Journal articles on the topic 'Small world scale-free transportation network'
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Shang, Jun, Hao Qiang Liu, Qiang Liu, and Zi Qi Liu. "Design of the Small World Model by NS2." Applied Mechanics and Materials 496-500 (January 2014): 2338–41. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.2338.
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WSN is the network which is used mostly in the world nowadays, and it has the characteristics that lower cost and better functions than other kinds of the network, and the WSN network is built by the ordinary nodes and the super nodes.Theoretical study of the complex network is widely involved in the fields of computer networks, and the applied research becomes more and more important in the future. It has caused many academic attention about how to apply the complex network theory among the specific application in recent years. In the complex network theory, there has been a number of important research results about the use of the small-world network, scale-free network in the field of transportation.
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Tarapata, Zbigniew. "Modelling and analysis of transportation networks using complex networks: Poland case study." Archives of Transport 36, no. 4 (December 31, 2015): 55–65. http://dx.doi.org/10.5604/08669546.1185207.
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In the paper a theoretical bases and empirical results deal with analysis and modelling of transportation networks in Poland using complex networks have been presented. Properties of complex networks (Scale Free and Small World) and network's characteristic measures have been described. In this context, results of empirical researches connected with characteristics of passenger air links network, express railway links network (EuroCity and InterCity) and expressways/highways network in Poland have been given. For passenger air links network in Poland results are compared with the same networks in USA, China, India, Italy and Spain. In the conclusion some suggestions, observations and perspective dealing with complex network in transportation networks have been presented.
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Wang, Yong, and Ta Zhou. "Complexity Analysis of Public Transportation Network in Zhangjiagang City Using Complex Network Theory." Advanced Materials Research 546-547 (July 2012): 1211–16. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.1211.
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Public transportation network has been proven that it can be simulated as a complex network. In this paper, a bus transport system of Zhangjiagang city is considered. Network degree distribution, average path length, and clustering coefficient are utilized as criteria to analyze as the complexity of the network. Experimental results show that the network which is in line with power-law distribution has a smaller average path length and a large clustering coefficient. It also indicates that, the networks of Zhangjiagang public bus system are not a small-world network with scale-free property.
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Trobajo, M. T., and M. V. Carriegos. "Spanish Airport Network Structure: Topological Characterization." Computational and Mathematical Methods 2022 (April 9, 2022): 1–9. http://dx.doi.org/10.1155/2022/4952613.
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Applied complex network theory has become an interesting research field in the last years. Many papers have appeared on this subject dealing with the topological description of real transport systems, from small networks like the Italian airport network to the worldwide air transportation network. A comprehensive topological description of those critical structures is relevant in order to understand their dynamics, capacities, and vulnerabilities. In this work, for the first time, we describe the Spanish airport network (SAN) as a complex network. Nodes are airports, and links are flight connections weighed by traffic flow. We study its topological features and traffic dynamics. Our analysis shows that SAN has complex dynamics similar to small-size air transportation networks of other developed economies. It shares properties of small-world and scale-free networks, and it is highly connected and efficient and has a disassortative pattern for high-degree nodes.
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ZHAO, HUI, and ZIYOU GAO. "GENERALIZED SHORTEST PATH AND TRAFFIC EQUILIBRIUM IN COMPLEX TRANSPORTATION NETWORKS." Modern Physics Letters B 21, no. 20 (August 30, 2007): 1343–49. http://dx.doi.org/10.1142/s021798490701350x.
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Shortest path plays an important role in the study of complex networks. But in real transportation systems, choosing the shortest path may not be the best way for the drivers. Based on the traffic equilibrium theory, we generalize the concept of shortest path. Flux distribution is also investigated by using the generalized concept on various types of complex networks. We find that the flux differs little in all the edges of lattice while in small-world and scale-free networks, the flux distribution follows a power law, and in the random network, the flux distribution has an exponential tail. We consider lattice may be the optimal topology in design a transportation network.
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Chong, Pengyun, Bin Shuai, Shaowei Deng, Jianting Yang, and Hui Yin. "Analysis on Topological Properties of Dalian Hazardous Materials Road Transportation Network." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/340780.
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To analyze the topological properties of hazardous materials road transportation network (HMRTN), this paper proposed two different ways to construct the cyberspace of HMRTN and constructed their complex network models, respectively. One was the physical network model of HMRTN based on the primal approach and the other was the service network model of HMRTN based on neighboring nodes. The two complex network models were built by using the case of Dalian HMRTN. The physical network model contained 154 nodes and 238 edges, and the statistical analysis results showed that (1) the cumulative node degree of physical network was subjected to exponential distribution, showing the network properties of random network and that (2) the HMRTN had small characteristic path length and large network clustering coefficient, which was a typical small-world network. The service network model contained 569 nodes and 1318 edges, and the statistical analysis results showed that (1) the cumulative node degree of service network was subjected to power-law distribution, showing the network properties of scale-free network and that (2) the relationship between nodes strength and their descending order ordinal and the relationship between nodes strength and cumulative nodes strength were both subjected to power-law distribution, also showing the network properties of scale-free network.
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De Bona, A. A., K. V. O. Fonseca, M. O. Rosa, R. Lüders, and M. R. B. S. Delgado. "Analysis of Public Bus Transportation of a Brazilian City Based on the Theory of Complex Networks Using the P-Space." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/3898762.
