Small-world Network Model Research Articles

Abnormal suppression of thermal transport by long-range interactions in networks

Heat and electricity are two fundamental forms of energy widely utilized in our daily lives. Recently, in the study of complex networks, there is growing evidence that they behave significantly different at the micro-nanoscale. Here, we use a small-world network model to investigate the effects of reconnection probability p and decay exponent α on thermal and electrical transport within the network. Our results demonstrate that the electrical transport efficiency increases by nearly one order of magnitude, while the thermal transport efficiency falls off a cliff by three to four orders of magnitude, breaking the traditional rule that shortcuts enhance energy transport in small-world networks. Furthermore, we elucidate that phonon localization is a crucial factor in the weakening of thermal transport efficiency in small-world networks by characterizing the density of states, phonon participation ratio, and nearest-neighbor spacing distribution. These insights will pave new ways for designing thermoelectric materials with high electrical conductance and low thermal conductance.

Synchronizability of multi-layer small-world dynamical networks

This paper investigates the synchronizability of multi-layer small-world dynamical networks and discusses the significant factors affecting the synchronizability. First, we introduce the network model of multi-layer small-world dynamical networks with one-to-one connections in the inter-layer connections and each layer has the same topology. Second, we consider the topological parameters including adding probability, intra-layer coupling strength, inter-layer coupling strength, number of nodes per layer, initial node degree, and number of network layers which will influence the network’s synchronizability. Third, we adopt the master stability function method and numerical simulations to analyze the synchronizability of the network. We also examine how the topological parameters influence the synchronizability of multi-layer small-world dynamical networks and the relationships among these parameters. Finally, synchronization control experiments are conducted to verify our results. As a result, we find that only increasing the number of nodes per layer will weaken the synchronizability of multi-layer small-world dynamical networks, while increasing other topological parameters will enhance the synchronizability. The current findings enable us to gain a deeper understanding of the synchronization behavior and characteristics of multi-layer small-world dynamical networks.

The small-world effect for interferometer networks

Complex network theory has focused on properties of networks with real-valued edge weights. However, in signal transfer networks, such as those representing the transfer of light across an interferometer, complex-valued edge weights are needed to represent the manipulation of the signal in both magnitude and phase. These complex-valued edge weights introduce interference into the signal transfer, but it is unknown how such interference affects network properties such as small-worldness. To address this gap, we have introduced a small-world interferometer network model with complex-valued edge weights and generalized existing network measures to define the interferometric clustering coefficient, the apparent path length, and the interferometric small-world coefficient. Using high-performance computing resources, we generated a large set of small-world interferometers over a wide range of parameters in system size, nearest-neighbor count, and edge-weight phase and computed their interferometric network measures. We found that the interferometric small-world coefficient depends significantly on the amount of phase on complex-valued edge weights: for small edge-weight phases, constructive interference led to a higher interferometric small-world coefficient; while larger edge-weight phases induced destructive interference which led to a lower interferometric small-world coefficient. Thus, for the small-world interferometer model, interferometric measures are necessary to capture the effect of interference on signal transfer. This model is an example of the type of problem that necessitates interferometric measures, and applies to any wave-based network including quantum networks.

Uncovering the hidden structure of small-world networks

The small-world (SW) network model introduced by Watts and Strogatz has significantly influenced the study of complex systems, spurring the development of network science as an interdisciplinary field. The Newman-Watts model is widely applied to analyze SW networks by adding several randomly placed shortcuts to a regular lattice. We meticulously examine related previous works and conclude that the scaling of various pertinent quantities lacks convincing evidence. We demonstrate that the SW property primarily stems from the existence of clusters of nodes linked by shortcuts rather than just the mean number of shortcuts. Introducing the mean degree of clusters linked by shortcuts as a new key parameter resolves the scaling ambiguity, yielding a more precise characterization of the network. Our findings provide a new framework for analyzing SW networks, highlighting the significance of considering emergent structures in complex systems. We also develop a phase diagram of the crossover transition from the small to the large world, offering profound insights into the nature of complex networks and highlighting the power of emergence in shaping their behavior.

