Scale-free Networks Research Articles

Impacts of the Middle Route of China's South-to-North Water Diversion Project on the water network structure in the receiving basin.

The Middle Route of South-to-North Water Diversion Project (MRSNWD) is the main skeleton of China's National Water Network, its construction has changed the structure of the original water network, and analyzing the topological change of the water network in context with MRSNWD is significant for water network planning and management. In this study, the overall network characteristics of the water network in 2010 and 2020 were analyzed based on the small-world and scale-free characteristics of complex network theory. The topological changes of the water network from a node perspective were examined using three network centrality indexes: degree centrality (DC), closeness centrality (CC), and betweenness centrality (BC), while assessing the important nodes of the water network and recognizing functional areas of cold-hot spots. The results show that the water network's centrality in the study area improved after the project construction, with the average degree of the water network increasing from 2.39 to 2.42 and the average path length decreasing from 111.81 to 97.08. The propagation efficiency and network stability also increased, with a rise in important node proportion from 9.8 to 14.4%. The nodes in the DC hotspot zone along the project route have increased by 1.5%, implying an increase in the connectivity of the water network, while MRSNWD optimizes its north-south hub propagation path. "Small-worldness" indicates that most nodes of a network can be accessed and connected over shorter paths. The water network has a significant "small-worldness" and has been enhanced by the MRSNWD's construction. Approximating the water network as a scale-free network can impact its security by identifying critical nodes. The results of this research can provide the necessary technical support and reference significance for China's National Water Network.

A new evolutional model for institutional field knowledge flow network

Abstract Purpose This paper aims to address the limitations in existing research on the evolution of knowledge flow networks by proposing a meso-level institutional field knowledge flow network evolution model (IKM). The purpose is to simulate the construction process of a knowledge flow network using knowledge organizations as units and to investigate its effectiveness in replicating institutional field knowledge flow networks. Design/Methodology/Approach The IKM model enhances the preferential attachment and growth observed in scale-free BA networks, while incorporating three adjustment parameters to simulate the selection of connection targets and the types of nodes involved in the network evolution process Using the PageRank algorithm to calculate the significance of nodes within the knowledge flow network. To compare its performance, the BA and DMS models are also employed for simulating the network. Pearson coefficient analysis is conducted on the simulated networks generated by the IKM, BA and DMS models, as well as on the actual network. Findings The research findings demonstrate that the IKM model outperforms the BA and DMS models in replicating the institutional field knowledge flow network. It provides comprehensive insights into the evolution mechanism of knowledge flow networks in the scientific research realm. The model also exhibits potential applicability to other knowledge networks that involve knowledge organizations as node units. Research Limitations This study has some limitations. Firstly, it primarily focuses on the evolution of knowledge flow networks within the field of physics, neglecting other fields. Additionally, the analysis is based on a specific set of data, which may limit the generalizability of the findings. Future research could address these limitations by exploring knowledge flow networks in diverse fields and utilizing broader datasets. Practical Implications The proposed IKM model offers practical implications for the construction and analysis of knowledge flow networks within institutions. It provides a valuable tool for understanding and managing knowledge exchange between knowledge organizations. The model can aid in optimizing knowledge flow and enhancing collaboration within organizations. Originality/value This research highlights the significance of meso-level studies in understanding knowledge organization and its impact on knowledge flow networks. The IKM model demonstrates its effectiveness in replicating institutional field knowledge flow networks and offers practical implications for knowledge management in institutions. Moreover, the model has the potential to be applied to other knowledge networks, which are formed by knowledge organizations as node units.

Gut microbiota-driven metabolic alterations reveal gut–brain communication in Alzheimer’s disease model mice