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The city of Curitiba, located at Southern Brazil, is recognized by its urban planning structured on three pillars: land use, collective transportation, and traffic. With 3.8 million people in its metropolitan area, the public transport system deals with approximately 2.5 million passengers daily. The structure and properties of such a transportation system have substantial implications for the urban planning and public politics for sustainable development of Curitiba. Therefore, this paper analyzes the structure of the public transportation system of Curitiba through the theory of complex networks in a static approach of network topology and presents a comparative analysis of the results from Curitiba, three cities from China (Shanghai, Beijing, and Guangzhou), and three cities from Poland (GOP, Warszawa, and Łódź). The transportation network was modeled as a complex network with exact geographical coordinates of its bus stops. In all bus lines, the method used was the P-Space. The results show that this bus network has characteristics of both small-world and scale-free networks.
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Zhang, Ling, Jingjing Hao, Xiaofeng Ji, and Lan Liu. "Research on the Complex Characteristics of Freight Transportation from a Multiscale Perspective Using Freight Vehicle Trip Data." Sustainability 11, no. 7 (March 29, 2019): 1897. http://dx.doi.org/10.3390/su11071897.
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To better guide the sustainable developing of freight transport aligning with environmental objectives it is of strategic importance to capture freight transportation characteristics more realistically. This paper characterizes freight transportation by using a complex network approach from multidimensional perspectives based on freight vehicle trips data. We first build two subnetworks from prefecture-level city-scale and county-level city-scale. Subsequently, network analysis indices based on complex network theory were applied to examine the topological structure and complexity of the freight transportation networks. Furthermore, the community detection method is introduced to reveal the networks’ clustering characteristics. The findings show that the prefecture-level city-scale network and the county-level city-scale network both have obvious small-world network characteristics, but the prefecture-level city-scale network has higher operating efficiency for goods movement. Additionally, the influence of the cross-border effect on the freight transportation network was verified. In terms of the community structure, the freight network shows distinct clustering features only at the county-level city-scale.
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Ren, Cuiping, Bianbian Chen, Fengjie Xie, Xuan Zhao, Jiaqian Zhang, and Xueyan Zhou. "Understanding Hazardous Materials Transportation Accidents Based on Higher-Order Network Theory." International Journal of Environmental Research and Public Health 19, no. 20 (October 16, 2022): 13337. http://dx.doi.org/10.3390/ijerph192013337.
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In hazardous materials transportation systems, accident causation analysis is important to transportation safety. Complex network theory can be effectively used to understand the causal factors of and their relationships within accidents. In this paper, a higher-order network method is proposed to establish a hazardous materials transportation accident causation network (HMTACN), which considers the sequences and dependences of causal factors. The HMTACN is composed of 125 first- and 118 higher-order nodes that represent causes, and 545 directed edges that denote complex relationships among causes. By analyzing topological properties, the results show that the HMTACN has the characteristics of small-world networks and displays the properties of scale-free networks. Additionally, critical causal factors and key relationships of the HMTACN are discovered. Moreover, unsafe tank or valve states are important causal factors; and leakage, roll-over, collision, and fire are most likely to trigger chain reactions. Important higher-order nodes are discovered, which can represent key relationships in the HMTACN. For example, unsafe distance and improper operation usually lead to collision and roll-over. These results of higher-order nodes cannot be found by the traditional Markov network model. This study provides a practical way to extract and construct an accident causation network from numerous accident investigation reports. It also provides insights into safety management of hazardous materials transportation.
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Cao, Weiwei, Xiangnan Feng, Jianmin Jia, and Hong Zhang. "Characterizing the Structure of the Railway Network in China: A Complex Weighted Network Approach." Journal of Advanced Transportation 2019 (February 3, 2019): 1–10. http://dx.doi.org/10.1155/2019/3928260.
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Understanding the structure of the Chinese railway network (CRN) is crucial for maintaining its efficiency and planning its future development. To advance our knowledge of CRN, we modeled CRN as a complex weighted network and explored the structural characteristics of the network via statistical evaluations and spatial analysis. Our results show CRN as a small-world network whose train flow obeys power-law decaying, demonstrating that CRN is a mature transportation infrastructure with a scale-free structure. CRN also shows significant spatial heterogeneity and hierarchy in its regionally uneven train flow distribution. We then examined the nodal centralities of CRN using four topological measures: degree, strength, betweenness, and closeness. Nodal degree is positively correlated with strength, betweenness, and closeness. Unlike the common feature of a scale-free network, the most connected nodes in CRN are not necessarily the most central due to underlying geographical, political, and socioeconomic factors. We proposed an integrated measure based on the four centrality measures to identify the global role of each node and the multilayer structure of CRN and confirm that stable connections hold between different layers of CRN.
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Zou, Zhiyun, Peng Liu, Saisai Zhou, Yao Xiao, Xuecai Xu, and Jianzhi Gao. "Analysis on evolving model with modular growth of urban roadway network topology structure." Kybernetes 44, no. 4 (April 7, 2015): 505–17. http://dx.doi.org/10.1108/k-12-2013-0272.
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Purpose – The purpose of this paper is to explore the evolving mechanism of urban roadway network. With the consideration of self-organization effect and planning effect during evolution, the authors try to demonstrate the impact of preferential attachment, module scale and module structure on the evolving network model. Design/methodology/approach – The roadway network is built in the form of abstract network by dual approach. By using the evolving model of modular growth, the authors analyze the effects and mechanism of the evolving process. Then through numerical analysis, the impact of evolving effects on urban roadway network topology structure is discussed from the aspects of preferential attachment, module scale and module structure. Findings – The module structure property, small-world property and scale-free property of roadway network can be affected with various degrees by the change of preferential attachment and module scale. However, the impact of module structure on network properties is small, which can be ignored. Therefore, in practice, the self-organization effect and planning effect of evolving network can be reached by changing the preferential attachment and module scale, so as to generate the network structure with specific properties. Research limitations/implications – Some local events, such as road extensions, road demolition and intersection rebuilding, exist during the evolving process under real-world situation. While those cases have not been considered in preferential attachment. Therefore, researchers are encouraged to take these factors into consideration in further research. Practical implications – The paper has implications for practice in urban transportation planning and roadway constructions, which can help to guide the planning of urban roadway and to adjust or restore partial network when broken down according to the evolving law. Originality/value – The impact of preferential attachment, module scale and module structure on the evolving network model is measured. And the relationship between different network properties can be used to build some patterns of network. From this point of view, the development of urban roadway network can be predicted and intervened.