Analytical modeling of robustness and stochastic resilience of temporal small-world complex networks

This article explores the impact of online/offline node processes and Byzantine failures on the resilience of small-world network models, considering the lifetime of network nodes. We present novel analytical equations for estimating the expected communication time before user and network isolation, offering a unique perspective on network resilience through the lens of user behavior and involvement. Unlike most analyses focusing on stationary conditions, we employ network renewal processes to model these occurrences in temporal small-world networks where nodes can be online or offline. Our analytical equations, based on node lifetime distributions, shed light on the likelihood of network isolation under these conditions, offering valuable insights for optimizing network design and management. The validation of our analytical models through extensive simulations not only underscores their accuracy but also paves the way for a deeper understanding of temporal network behavior and resilience beyond the small-world paradigm.

Sustainable Regional Straw Utilization: Collaborative Approaches and Network Optimization

The SDGS repeatedly emphasizes the importance of reducing greenhouse gas emissions such as carbon dioxide. The strategic utilization of straw resources to curtail open-air burning not only epitomizes optimal resource deployment but also constitutes a significant stride in environmental preservation and sustainable development. Globally, the imperative of this challenge is increasingly recognized, prompting nations to enhance straw resource utilization technologies, devise regional management strategies, and extend requisite policy support. Regional straw utilization encapsulates a comprehensive concept involving an array of stakeholders including governments, farmers, corporations, brokers, and rural cooperatives, with each one of these uniquely contributing to a multifaceted network that is influenced by their respective resource utilization intentions. This heterogeneity, coupled with the diverse roles of these stakeholders, renders the identification of the pivotal participants and their specific functions within the intricate network. To navigate this complexity, this study employed text analysis and social network analysis, uncovering 30 robust associative rules within this domain. Our findings elucidate that the stakeholder network in regional straw resource utilization exhibits characteristics akin to the NW small-world network model. The key network entities identified include farmers, corporations, governments, and rural cooperatives. Furthermore, the study systematically categorizes the principal entities and elucidates the dynamics of this multi-stakeholder network. This research delineates four developmental models that are pertinent to regional straw resource utilization, which is a framework that is instrumental in pinpointing the accountable parties and optimizing the overarching benefits derived from these resources. The significance of this research lies not only in showcasing the potential of straw resources for environmental conservation but also in underscoring the importance of collaborative strategies and network optimization in order to achieve sustainable development goals.

Mosaic: in-memory computing and routing for small-world spike-based neuromorphic systems

The brain’s connectivity is locally dense and globally sparse, forming a small-world graph—a principle prevalent in the evolution of various species, suggesting a universal solution for efficient information routing. However, current artificial neural network circuit architectures do not fully embrace small-world neural network models. Here, we present the neuromorphic Mosaic: a non-von Neumann systolic architecture employing distributed memristors for in-memory computing and in-memory routing, efficiently implementing small-world graph topologies for Spiking Neural Networks (SNNs). We’ve designed, fabricated, and experimentally demonstrated the Mosaic’s building blocks, using integrated memristors with 130 nm CMOS technology. We show that thanks to enforcing locality in the connectivity, routing efficiency of Mosaic is at least one order of magnitude higher than other SNN hardware platforms. This is while Mosaic achieves a competitive accuracy in a variety of edge benchmarks. Mosaic offers a scalable approach for edge systems based on distributed spike-based computing and in-memory routing.

The Main Mechanisms and Characteristics of the Impart of Social Network on Consumer Behavior

Based on the contemporary social network environment, this paper discusses the practical significance of its impact on consumer behavior, and influencers as the main component of social network, this paper mainly take the mega-influencers and small influencers as the research object, through the analysis of the characteristics and application of the small-world network social network model to the micro-influencers, it is concluded that the influence of the mega- influencers on consumer decision-making is very important, but micro-influencers also play a subtle role in consumer behavior, which can be perceived as inseparable. At the same time, the application of small-world network model in economic management is a relatively new research field, which brings new ideas for economic management research and provides an effective technical tool. For example, this paper studies a new model of marketing through small-world network community, and innovates marketing strategy from two aspects of dominance and suggestion according to the different characteristics of mega-influencers and micro-influencers.