ABSTRACT The gut microbiota (GM) and its metabolites affect the host nervous system and are involved in the pathogeneses of various neurological diseases. However, the specific GM alterations under pathogenetic pressure and their contributions to the “microbiota – metabolite – brain axis” in Alzheimer’s disease (AD) remain unclear. Here, we investigated the GM and the fecal, serum, cortical metabolomes in APP/PS1 and wild-type (WT) mice, revealing distinct hub bacteria in AD mice within scale-free GM networks shared by both groups. Moreover, we identified diverse peripheral – central metabolic landscapes between AD and WT mice that featured bile acids (e.g. deoxycholic and isodeoxycholic acid) and unsaturated fatty acids (e.g. 11Z-eicosenoic and palmitoleic acid). Machine-learning models revealed the relationships between the differential/hub bacteria and these metabolic signatures from the periphery to the brain. Notably, AD-enriched Dubosiella affected AD occurrence via cortical palmitoleic acid and vice versa. Considering the transgenic background of the AD mice, we propose that Dubosiella enrichment impedes AD progression via the synthesis of palmitoleic acid, which has protective properties against inflammation and metabolic disorders. We identified another association involving fecal deoxycholic acid-mediated interactions between the AD hub bacteria Erysipelatoclostridium and AD occurrence, which was corroborated by the correlation between deoxycholate levels and cognitive scores in humans. Overall, this study elucidated the GM network alterations, contributions of the GM to peripheral – central metabolic landscapes, and mediatory roles of metabolites between the GM and AD occurrence, thus revealing the critical roles of bacteria in AD pathogenesis and gut – brain communications under pathogenetic pressure.

Coupling resonance of signal responses induced by heterogeneously mixed positive and negative couplings in cognitive subnetworks

How weak external signals are detected in cognitive subnetworks is one of the key problems to understand how brain functions work. So far, most studies on signal responses are focused on artificial complex networks and it is found that a topological resonance can be induced by the feature of scale-free networks, but little attention has been paid to real brain networks, especially the cognitive subnetworks responsible for signal responses. Herein we address this problem in real brain networks but do not find such a topological resonance, indicating that scale-free is not the key feature of brain networks. Surprisingly, we find a novel resonance effect of signal response induced by heterogeneously mixed positive and negative couplings and thus name it as coupling resonance of signal responses, which explains the mechanism of how brain networks, especially the cognitive subnetworks, detects weak signals. We investigate this coupling resonance in the cases of both heterogeneous couplings and heterogeneous oscillators and find that there is an optimal phenomenon on both the average and standard deviation of coupling strengths. Further, we confirm this coupling resonance in real cognitive subnetworks with weighted links. Finally, we provide a theoretical analysis to show that this coupling resonant comes from the coexistence of the two different local states of neighboring nodes.

Exploring universality of the β-Gaussian ensemble in complex networks via intermediate eigenvalue statistics.

The eigenvalue statistics are an important tool to capture localization to delocalization transition in physical systems. Recently, a β-Gaussian ensemble is being proposed as a single parameter to describe the intermediate eigenvalue statistics of many physical systems. It is critical to explore the universality of a β-Gaussian ensemble in complex networks. In this work, we study the eigenvalue statistics of various network models, such as small-world, Erdős-Rényi random, and scale-free networks, as well as in comparing the intermediate level statistics of the model networks with that of a β-Gaussian ensemble. It is found that the nearest-neighbor eigenvalue statistics of all the model networks are in excellent agreement with the β-Gaussian ensemble. However, the β-Gaussian ensemble fails to describe the intermediate level statistics of higher order eigenvalue statistics, though there is qualitative agreement till n<4. Additionally, we show that the nearest-neighbor eigenvalue statistics of the β-Gaussian ensemble is in excellent agreement with the intermediate higher order eigenvalue statistics of model networks.

Identifying critical nodes of cyber–physical power systems based on improved adaptive differential evolution

The identification and protection of critical nodes have a significant influence on the reliability and robustness of the cyber–physical power system (CPPS), which can effectively reduce the risk of cascading failures. Firstly, this paper establishes a one-to-one coupled cascading fault model, which considers different topological characteristics of power and cyber networks. Based on the interdependence between the two networks, the cascading fault propagation mechanism after node failures in CPPS is analyzed. Then, a critical node identification method based on improved adaptive differential evolution (JADE) is proposed to identify the sets of critical nodes that can maximize the impact on the system load of CPPS. Combined with the cascading failure characteristics of CPPS, in the population generation strategy, the test vectors that do not meet the conditions after the crossover operation are filtered and replaced to improve the search efficiency of the algorithm. Finally, in the case study, an interdependent CPPS is constructed with an IEEE 39-bus system and a scale-free network of the same nodes. The simulation results verify the effectiveness of the proposed node importance assessment strategy. In addition, it is also shown that evaluating the critical nodes in power systems is important for enhancing the robustness and ensuring the security of the power grid operation.