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Ding, Lin, Victor C. M. Leung, and Min-Sheng Tan. "Robustness of complex networks with both unidirectional and bidirectional links against cascading failures." Modern Physics Letters B 31, no. 27 (September 28, 2017): 1750252. http://dx.doi.org/10.1142/s0217984917502529.
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The robustness of complex networks against cascading failures has been of great interest, while most of the researchers have considered undirected networks. However, to be more realistic, a part of links of many real systems should be described as unidirectional. In this paper, by applying three link direction-determining (DD) strategies, the tolerance of cascading failures is investigated in various networks with both unidirectional and bidirectional links. By extending the utilization of a classical global betweenness method, we propose a new cascading model, taking into account the weights of nodes and the directions of links. Then, the effects of unidirectional links on the network robustness against cascaded attacks are examined under the global load-based distribution mechanism. The simulation results show that the link-directed methods could not always lead to the decrease of the network robustness as indicated in the previous studies. For small-world networks, these methods certainly make the network weaker. However, for scale-free networks, the network robustness can be significantly improved by the link-directed method, especially for the method with non-random DD strategies. These results are independent of the weight parameter of the nodes. Due to the strongly improved robustness and easy realization with low cost on networks, the method for enforcing proper links to the unidirectional ones may be useful for leading to insights into the control of cascading failures in real-world networks, like communication and transportation networks.
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Li, Hongqi, Haotian Wang, Ming Bai, and Bin Duan. "The Structure and Periodicity of the Chinese Air Passenger Network." Sustainability 11, no. 1 (December 21, 2018): 54. http://dx.doi.org/10.3390/su11010054.
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China’s air transportation system is evolving with its own unique mechanism. In particular, the structural features of the Chinese air passenger network (CAPN) are of interest. This paper aims to analyze the CAPN from holistic and microcosmic perspectives. Considering that the topological structure and the capacity (i.e., available passenger-seats) flow are important to the air network’s performance, the CAPN structure features from non-weighted and weighted perspectives are analyzed. Subnets extracted by time-scale constraints of one day or every two-hours are used to find the temporal features. This paper provides some valuable conclusions about the structural characteristics and temporal features of the CAPN. The results indicate that the CAPN has a small-world and scale-free structure. The cumulative degree distribution of the CAPN follows a two-regime power-law distribution. The CAPN tends to be disassortative. Some important airports, including national air-hubs and local air-hubs, remarkably affect the CAPN. About 90% of large capacities exist between airports with large degrees. The properties of CAPN subnets extracted by taking two hours as the time-scale interval shed light on the air network performance and the changing rule more accurately and microcosmically. The method of the spectral destiny estimation is used to find the implicit periodicity mathematically. For most indicators, a one-day cycle, two-day cycle, and/or three-day cycle can be found.
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Gao, Jianxi, Daqing Li, and Shlomo Havlin. "From a single network to a network of networks." National Science Review 1, no. 3 (July 16, 2014): 346–56. http://dx.doi.org/10.1093/nsr/nwu020.
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Abstract Network science has attracted much attention in recent years due to its interdisciplinary applications. We witnessed the revolution of network science in 1998 and 1999 started with small-world and scale-free networks having now thousands of high-profile publications, and it seems that since 2010 studies of ‘network of networks’ (NON), sometimes called multilayer networks or multiplex, have attracted more and more attention. The analytic framework for NON yields a novel percolation law for n interdependent networks that shows that percolation theory of single networks studied extensively in physics and mathematics in the last 50 years is a specific limit of the rich and very different general case of n coupled networks. Since then, properties and dynamics of interdependent and interconnected networks have been studied extensively, and scientists are finding many interesting results and discovering many surprising phenomena. Because most natural and engineered systems are composed of multiple subsystems and layers of connectivity, it is important to consider these features in order to improve our understanding of such complex systems. Now the study of NON has become one of the important directions in network science. In this paper, we review recent studies on the new emerging area—NON. Due to the fast growth of this field, there are many definitions of different types of NON, such as interdependent networks, interconnected networks, multilayered networks, multiplex networks and many others. There exist many datasets that can be represented as NON, such as network of different transportation networks including flight networks, railway networks and road networks, network of ecological networks including species interacting networks and food webs, network of biological networks including gene regulation network, metabolic network and protein–protein interacting network, network of social networks and so on. Among them, many interdependent networks including critical infrastructures are embedded in space, introducing spatial constraints. Thus, we also review the progress on study of spatially embedded networks. As a result of spatial constraints, such interdependent networks exhibit extreme vulnerabilities compared with their non-embedded counterparts. Such studies help us to understand, realize and hopefully mitigate the increasing risk in NON.
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Natera Orozco, Luis Guillermo, Federico Battiston, Gerardo Iñiguez, and Michael Szell. "Data-driven strategies for optimal bicycle network growth." Royal Society Open Science 7, no. 12 (December 2020): 201130. http://dx.doi.org/10.1098/rsos.201130.