Synchronization in Coupled Neural Networks With Hybrid Delayed Impulses: Average Impulsive Delay-Gain Method.

In this article, we propose a new concept called average impulsive delay-gain (AIDG) for studying the synchronization of coupled neural networks (CNNs). Based on the viewpoints of impulsive control and impulsive perturbation, we establish some globally exponential synchronization criteria for CNNs. Our methods are well-suited for addressing the synchronization problems of systems subject to hybrid delayed impulses with time-varying impulsive delay and gain. Moreover, we prove that the AIDG has both positive and negative effects on synchronization. Compared to existing research, our conclusions are more applicable and less conservative as the considered hybrid delayed impulses involve more flexible cases. Finally, we validate the effectiveness of our proposed results by applying them to small-world and scale-free network models.

Evolution prediction method for electric private car ownership considering the decision-making behaviour of consumers

A global consensus has been reached that promotes full electrification in the automotive field to solve environmental problems, and Electric Vehicles (EVs) have developed rapidly in recent years. China has gradually promoted electrification for taxis, trucks, and private cars. Due to the large number of electric private cars (EPCs), the evolutionary impact of EPC ownership on the charging demand and even the power grid at different stages cannot be ignored. But the evolution of EPC ownership is affected by many factors, and the prediction accuracy is low. Thus, an evolution prediction method of EPC ownership considering the decision-making behaviour of consumers is proposed. Firstly, considering the mutual influence of the individual mental state of consumers for EPC, the social network of consumers is generated based on the small-world network model. Secondly, to simulate the psychological state of consumers and decision-making behaviour, a consumer-state decision model is built based on the Markov chain. Considering the influence of multiple factors on the individual decision-making behaviour of consumers, transfer indicators are constructed to quantify the transfer of states of consumers. Then, combined with the historical data, the development of EPC ownership is predicted. Finally, the effectiveness of the prediction method is verified based on the Shanghai EPC ownership. Compared with other methods, the prediction accuracy of the proposed method is improved by 6.4%, and the evolution of EPC ownership in Chinese different regions can be quantified to provide a basis for related research.

Nearest-neighbor directed random hyperbolic graphs.

Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model where nodes randomly distributed on a hyperbolic disk are connected to a fixed number m of their nearest spatial neighbors. We introduce also a canonical version of this network (which we call "network with varied connection radius"), where maximal length of outgoing bond is space dependent and is determined by fixing the average out-degree to m. We study local bond length, in-degree, and reciprocity in these networks as a function of spacial coordinates of the nodes and show that the network has a distinct core-periphery structure. We show that for small densities of nodes the overall in-degree has a truncated power-law distribution. We demonstrate that reciprocity of the network can be regulated by adjusting an additional temperature-like parameter without changing other global properties of the network.

Desynchronization of neuronal firing in multiparameter ultrasound stimulation

Low-intensity transcranial ultrasound stimulation, a novel neuromodulation technique, that possesses the advantages of non-invasiveness, high penetration depth, and high spatial resolution, has achieved positive neuromodulation effects in animal studies. But the regulatory mechanism remains controversial. The intramembrane cavitation effect is considered one of the mechanisms for ultrasound neuromodulation. In this study, the modified equations of ultrasonic cavitation bubble dynamics were coupled with the dual-coupled neuron Hindmarsh-Rose model, small-world neural network model, and the Jansen-Rit neural mass model, which simulate simple coupled neurons, complex neuronal networks, and discharge signals in epileptic disorders respectively. The results demonstrated that ultrasound stimulation has an appreciable modulatory effect on neuronal firing desynchronization in Hindmarsh-Rose model and small-world neural network model. The desynchronization effect is related to the stimulation frequency and intensity. Furthermore, ultrasound stimulation has an inhibitory effect on epileptic seizures, and the effect is enhanced by increasing ultrasound frequency from 0.1–1.0 MHz. This is the first combination of ultrasonic intramembrane cavitation effect theory with neurons and neural network firing desynchronization, which can provide guidance of parametric and theories support for the studies of neurological diseases such as epilepsy and Parkinson’s disease.

