–Strogatz small-world network, the effects of Spike-timing-dependent plasticity (STDP) on CR were systematically investigated. Numerical simulations showed that, under moderately strong chaotic current inputs, CR is enhanced due to the increase in average coupling strength after STDP learning. The above-mentioned phenomenon was observed even with changes in frequency and the network topology. For networks with different initial coupling strengths, their responses to weak signals after STDP learning are almost the same, indicating that networks with weaker coupling strengths have better plasticity. In addition, the effects of adjusting STDP windows on CR is also investigated. It was found that CR is promoted by STDP with a relatively larger long-time potentiation window, while, suppressed by a STDP with a relatively larger long-time depression window. Also, the area difference between long-time depression and long-time potentiation windows is highly correlated with average coupling strength after STDP learning. These conclusions might provide novel insights into weak signal detection and information transmission in different adaptive neural networks.

Supernodes: a generalization of the rich-club

Abstract In this article, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph $H$, but on the frequency with which a vertex or an edge belongs to such subgraphs. In particular, we are interested in the case where $H$ is a complete graph. These new concepts are termed vertex participation and edge participation, respectively. We combine these concepts with that of the rich-club to identify what we call a Super rich-club and rich edge-club. We show that the concept of vertex participation is a generalization of the rich-club. We present experimental results on randomized Erdös–Rényi and Watts–Strogatz small-world networks. We further demonstrate both concepts on a complex brain network and compare our results to the rich-club of the brain.

Time-delayed Kuramoto model in the Watts-Strogatz small-world networks.

We study the synchronization of small-world networks of identical coupled phase oscillators through the Kuramoto interaction and uniform time delay. For a given intrinsic frequency and coupling constant, we observe synchronization enhancement in a range of time delays and discontinuous transition from the partially synchronized state with defect patterns to a glassy phase, characterized by a distribution of randomly frozen phase-locked oscillators. By further increasing the time delay, this phase undergoes a discontinuous transition to another partially synchronized state. We found the bimodal frequency distributions and hysteresis loops as indicators of the discontinuous nature of these transitions. Moreover, we found the existence of Chimera states at the onset of transitions.

Modeling the Adoption and Diffusion of Mobile Telecommunications Technologies in Iran: A Computational Approach Based on Agent-Based Modeling and Social Network Theory

Understanding the mechanism underlying the mobile telecommunications technologies (MTTs) diffusion in a country is crucial for telecom planners to know how to accelerate their diffusion by designing appropriate scenarios. Considering the technology diffusion as a bottom-up process, this study is aimed at exploring this mechanism, drawing on insights from diffusion of innovation theory and social network theory. Accordingly, an agent-based model is proposed to investigate how MTTs are diffused in Iran over time. The results of this study show, (1) social network of Iranian society seems more similar to a Watts–Strogatz small-world network than a Barabási–Albert preferential attachment network, where the clustering coefficient is high and average path length is low, (2) compared to the compatibility parameter, the advertisement parameter not only is less influential on diffusion of a targeted MTT (i.e., 4G) but also is not necessary for it, and (3) scenarios having the least number of steps and turning points are more appropriate for continuous diffusion of 4G. The proposed study is empirically validated against real-world data ranging from 7/1/2017 to 12/31/2017. We believe it provides telecom planners insights regarding MTTs diffusion mechanism in a social complex structure and the how of scenario designing for increasing their diffusion.

Inter network synchronisation of complex dynamical networks by using smooth proportional integral SMC technique

This paper puts forward the inter network synchronisation of complex dynamical networks (CDNs) using drive-response philosophy. The inter networks consist of a drive network (each node represents a hyperchaotic system) and a response network (consists of chaotic system at each node). Synchronisation is achieved using a novel proportional integral (PI) based sliding mode control (SMC) scheme and inter network synchronisation criterion is derived. Unlike the conventional SMC technique, the proposed proportional integral-sliding mode control (PI-SMC) technique does not result decoupled error dynamics. A smooth switching surface is designed to eliminate the chattering effect. The different network configurations: small-world and scale-free networks, are simulated and the simulation results show that the proposed synchronisation scheme is effective for the inter network synchronisation between two or more CDNs. The effect of relevant parameters on the synchronisation process in the Watts-Strogatz (WS) small-world and Barabasi-Albert (BA) scale-free networks are analysed. Finally, the proposed PI-SMC technique is compared with standard SMC technique to justify the advantages over the standard SMC technique.

Research on optimal control model of complex networks security risk

To solve the problems such as the security risk control and the optimization of the complex networks, an optimal control model of complex networks security risk based on discrete glowworm swarm optimization with key strategy adjustment is proposed. The basic framework of this model is built based on four functional modules including detection and evaluation, strategy selection, control optimization and performance feedback. The optimal evaluation criterions of the security control strategy are constituted of factors such as control cost, benefit reward and negative effect. The discrete glowworm swarm optimization algorithm with key strategy ad-justment is proposed to search for the optimal control strategy of complex network security risk. The concept of control parameter is introduced, whose feedback and adjustment make the optimal control model get evolution-ary. Finally, the model and the algorithm are tested for network security risk optimal control in the Nearest-Neighbor coupled with network, Erdos-Renyi random graph network, Watts-Strogatz small world network and Ba-rabasi-Albert power law network, separately. The availability of the model and the superiority of the algorithm are validated and the effect of the change for the attack strategy to the security risk optimal control model is analyzed by simulations.