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Urban transportation networks, from pavements and bicycle paths to streets and railways, provide the backbone for movement and socioeconomic life in cities. To make urban transport sustainable, cities are increasingly investing to develop their bicycle networks. However, it is yet unclear how to extend them comprehensively and effectively given a limited budget. Here we investigate the structure of bicycle networks in cities around the world, and find that they consist of hundreds of disconnected patches, even in cycling-friendly cities like Copenhagen. To connect these patches, we develop and apply data-driven, algorithmic network growth strategies, showing that small but focused investments allow to significantly increase the connectedness and directness of urban bicycle networks. We introduce two greedy algorithms to add the most critical missing links in the bicycle network focusing on connectedness, and show that they outmatch both a random approach and a baseline minimum investment strategy. Our computational approach outlines novel pathways from car-centric towards sustainable cities by taking advantage of urban data available on a city-wide scale. It is a first step towards a quantitative consolidation of bicycle infrastructure development that can become valuable for urban planners and stakeholders.
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Wan, Dan, Yong Huang, Jie Feng, Yaling Shi, Kairui Guo, and Ran Zhang. "Understanding Topological and Spatial Attributes of Bus Transportation Networks in Cities of Chongqing and Chengdu." Mathematical Problems in Engineering 2018 (October 17, 2018): 1–14. http://dx.doi.org/10.1155/2018/4137806.
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It is critical to understand the characteristics of public transportation networks (PTNs). Existing studies have mainly focused on the topological structure of PTNs and have revealed the commonalities of the topological structures of PTNs. However, few studies have examined the differences regarding topological structure characteristics between the PTNs of different cities. In addition, the nature and extent of the influence of specific urban geographic conditions and morphology on PTNs are unclear. This paper focuses on the influence of urban spatial and geographic environments on bus transportation networks (BTNs) by comparatively studying the topological and spatial attributes of two typical BTNs, respectively, from a mountainous city and a plain city in China, from the perspectives of basic statistical properties, types, connection properties, and spatial attributes, by using the complex networks theory and spatial analysis method. The results reveal that the two BTNs have similar statistical properties and they both have scale-free features as well as small-world features. However, these two BTNs are significantly different in the connection properties and spatial attributes. The difference is found closely related to the city’s geographic conditions and spatial morphology. The implications of this study regarding urban traffic planning and land planning are discussed.
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Wang, Yong, Yaoyao Sun, Xiangyang Guan, and Yanyong Guo. "Two-Echelon Location-Routing Problem with Time Windows and Transportation Resource Sharing." Journal of Advanced Transportation 2021 (May 9, 2021): 1–20. http://dx.doi.org/10.1155/2021/8280686.
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In this work, a two-echelon location-routing problem with time windows and transportation resource sharing (2E-LRPTWTRS) is solved by selecting facility locations and optimizing two-echelon vehicle routes. The optimal solutions improve the efficiency of a logistics network based on the geographical distribution and service time windows of logistics facilities and customers. Furthermore, resource utilization is maximized by enabling resource sharing strategies within and among different logistics facilities simultaneously. The 2E-LRPTWTRS is formulated as a biobjective optimization model, and obtaining the smallest number of required delivery vehicles and the minimum total operating cost are the two objective functions. A two-stage hybrid algorithm composed of k-means clustering and extended multiobjective particle swarm optimization algorithm is proposed for 2E-LRPTWTRS optimization. A self-adaptive mechanism of flight parameters is introduced and adopted during the iterative process to balance the evolution of particles and improve the efficiency of the two-stage hybrid algorithm. Moreover, 20 small-scale instances are used for an algorithm comparison with multiobjective genetic algorithm and nondominated sorting genetic algorithm-II, and the solutions demonstrate the superiority of the proposed algorithm in optimizing logistics networks. The proposed optimization model and hybrid algorithm are tested by employing a real-world case of 2E-LRPTWTRS in Chongqing, China, and the optimization results verify the positive role of the developed model and algorithm in improving logistics efficiency, reducing operating cost, and saving transportation resources in the operations of two-echelon logistics networks.
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Valjarević, Aleksandar, Marija Milić, Dragana Valjarević, Zorica Stanojević-Ristić, Ljiljana Petrović, Miško Milanović, Dejan Filipović, Branko Ristanović, Biljana Basarin, and Tin Lukić. "Modelling and mapping of the COVID-19 trajectory and pandemic paths at global scale: A geographer’s perspective." Open Geosciences 12, no. 1 (December 13, 2020): 1603–16. http://dx.doi.org/10.1515/geo-2020-0156.
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AbstractIn December 2019, the virus SARS-CoV-2 responsible for the COVID-19 pandemic was detected in the Chinese city of Wuhan. The virus started to spread from China and dispersed over the rest of the world. In March 2020, WHO (World Health Organization) declared COVID-19 a pandemic. The transmission path of the pandemic was accelerated by different types of transportation. With complete analysis of spatial data, population density, types of traffic networks, and their properties, the spatial distribution of COVID-19 was estimated. GIS (Geographical Information System), numerical methods, and software for network analysis were used in this research to model scenarios of virus distribution on a global scale. The analyzed data included air, railway, marine, and road traffic. In the pandemic research, numerous models of possible trajectory of viruses can be created. Many have a stochastic character. This study includes all countries in the world affected by the COVID-19 up to date. In this study, GIS methods such as buffer, interpolations, and numerical analysis were used in order to estimate and visualize ongoing COVID-19 pandemic situation. According to the availability of new data, trajectory of virus paths was estimated. On the other hand, sparsely populated areas with poorly developed and small traffic networks (and isolated island territories) tend to be less or not affected as shown by the model. This low-cost approach can be used in order to define important measures that need to be addressed and implemented in order to successfully mitigate the implications of COVID-19 not only on global, but local and regional scales as well.