Revisiting small-world network models: exploring technical realizations and the equivalence of the Newman–Watts and Harary models

Revisiting small-world network models: exploring technical realizations and the equivalence of the Newman–Watts and Harary models

Nonlinear dynamic model for COVID-19 epidemics using the Gaussian distributed wiring small-world network technique

The coronavirus (COVID-19) pandemic began in late 2019, unleashing a severe human health crisis that lasted three years and caused immeasurable economic losses worldwide. Although the World Health Organization declared the end of its emergency phase in May 2023, formulating measures by predicting transmission trends of the epidemic is one of the crucial ways to monitor and contain this disease. On the other hand, epidemiological studies have shown that the spatial structure of the population is a vital factor in the spread of epidemics. When infectious diseases invade a region, epidemics are often transmitted through connectivity between hosts. Therefore, in this study, we propose a small-world network model to simulate the transmission of the COVID-19 epidemic. However, the small-world network is organized by Gaussian distributed wiring that satisfies the frequency-distance rule in human mobility theory. Based on its nonlinear dynamic properties, an epidemic prediction model is developed. We performed numerical simulations and evaluated the accuracy of the prediction model. The results show that a high level of accuracy was achieved. The prediction model is examined using the MoH Malaysia COVID-19 dataset. When compared, our model showed lower fitting errors and was closer to the actual curves than the SIR model.

Synchronous oscillation characteristic and finite-time function projection synchronization control method for microgrids

Due to the nonsynchronization of each microsource node in a microgrid, the physical parameters of each node are not uniform. Therefore, unstable oscillation will occur for the whole microgrid system. To solve the oscillation problem caused by the nonsynchronization of each microsource node in the microgrid, a hierarchical control structure microgrid model is researched in this paper. Based on the theory of chaotic synchronization and finite time, a new microgrid synchronous oscillation characteristic and finite-time function projection synchronization control method is proposed. First, combining complex networks and microgrids, a nonlinear dynamic model of microgrid hierarchical control is established, and the abilities of the small-world network model and the formal network model to adjust for asynchronous oscillations are verified by comparing the two models. Then, aiming at the unsynchronized oscillations caused by external system noise, a new finite-time function projection synchronization control method is proposed. According to the verification results, the method can control external disturbances, avoiding system oscillation.

Dynamic analysis of the optimal guiding mechanism for second emission trading market in China

Second emission trading market is not active in China so far, and the reason mainly lies in that enterprises do not have strong initiative for transaction. Thus it's meaningful to study related guiding mechanisms from the perspective of enterprises behavior. In this paper, an evolutionary game model and a small-world network model considering stock heterogeneity are constructed based on four given guiding mechanisms, and a simulation study is conducted through China Zhejiang emission trading market. The result shows that: (1) the optimal guiding mechanism is dynamic and changes from reward-punishment for both enterprises with surplus stock and enterprises with insufficient stock to reward-punishment for enterprises with insufficient stock when trading preferential profit coefficient increases to 1. (2) when penalty coefficient changes, the optimal guiding mechanism is the reward-punishment for both enterprises with surplus stock and enterprises with insufficient stock and keeps unchanged. (3) the enterprises with insufficient stock are more sensitive to penalty coefficient and trading preferential profit coefficient, especially to the latter, so it's better to stimulate the emission rights purchasing side and formulate positive reinforcement methods. The study of this paper can provide decision-making suggestions for Chinese government to stimulate the activity of second emission trading market.