Large-scale robustness-oriented efficient edge addition through traversal tree-based weak edge identification

To build robust networks, a popular way is to add edges to existing networks, which can help defend against natural disasters or malicious attacks that randomly or intentionally break several key links at once. There is an urgent need to optimally add edges to improve robustness, e.g., measured by general metrics such as graph connectivity. However, although exhausting and connecting both sides of all small cuts is a sure way to achieve feasible solutions, since the number of possible edges to add is much more than the existing number of edges, even the problem instances in the small graphs are too complex to be solved efficiently, while applying heuristic algorithms to large-scale graphs can only achieve very inefficient results. Fortunately, we find an efficient way to represent all candidate cuts based on the mapping between trees and cuts, and find the near-optimal set of endpoints that cross both sides of all these cuts, and finally find the optimal number of edges reinforcing these cuts to improve edge connectivity. Experiments in representative Erdos–Renyi and scale-free graphs show that the proposed algorithm can achieve perfectly improved results as the optimal algorithm, and the computing speed can be at most 6 orders of magnitude faster than the optimal algorithm, at the expense of slightly increased edge count. The large graph results show the obvious advantage of the proposed algorithms in providing near-perfect results, while popular heuristic algorithms are almost useless in protecting these networks. The proposed algorithm can be further efficient by exploiting its ready-to-parallelize logics for further acceleration.

Epidemic modelling requires knowledge of the social network

‘Compartmental models’ of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of ‘random mixing’ is usually made, which ignores network structure. However, ‘super-spreading events’ have been found to be power-law distributed, suggesting that the underlying networks may be scale free or at least highly heterogeneous. The random-mixing assumption would then produce an overestimation of the herd-immunity threshold for given R 0; and a (more significant) overestimation of R 0 itself. These two errors compound each other, and can lead to forecasts greatly overestimating the number of infections. Moreover, if networks are heterogeneous and change in time, multiple waves of infection can occur, which are not predicted by random mixing. A simple SIR model simulated on both Erdős–Rényi and scale-free networks shows that details of the network structure can be more important than the intrinsic transmissibility of a disease. It is therefore crucial to incorporate network information into standard models of epidemics.

Turing instability analysis of a reaction–diffusion system for rumor propagation in continuous space and complex networks

Research on the propagation of online rumors necessitates careful consideration of rumor-spreading mechanisms. Media correction, self-correction, and the time delays associated with contact propagation are expressly introduced into the established reactive–diffusion rumor-spreading model in this paper. The conditions for a unique positive equilibrium point in the model are analyzed, laying the necessary groundwork for the occurrence of Turing instability in reaction–diffusion rumor propagation systems. A linearization approach is employed to derive the conditions for Turing instability in scenarios involving small delay to address the challenges posed by models with time delay. Furthermore, in order to anticipate the Turing pattern formation in advance, we employed a multiscale analysis approach to derive the amplitude equation within this model. The validity of the theoretical results is verified through numerical simulations, while the propagation dynamics of the model were analyzed within two complex network models, namely small-world networks and scale-free networks. Simulation results indicate that increasing time delay decelerates rumor propagation, while higher degrees of cross-diffusion, contact spreading, media correction, and self-correction expedite the spread of rumors. In small-world networks, the trust level in rumors has a narrower range, while in scale-free networks, the stability of rumors is faster. This indicates how to effectively adjust network structures for controlling or managing the spread of rumors.