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Xiao, Jie, Yi Xie, Haowei Yu, and Hongying Yan. "An Optimization Method for the Train Service Network Design Problem." Discrete Dynamics in Nature and Society 2020 (January 17, 2020): 1–18. http://dx.doi.org/10.1155/2020/9519267.
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Effective railway freight transportation relies on a well-designed train service network. This paper investigates the train service network design problem at the tactical level for the Chinese railway system. It aims to determine the types of train services to be offered, how many trains of each service are to be dispatched per day (service frequency), and by which train services shipments are to be transported. An integer programming model is proposed to address this problem. The optimization model considers both through train services between nonadjacent yards, and two classes of service between two adjacent yards ( i.e., shuttle train services directly from one yard to its adjacent yard, and local train services that make at least one intermediate stop). The objective of the model is to optimize the transportation of all the shipments with minimal costs. The costs consist of accumulation costs, classification coststrain operation costs, and train travel costs. The NP-hard nature of the problem prevents an exact solution algorithm from finding the optimal solution within a reasonable time, even for small-scale cases. Therefore, an improved genetic algorithm is designed and employed here. To demonstrate the proposed model and the algorithm, a case study on a real-world sub-network in China is carried out. The computational results show that the proposed approach can obtain high-quality solutions with satisfactory speed. Moreover, comparative analysis on a case that assumes all the shuttle train services between any two adjacent yards to be provided without optimization reveals some interesting insights.
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Carreras Guzman, Nelson H., and Adam Gergo Mezovari. "Design of IoT-based Cyber–Physical Systems: A Driverless Bulldozer Prototype." Information 10, no. 11 (November 5, 2019): 343. http://dx.doi.org/10.3390/info10110343.
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From autonomous vehicles to robotics and machinery, organizations are developing autonomous transportation systems in various domains. Strategic incentives point towards a fourth industrial revolution of cyber–physical systems with higher levels of automation and connectivity throughout the Internet of Things (IoT) that interact with the physical world. In the construction and mining sectors, these developments are still at their infancy, and practitioners are interested in autonomous solutions to enhance efficiency and reliability. This paper illustrates the enhanced design of a driverless bulldozer prototype using IoT-based solutions for the remote control and navigation tracking of the mobile machinery. We illustrate the integration of a cloud application, communication protocols and a wireless communication network to control a small-scale bulldozer from a remote workstation. Furthermore, we explain a new tracking functionality of work completion using maps and georeferenced indicators available via a user interface. Finally, we provide a preliminary safety and security risk assessment of the system prototype and propose guidance for application in real-scale machinery.
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Shan, Shaonan, Yulong Li, Zicheng Zhang, Wei Zhu, and Tingting Zhang. "Identification of Key Carbon Emission Industries and Emission Reduction Control Based on Complex Network of Embodied Carbon Emission Transfers: The Case of Hei-Ji-Liao, China." International Journal of Environmental Research and Public Health 20, no. 3 (January 31, 2023): 2603. http://dx.doi.org/10.3390/ijerph20032603.
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Similar to the problems surrounding carbon transfers that exist in international trade, there are severe carbon emission headaches in regional industrial systems within countries. It is essential for emission reduction control and regional industrial restructuring to clarify the relationship of carbon emissions flows between industrial sectors and identify key carbon-emitting industrial sectors. Supported by the input–output model (I-O model) and social network analysis (SNA), this research adopts input–output tables (2017), energy balance sheets (2021) and the energy statistics yearbooks (2021) of the three Chinese provinces of Hei-Ji-Liao to construct an Embodied carbon emission transfer network (ECETN) and determine key carbon-emitting industrial sectors with a series of complex network measurement indicators and analysis methods. The key abatement control pathways are obtained based on the flow relationships between the chains in the industrial system. The results demonstrate that the ECETNs in all three provinces of Hei-Ji-Liao are small-world in nature with scale-free characteristics (varying according to the power function). The key carbon emission industry sectors in the three provinces are identified through centrality, influence, aggregation and diffusion, comprising coal mining, the chemical industry, metal products industry, machinery manufacturing and transportation in Liaoning Province; coal mining, non-metal mining, non-metal products, metal processing and the electricity industry in Jilin Province; and agriculture, metal processing and machinery manufacturing in Heilongjiang. Additionally, key emission reduction control pathways in the three provinces are also identified based on embodied carbon emission flow relationships between industry sectors. Following the above findings, corresponding policy recommendations are proposed to tackle the responsibility of carbon reduction among industrial sectors in the province. Moreover, these findings provide some theoretical support and policy considerations for policymakers.
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Busse, Christian, Martin C. Schleper, Jenny Weilenmann, and Stephan M. Wagner. "Extending the supply chain visibility boundary." International Journal of Physical Distribution & Logistics Management 47, no. 1 (February 13, 2017): 18–40. http://dx.doi.org/10.1108/ijpdlm-02-2015-0043.