Evolutionary Cooperation in Networked Public Goods Game with Dependency Groups

Either in microlevel organizations or macrolevel societies, the individuals acquire benefits or payoffs by forming interdependency groups linked by common interests. Conducting research on the effects of interdependency groups on the evolution of cooperation could have a better understanding of the social dilemma problem. In this paper, we studied a spatial public goods game with nonlocal interdependency groups where each of participants is located in a two-dimensional square lattice or Watts–Strogatz small-world network with payoffs obtaining from the interactions with nearest neighbors. In terms of the enhancement factor, the effects of group density on the evolutionary cooperation can be quite different. For a low enhancement factor, the cooperation level is a nonmonotonic function with the varying density of interdependency groups in the system, which means a proper density of interdependency groups can best promote the cooperative level. For a moderate enhancement factor, a higher density of interdependency groups can always correspond to a higher cooperative level. However, if the enhancement factor is too high, a high density of interdependency groups can impede the evolutionary cooperation. We give the explanations for the different roles of group density of interdependency by using the transition probabilities of C players into D players as well as the reverse. Our findings are very helpful for the understanding of emergence cooperation as well as the cooperation regulation in the selfish individuals.

Small-world networks and synchronisation in an agent-based model of civil violence

ABSTRACTThe rapid evolution and current ubiquity of social media as a form of communication calls for a revision of many models of collective behaviour. In this paper, we modify a classic agent-based model of civil violence by Epstein (2002) consisting of citizen and law-enforcement agents by integrating a Watts-Strogatz small-world network (SWN). The SWN simulates non-local connections between citizens, enabling influence by both local and distant neighbours and providing an analogue to social media. The objective was to examine the influence of non-local connections on civil violence dynamics for varied law-enforcement concentration and network density. For lower law-enforcement concentrations, the SWN influence leads to more frequent large-scale violent outbursts, while for higher law-enforcement concentrations, outcomes depended most strongly on the number of local neighbours. The long-range coupling across the lattice due to the SWN provides a new mechanism for non-trivial dynamics and leads to a synchronisation effect.

A simple and generic paradigm for creating complex networks using the strategy of vertex selecting-and-pairing

In many networks of scientific interest we know that the link between any pair of vertices conforms to a specific probability, such as the link probability in the Barab\'asi-Albert scale-free networks. Here we demonstrate how the distributions of link probabilities can be utilized to generate various complex networks simply and effectively. We focus in particular on the problem of complex network generation and develop a straightforward paradigm by using the strategy of vertex selecting-and-pairing to create complex networks more generic than other relevant approaches. Crucially, our paradigm is capable of generating various complex networks with varied degree distributions by using different probabilities for selecting vertices, while in contrast other relevant approaches can only be used to generate a specific type of complex networks. We demonstrate our paradigm on four synthetic Barab\'asi-Albert scale-free networks, four synthetic Watts-Strogatz small-world networks, and on a real email network with known degree distributions.

Cascading failures with coupled map lattices on Watts–Strogatz networks

In this paper, we present a cascading failure model based on coupled map lattices, in which a given number of crucial nodes are perturbed at the same time. By comparing the effect of five attacking strategies: random strategy, high-degree strategy, high-clustering coefficient strategy, high-betweenness strategy and high-closeness strategy (HCS) on Watts–Strogatz (WS) small-world networks, we found that HCS outperforms the other attacking strategies with different number of perturbed nodes. The efficiency of HCS on WS small-world networks is explored extensively. The results show that increasing the rewiring probability can reduce the range of cascading failures, but it will enhance the propagation speed of cascades. Furthermore, a more compact network structure will lead to a faster cascading failure propagation speed, and the propagation speed of cascades is inversely proportional to the characteristic path length of WS small-world networks. Our work will highlight a better understanding of cascading failures on complex networks.

An optimal routing strategy for transport networks with minimal transmission cost and high network capacity

This paper proposes a routing strategy by minimizing an integrated transmission cost including route cost, distance cost, and traffic pressure cost, which are quantified based on the available transportation routes and travel distance of edges, and the degree of nodes, respectively. In the routing strategy, an arriving rate function is proposed based on the characteristics of heterogeneous traffic demand of nodes, and two parameters, congestion parameter and cost importance parameter are proposed to evaluate the importance of different transmission costs. By tuning the parameters, an optimal routing strategy with high capacity is obtained for different applications. The numerical results on theoretical networks (Watts–Strogatz small-world network and Barabási–Albert network) and real networks (the bus and metro network in Beijing, China) show that the generated new routing strategy can significantly improve the system capacity and operation efficiency. Moreover, the significance of the proposed parameters on evaluating the importance of different transmission costs is precisely proved based on the experimental results, which indicates the effectiveness of the proposed routing strategy.

Market efficiency, strategies and incomes of heterogeneously informed investors in a social network environment

This study introduces a two factor interaction function and a strategy improvement mechanism to construct a heterogeneous information model in a social network environment. Due to the different environmental characteristics of offline and online communication, the Watts Strogatz small world network and the modified Barabási Albert network were used to simulate real-world offline and online environments, respectively, and a market without social networking is added to facilitate comparison. We conducted the market simulation under three different network environments. With simulated market data, the evolution of the investor's strategy, net income, and market efficiency was analyzed. The results show that after three markets reached equilibrium, the number of insider investors and the information cost is the highest in the online environment and the lowest in the noninteractive environment, while market efficiency shows the converse pattern. With social interaction, private signals purchased by investors are publicized in their social circles. This pattern could result in a herd effect of decision making under a false belief, followed by a decrease in market efficiency and an increase in the insider investor ratio. Investors in an online environment have more neighbors and more interlaced social ties than investors in an offline environment. Thus, the increase in information channels facilitates the transformation of private signals into public ones, which further reduces market efficiency and increases the number of insider investors.