Majority-vote model with collective influence of hierarchical structures

Majority-vote model is a commonly used model in the study of opinion dynamics. In the original majority-vote model, the influence of node is determined by their neighbors. But there are nodes with low degree surrounded by nodes with high degree so they also have a great influence on the evolution of opinions. Therefore, the influence of a node should not only be measured by neighbors but also be connected to itself directly. Thus, this paper adds collective influence with hierarchical structures into the majority-vote model and measures opinion weight of center node by degree of their neighbors on hierarchical structures surround it with the set distance. The collective influence parameters used in this paper are related to the value of collective influence mentioned above and normalized by the maximum value of all nodes in system. The opinions’ evolution of majority-vote model with collective influence is studied in ER random networks and scale-free networks with different degree distribution exponents by Monte Carlo simulations. It is found that all systems have order-to-disorder phase transitions with the increase of noise parameter. When the depth of hierarchical structure is not zero, the system with collective influence is much easier to turn to disordered states so their critical noise parameters of phase transition are smaller than those of 0-depth systems and original majority-vote model. The reason is that high degree nodes in original majority-vote model have high influence because they are connected to more neighbors and nodes’ influence is also directly determined by degree in 0-depth collective influence model. Furthermore, nodes’ collective influence parameters in the system will all decrease when hierarchical structure of nonzero depth is considered, only a small number of individuals have high influence parameters in the system and they will make the opinions of surrounding individuals follow theirs, so if the opinions of a few highly influential individuals are out of order, then the system will reach a state of disorder. Because of the above factors, the collective influence model of nonzero depth is much easier to disorder with the increase of noise parameter. Besides, the system proves to be easier to reach a disordered state with the increase of degree distribution exponents in scale-free networks because all nodes’ degree will be lower so that the system will be dominated by less nodes with high degree. This conclusion verifies that scale-free networks are more similar to ER random networks with the increase of degree distribution exponents. Finally, through the finite-size scaling method, it is found that the phase transition of the majority-vote model with collective influence of hierarchical structures belongs in the Ising model universal class, whether in ER random networks or in scale-free networks.

A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions

&lt;abstract&gt;&lt;p&gt;Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.&lt;/p&gt;&lt;/abstract&gt;

A dynamic incentive mechanism for data sharing in manufacturing industry

Data sharing is a critical component in a blockchain traceability platform. Therefore, creating a reasonable incentive mechanism to ensure that all enterprises participate in data sharing is vital for blockchain platforms. Currently, many researchers employ evolutionary game theory to analyze problems related to data sharing. However, evolutionary game theory typically assumes that the population composed of enterprises is mixed uniformly. Enterprises in the manufacturing industry are not uniformly mixed, as they tend to have specific connections with each other due to the size of enterprises and volume of business. Therefore, a networked evolutionary game is introduced to solve this problem. Firstly, an incentive model for enterprises sharing data is established. Then, a scale-free network is employed to simulate the connections between enterprises. To comprehensively consider the individual and group benefits of enterprises in the game, this study designs a strategy update rule for networked evolutionary game based on Discrete Particle Swarm Optimization and Variable Neighborhood Descent algorithm. To tackle the challenge of determining reasonable incentive values in networked evolutionary games, this study proposes a dynamic incentive mechanism based on the Q-Learning algorithm. Finally, the experiments indicate that this method can successfully facilitate the stable involvement of enterprises in data sharing.

Stability analysis of a SAIR epidemic model on scale-free community networks.

The presence of asymptomatic carriers, often unrecognized as infectious disease vectors, complicates epidemic management, particularly when inter-community migrations are involved. We introduced a SAIR (susceptible-asymptomatic-infected-recovered) infectious disease model within a network framework to explore the dynamics of disease transmission amid asymptomatic carriers. This model facilitated an in-depth analysis of outbreak control strategies in scenarios with active community migrations. Key contributions included determining the basic reproduction number, $ R_0 $, and analyzing two equilibrium states. Local asymptotic stability of the disease-free equilibrium is confirmed through characteristic equation analysis, while its global asymptotic stability is investigated using the decomposition theorem. Additionally, the global stability of the endemic equilibrium is established using the Lyapunov functional theory.

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.

Automated hubs-patching: Protection against malware spread through reduced scale-free networks and external storage devices

Automated hubs-patching: Protection against malware spread through reduced scale-free networks and external storage devices

The structure, dynamics, and vulnerability of the global food trade network

The global food trade network (FTN) plays a critical role in ensuring food security. Given the increasing scale and complexity of trade, understanding the inherent dynamics and potential vulnerabilities of FTN becomes an urgent concern. Here, this study employed complex network method to investigate the structure, dynamics, and vulnerabilities of the trade networks associated with four main food crops (rice, maize, wheat, and soybeans) over the period 2000 to 2019. Our results show that the FTN has features consistent with both scale-free and small-world networks. A small percentage of 10% of major food producing countries trade with a significant proportion of 80% of all countries within the network. In the examined period, FTN has experienced remarkable changes, emerging economies such as China, India, Brazil and Russia have become more important, offsetting the historical dominance of nations such as the United States, Canada and Australia. In addition, many countries become increasingly reliant on food imports, the number of their trading partners within the FTN is decreasing, highlights potential increasing vulnerabilities. Simulation analysis also show that disruptions affecting about 5% of nations could seriously destabilize the FTN, which would be a cautionary tale for the stability of future food systems. This research provides policymakers with a fundamental perspective on mitigating potential risks in global FTN.