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Purpose The purpose of this paper is to investigate how buying firms facing low supply chain visibility can utilize their stakeholder network to identify salient supply chain sustainability risks (SCSR). Design/methodology/approach The study employs a design science approach to develop a procedural model for identifying SCSR as a new artifact. A small-scale field-testing study in a food supply chain of a Swiss retail firm demonstrates its applicability and pragmatic validity. Findings When stakeholder knowledge external to the supply chain is regarded as a valuable resource, a generic understanding of a buying firm’s supply chain suffices to identify SCSR hotspots without creating complexity for the SCSR management. Research limitations/implications The paper contributes to the study of SCSR by identifying mechanisms buying firms can employ to identify SCSR hotspots and fostering the nascent understanding of responsibility attribution by stakeholders. Moreover, the emerging theory of the supply chain is enriched by paving a way to extend the supply chain visibility boundary. The procedural model is presumably most useful in contexts of elevated stakeholder pressure and low supply chain visibility. Future research should seek to validate and improve the effectiveness of the newly designed artifact. Practical implications The procedural model is directly applicable in corporate practice to the identification of SCSR. Moreover, its application fosters the understanding of a firm’s supply chain and its stakeholder network. Originality/value SCSR is an increasingly important phenomenon in corporate practice that has received only scarce research attention. The design science approach represents a valuable means for generating theoretical insights and emergent solutions to the real-world problem of SCSR identification.
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Lee, Kang-won, Jae-hoon Lee, and Hye-zin Choe. "Generalized Network Generation Method for Small-World Network and Scale-Free Network." Journal of Korean Institute of Communications and Information Sciences 41, no. 7 (July 31, 2016): 754–64. http://dx.doi.org/10.7840/kics.2016.41.7.754.
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ZHU, LING-ZAN, BEI-BEI YIN, LEI ZHAO, and KAI-YUAN CAI. "SCALE-FREE NETWORKS CAN BE LINEAR-WORLD." International Journal of Modern Physics B 25, no. 32 (December 30, 2011): 4593–603. http://dx.doi.org/10.1142/s0217979211059206.
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It was generally believed that scale-free networks would be small-world. In this paper, two models, named Model A and Model B, are proposed to show that certain scale-free networks can be linear-world instead of small-world. By linear-world, it means that the average path length L of the network grows linearly with the total number of nodes N, i.e., L~N. Model A generates a deterministic scale-free network with high assortativity and numerical simulations demonstrate that the network is linear-world when it satisfies degree exponent λ>1. Model B constructs a partially deterministic scale-free network, which is connected by identical small scale-free networks following certain rules. Analytical arguments and numerical simulations both yield L~N which suggests that it is also linear-world. It is further discussed in this paper that the network generated by Model Bcould be either correlated or uncorrelated. This suggests that, inconsistent with the results in related works, uncorrelated scale-free networks can also be linear-world.
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Lee, Kang-won, Hee-kwan Uhm, and Hye-jin Choe. "Tunable Network Generation Model for Small-World and Scale-Free Network." Journal of Korean Institute of Communications and Information Sciences 42, no. 7 (July 31, 2017): 1392–401. http://dx.doi.org/10.7840/kics.2017.42.7.1392.
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Zhang, Zhongzhi, Yibin Sheng, and Qiang Jiang. "Monomer–dimer model on a scale-free small-world network." Physica A: Statistical Mechanics and its Applications 391, no. 3 (February 2012): 828–33. http://dx.doi.org/10.1016/j.physa.2011.08.007.
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Sohn, Insoo. "Small-World and Scale-Free Network Models for IoT Systems." Mobile Information Systems 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/6752048.
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It is expected that Internet of Things (IoT) revolution will enable new solutions and business for consumers and entrepreneurs by connecting billions of physical world devices with varying capabilities. However, for successful realization of IoT, challenges such as heterogeneous connectivity, ubiquitous coverage, reduced network and device complexity, enhanced power savings, and enhanced resource management have to be solved. All these challenges are heavily impacted by the IoT network topology supported by massive number of connected devices. Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the network topology of brain networks, social networks, and wireless networks. These models, also, have been applied to IoT networks to enhance synchronization, error tolerance, and more. However, due to interdisciplinary nature of the network science, with heavy emphasis on graph theory, it is not easy to study the various tools provided by complex network models. Therefore, in this paper, we attempt to introduce basic concepts of graph theory, including small-world networks and scale-free networks, and provide system models that can be easily implemented to be used as a powerful tool in solving various research problems related to IoT.
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Singh, Arun Kumar. "Development Induced Displacement: Issues and Indian Experiences." Journal of the Anthropological Survey of India 69, no. 2 (December 2020): 276–89. http://dx.doi.org/10.1177/2277436x20979760.
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Development-induced displacement debate has attracted academicians, planners and policymakers in the last hundred years because of its contradictory connotation. The twentieth century is considered to be the period of unprecedented economic development in many areas of the world. Megaprojects, like irrigation projects and large dams, have become symbols of economic development; apart from generating energy, these projects have also generated employment and income for the people affected. Post-Independence India has witnessed a large number of development projects for fulfilling the socio-economic needs of a different section of society residing in different parts of the country. Efforts have been made by government authorities for the promotion of major, medium and small-scale developmental projects in sectors like irrigation, industries, power, transportation and so on. However such mega-development projects involve the acquisition of land from common and poor people resulting in forced mass displacement which disrupts the socio-economic fabric and spoils the environmental flavour of the surrounding areas. A large number of people are deprived of their cultural identities and livelihood primarily as a direct consequence of land acquisition. The experiences suggest that the long drawn-out process of displacement has caused widespread traumatic psychological and socio-cultural consequences including the dismantling of traditional production systems, desecration of ancestral sacred zones, graves and places of worship, scattering of kinship groups, disruptions of the family system and informal social network ( Kothari, 1995 . Economic & Political Weekly, 31(24), 1476–1485). Under this type of parochial treatment, the fundamental goal of economic development, that is, to promote the welfare and wellbeing of the people remains a daydream, and the vulnerable groups of human society are denied of their fundamental/human rights and have to bear the situation at the cost of development.