Large-deviation properties of SIR model incorporating protective measures

We simulate spreads of diseases for the susceptible–infected–recovered (SIR) model on contact networks with a particular focus on incorporated protective measures such as face masks. We consider the small-world network model. By using a large-deviation approach, in particular the Wang–Landau algorithm, we obtained the full probability density function (pdf) of the cumulative number C of infected people over the full range of its support. In this way we are able to reach probabilities as small as 10−50. We obtain distinct characteristics in the pdf such as non-analyticities induced by the onset of the protective measures. Still, the results indicate that the mathematical large-deviation principle also holds for this extended SIR model, meaning that the size-dependence enters in P(C) in a simple fashion and the distribution is determined by the so-called rate function. We observe different phases in the pdf, which we investigate by analyzing the corresponding infection courses, i.e. time series, and and their correlations to the observed values of C.

The Diffusion of Competitive Platform-Based Products with Network Effects

The existence of network effects not only changes traditional product diffusion patterns but also has significant impacts on individuals’ decision behaviors. Previous studies on competitive product diffusion have focused on macro-level diffusion speed and effects while neglecting the micro-level impacts of individual heterogeneity and social interaction on product diffusion. This paper introduces the individual heterogeneities and social interactions of consumers into the competitive product diffusion model on the basis of a two-sided market framework and complex network theory. We proposed a small world network model and behavioral game theory. Specifically, the small world network model was used to build interactions between users, and behavioral game theory was utilized to describe the interactions between users. In our model, the direct network effect was distinguished from the indirect network effect on the basis of the synergy of multiple complementary products. The results show that the final distribution often presented a situation wherein two products coexisted, but the market share was very different. In an asymmetric first-mover situation, the direct network effect dominated the indirect network effect. Moreover, the dominant position of one product at present can be changed by the other under certain conditions. Finally, when the switching and learning costs were high, the market maintained its concentration, and the prior platform was unable to dominate the market. A decrease in the costs raised the prior platform’s market share and the speed of market occupation.

Study on Characteristics and Invulnerability of Airspace Sector Network Using Complex Network Theory

The air traffic control (ATC) network’s airspace sector is a crucial component of air traffic management. The increasing demand for air transportation services has made limited airspace a significant challenge to sustainable and efficient air transport operations. To address the issue of traffic congestion and flight delays, improving the operational efficiency of ATC has been identified as a key strategy. A clear understanding of the characteristics of airspace sectors, which are the building blocks of ATC, is essential for optimizing air traffic management. In this research, a novel approach using complex network theory was applied to examine the features and invulnerability of the airspace sector network. We developed a model of the airspace sector network by treating air traffic control sectors as network nodes and the flow of air traffic between these sectors as edges. Network characteristics were analyzed using several metrics including degree, intensity, average path length, betweenness centrality, and clustering coefficient. The static invulnerability of the airspace sector network was evaluated through simulation, and the network efficiency and the size of the connected component were used to assess its invulnerability. A study was conducted in North China based on the ATC sector network. The findings of the study revealed that the sector network did not exhibit the traits of a small-world network model, characterized by short average path lengths and high clustering coefficients. The evaluation of network invulnerability showed that the network’s invulnerability varied depending on the attack strategy used. It was discovered that attacking sectors with high betweenness resulted in the most significant harm to network invulnerability, and betweenness centrality was considered to be a useful indicator for identifying critical sectors that require optimization.

Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme

Small-world networks have been of increasing interest because of their high similarity with complex networks in reality. Achievements about controlling the propagation and evolution of small world networks have been highlighted, but little is known about the tipping mechanism and control of such network. In this paper, a novel dynamic delayed feedback scheme is put forward and applied to successfully control the tipping phenomenon in small-world networks. Firstly, the linear characteristic equation of the controlled system is analyzed and the conditions for stability and the occurrence of bifurcation-induced tipping are given. Then, the direction of Hopf bifurcation, which reveals the further evolution mechanism of tipping, is analyzed by using the normal form theory and center manifold reduction. Finally, the numerical simulations are provided to support the theoretical analysis and to verify the effectiveness of the proposed dynamic delayed feedback controller for the small-world network.