Structural network characteristics affect epidemic severity and prediction in social contact networks

Understanding and mitigating epidemic spread in complex networks requires the measurement of structural network properties associated with epidemic risk. Classic measures of epidemic thresholds like the basic reproduction number (R0) have been adapted to account for the structure of social contact networks but still may be unable to capture epidemic potential relative to more recent measures based on spectral graph properties. Here, we explore the ability of R0 and the spectral radius of the social contact network to estimate epidemic susceptibility. To do so, we simulate epidemics on a series of constructed (small world, scale-free, and random networks) and a collection of over 700 empirical biological social contact networks. Further, we explore how other network properties are related to these two epidemic estimators (R0 and spectral radius) and mean infection prevalence in simulated epidemics. Overall, we find that network properties strongly influence epidemic dynamics and the subsequent utility of R0 and spectral radius as indicators of epidemic risk.

Greedy routing optimisation in hyperbolic networks

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods take advantage of the exponentially growing volume of the hyperbolic space as a function of the radius from the origin, allowing a (roughly) uniform spatial distribution of the nodes even for scale-free small-world networks, where the connection probability between pairs decays with hyperbolic distance. One of the motivations behind hyperbolic embedding is that optimal placement of the nodes in a hyperbolic space is widely thought to enable efficient navigation on top of the network. According to that, one of the measures that can be used to quantify the quality of different embeddings is given by the fraction of successful greedy paths following a simple navigation protocol based on the hyperbolic coordinates. In the present work, we develop an optimisation scheme for this score in the native disk representation of the hyperbolic space. This optimisation algorithm can be either used as an embedding method alone, or it can be applied to improve this score for embeddings obtained from other methods. According to our tests on synthetic and real networks, the proposed optimisation can considerably enhance the success rate of greedy paths in several cases, improving the given embedding from the point of view of navigability.

Quantification and comparison of hierarchy in Public Transport Networks

Network hierarchy describes the relative arrangement of network elements and reflects its fundamental structure. We propose a multi-dimensional topology-based method for quantifying and comparing the extent to which different Public Transport Networks (PTNs) exhibit a hierarchical structure. The proposed method considers the uneven distribution of node importance with different definitions (e.g., degree centrality and betweenness centrality) in a PTN, the clustering of nodes and the node connection patterns. We apply the developed method on 63 high-capacity PTNs worldwide using General Transit Feed Specification (GTFS) data. In addition to global indicators, we use the goodness-of-fit between the probability density function of local indicators and a skew-normal distribution to quantify the extent of PTN hierarchy. Results show that the scale-free network structure and preferential attachment do not vary much across PTNs. In contrast, stop accessibility and traffic intermediacy vary considerably across PTNs as reflected by the closeness centrality and betweenness centrality distributions. Lastly, metro systems exhibit a more hierarchical structure than their tram and Bus Rapid Transit (BRT) counterparts. This work makes a first step towards a better mapping and comparison of different PTNs, which can assist academics and practitioners in better (re)designing and planning the PTNs of the future.

Research on the Cultivation of Innovation and Entrepreneurship Ability of College Students under the Background of Big Data

Abstract This paper firstly coordinates the relationship between the internal elements of university innovation and entrepreneurship incubation systems through positive and negative feedback regulation so that the system reaches equilibrium or rises to a higher level of equilibrium. Secondly, based on the whole process of innovation and entrepreneurship, the diffusion model of the university innovation and entrepreneurship system is constructed, setting university students’ innovation and entrepreneurship ability as the expected benefit and cognitive bias as the cost and exploring the benefit curve of innovation and entrepreneurship ability and cognitive bias. Finally, we initialize the parameters of the simulation system for incubating innovation and entrepreneurship among college students and simulate the constructed scale-free network model using Matlab simulation. The results show that in the simulation Corporation1, when tick=5, the maximum value of the Y coordinate appears to be 27.5, which responds to the growing process of college students’ innovation and entrepreneurship incubation objects. The simulation of college students’ innovation and entrepreneurship proposed in this paper complements the short board of college students’ inability to practice innovation and entrepreneurship and provides a practical reference for the cultivation of innovation and entrepreneurship talent ability in college education.