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Ni, Yan, Yinghua Wang, Tao Yu, and Xiaoli Li. "Analysis of Epileptic Seizures with Complex Network." Computational and Mathematical Methods in Medicine 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/283146.
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Epilepsy is a disease of abnormal neural activities involving large area of brain networks. Until now the nature of functional brain network associated with epilepsy is still unclear. Recent researches indicate that the small world or scale-free attributes and the occurrence of highly clustered connection patterns could represent a general organizational principle in the human brain functional network. In this paper, we seek to find whether the small world or scale-free property of brain network is correlated with epilepsy seizure formation. A mass neural model was adopted to generate multiple channel EEG recordings based on regular, small world, random, and scale-free network models. Whether the connection patterns of cortical networks are directly associated with the epileptic seizures was investigated. The results showed that small world and scale-free cortical networks are highly correlated with the occurrence of epileptic seizures. In particular, the property of small world network is more significant during the epileptic seizures.
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LI, YAN-LAI, HUI-JUN SUN, and JIAN-JUN WU. "DYNAMICS BEHAVIORS OF SCALE-FREE NETWORKS WITH ELASTIC DEMAND." International Journal of Modern Physics C 19, no. 08 (August 2008): 1305–13. http://dx.doi.org/10.1142/s0129183108012893.
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Many real-world networks, such as transportation networks and Internet, have the scale-free properties. It is important to study the bearing capacity of such networks. Considering the elastic demand condition, we analyze load distributions and bearing capacities with different parameters through artificially created scale-free networks. The simulation results show that the load distribution follows a power-law form, which means some ordered pairs, playing the dominant role in the transportation network, have higher demand than other pairs. We found that, with the decrease of perceptual error, the total and average ordered pair demand will decrease and then stay in a steady state. However, with the increase of the network size, the average demand of each ordered pair will decrease, which is particularly interesting for the network design problem.
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CHEN, JIN, FEI GAO, ANBO LE, LIFENG XI, and SHUHUA YIN. "A SMALL-WORLD AND SCALE-FREE NETWORK GENERATED BY SIERPINSKI TETRAHEDRON." Fractals 24, no. 01 (March 2016): 1650001. http://dx.doi.org/10.1142/s0218348x16500018.
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The Sierpinski tetrahedron is used to construct evolving networks, whose vertexes are all solid regular tetrahedra in the construction of the Sierpinski tetrahedron up to the stage [Formula: see text] and any two vertexes are neighbors if and only if the corresponding tetrahedra are in contact with each other on boundary. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.
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WANG, DAOHUA, YUMEI XUE, QIAN ZHANG, and MIN NIU. "SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK." Fractals 27, no. 02 (March 2019): 1950010. http://dx.doi.org/10.1142/s0218348x19500105.
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Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.
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Zhang, Zhongzhi, Shuigeng Zhou, Zhan Su, Tao Zou, and Jihong Guan. "Random Sierpinski network with scale-free small-world and modular structure." European Physical Journal B 65, no. 1 (August 11, 2008): 141–47. http://dx.doi.org/10.1140/epjb/e2008-00305-8.
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Chen, Jin, Anbo Le, Qin Wang, and Lifeng Xi. "A small-world and scale-free network generated by Sierpinski Pentagon." Physica A: Statistical Mechanics and its Applications 449 (May 2016): 126–35. http://dx.doi.org/10.1016/j.physa.2015.12.089.
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Whigham, P. A., G. Dick, and M. Parry. "Network rewiring dynamics with convergence towards a star network." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2194 (October 2016): 20160236. http://dx.doi.org/10.1098/rspa.2016.0236.
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Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz ( Nature 393 , 440–442. ( doi:10.1038/30918 )). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.
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SMALL, MICHAEL, and CHI K. TSE. "SMALL WORLD AND SCALE FREE MODEL OF TRANSMISSION OF SARS." International Journal of Bifurcation and Chaos 15, no. 05 (May 2005): 1745–55. http://dx.doi.org/10.1142/s0218127405012776.
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We model transmission of the Severe Acute Respiratory Syndrome (SARS) associated coronavirus (SARS-CoV) in Hong Kong with a complex small world network. Each node in the network is connected to its immediate neighbors and a random number of geographically isolated nodes. Transmission can only occur along these links. We find that this model exhibits dynamics very similar to those observed during the SARS outbreak in 2003. We derive an analytic expression for the rate of infection and confirm this expression with computational simulations. An immediate consequence of this quantity is that the severity of the SARS epidemic in Hong Kong in 2003 was due to ineffectual infection control in hospitals (i.e. nosocomial transmission). If all infectious individuals were isolated as rapidly as they were identified the severity of the outbreak would have been minimal.
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Xiao, Wen Jun, Shi Zhong Jiang, and Guan Rong Chen. "A Small-World Model of Scale-Free Networks: Features and Verifications." Applied Mechanics and Materials 50-51 (February 2011): 166–70. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.166.
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It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent 2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.
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Wang, Lei, and Ping Wang. "Propagation and stability in software: A complex network perspective." International Journal of Modern Physics C 26, no. 05 (March 25, 2015): 1550052. http://dx.doi.org/10.1142/s0129183115500527.
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In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.
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Sun, Linan, Zuhan Liu, Jiayao Wang, Lili Wang, Xuecai Bao, Zhaoming Wu, and Bo Yu. "The evolving concept of air pollution: a small‐world network or scale‐free network?" Atmospheric Science Letters 17, no. 5 (April 20, 2016): 308–14. http://dx.doi.org/10.1002/asl.659.
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Yao, Bing, Ming Yao, Xiang En Chen, Xia Liu, and Wan Jia Zhang. "Research on Edge-Growing Models Related with Scale-Free Small-World Networks." Applied Mechanics and Materials 513-517 (February 2014): 2444–48. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.2444.
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Understanding the topological structure of scale-free networks or small world networks is required and useful for investigation of complex networks. We will build up a class of edge-growing network models and provide an algorithm for finding spanning trees of edge-growing network models in this article.
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Humphries, M. D., K. Gurney, and T. J. Prescott. "The brainstem reticular formation is a small-world, not scale-free, network." Proceedings of the Royal Society B: Biological Sciences 273, no. 1585 (November 17, 2005): 503–11. http://dx.doi.org/10.1098/rspb.2005.3354.
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He, Liang, and Shouwei Li. "Network Entropy and Systemic Risk in Dynamic Banking Systems." Complexity 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/1852897.
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We investigate network entropy of dynamic banking systems, where interbank networks analyzed include random networks, small-world networks, and scale-free networks. We find that network entropy is positively correlated with the effect of systemic risk in the three kinds of interbank networks and that network entropy in the small-world network is the largest, followed by those in the random network and the scale-free network.
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Kasthurirathna, Dharshana, Mahendra Piraveenan, and Gnanakumar Thedchanamoorthy. "On the Influence of Topological Characteristics on Robustness of Complex Networks." Journal of Artificial Intelligence and Soft Computing Research 3, no. 2 (April 1, 2013): 89–100. http://dx.doi.org/10.2478/jaiscr-2014-0007.
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Abstract In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.
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Ge, Mengke, Xiaobing Ni, Xu Qi, Song Chen, Jinglei Huang, Yi Kang, and Feng Wu. "Synthesizing Brain-network-inspired Interconnections for Large-scale Network-on-chips." ACM Transactions on Design Automation of Electronic Systems 27, no. 1 (January 31, 2022): 1–30. http://dx.doi.org/10.1145/3480961.
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Brain network is a large-scale complex network with scale-free, small-world, and modularity properties, which largely supports this high-efficiency massive system. In this article, we propose to synthesize brain-network-inspired interconnections for large-scale network-on-chips. First, we propose a method to generate brain-network-inspired topologies with limited scale-free and power-law small-world properties, which have a low total link length and extremely low average hop count approximately proportional to the logarithm of the network size. In addition, given the large-scale applications, considering the modularity of the brain-network-inspired topologies, we present an application mapping method, including task mapping and deterministic deadlock-free routing, to minimize the power consumption and hop count. Finally, a cycle-accurate simulator BookSim2 is used to validate the architecture performance with different synthetic traffic patterns and large-scale test cases, including real-world communication networks for the graph processing application. Experiments show that, compared with other topologies and methods, the brain-network-inspired network-on-chips (NoCs) generated by the proposed method present significantly lower average hop count and lower average latency. Especially in graph processing applications with a power-law and tightly coupled inter-core communication, the brain-network-inspired NoC has up to 70% lower average hop count and 75% lower average latency than mesh-based NoCs.
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Duan, Ying, Xiuwen Fu, Wenfeng Li, Yu Zhang, and Giancarlo Fortino. "Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks." Complexity 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2516742.
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Scale-free network and small-world network are the most impacting discoveries in the complex networks theories and have already been successfully proved to be highly effective in improving topology structures of wireless sensor networks. However, currently both theories are not jointly applied to have further improvements in the generation of WSN topologies. Therefore, this paper proposes a cluster-structured evolution model of WSNs considering the characteristics of both networks. With introduction of energy sensitivity and maximum limitation of degrees that a cluster head could have, the performance of our model can be ensured. In order to give an overall assessment of lifting effects of shortcuts, four placement schemes of shortcuts are analyzed. The characteristics of small-world network and scale-free network of our model are proved via theoretical derivation and simulations. Besides, we find that, by introducing shortcuts into scale-free wireless sensor network, the performance of the network can be improved concerning energy-saving and invulnerability, and we discover that the schemes constructing shortcuts between cluster heads and the sink node have better promoted effects than the scheme building shortcuts between pairs of cluster heads, and the schemes based on the preferential principle are superior to the schemes based on the random principle.
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Franceschetti, Massimo, and Ronald Meester. "Navigation in small-world networks: a scale-free continuum model." Journal of Applied Probability 43, no. 4 (December 2006): 1173–80. http://dx.doi.org/10.1239/jap/1165505216.
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The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to be pervasive both in nature and in engineering systems like the World Wide Web. Work of Jon Kleinberg has shown that people, using only local information, are very effective at finding short paths in a network of social contacts. In this paper we argue that the underlying key to finding short paths is scale invariance. In order to appreciate scale invariance we suggest a continuum setting, since true scale invariance happens at all scales, something which cannot be observed in a discrete model. We introduce a random-connection model that is related to continuum percolation, and we prove the existence of a unique scale-free model, among a large class of models, that allows the construction, with high probability, of short paths between pairs of points separated by any distance.
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Franceschetti, Massimo, and Ronald Meester. "Navigation in small-world networks: a scale-free continuum model." Journal of Applied Probability 43, no. 04 (December 2006): 1173–80. http://dx.doi.org/10.1017/s0021900200002515.
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The small-world phenomenon, the principle that we are all linked by a short chain of intermediate acquaintances, has been investigated in mathematics and social sciences. It has been shown to be pervasive both in nature and in engineering systems like the World Wide Web. Work of Jon Kleinberg has shown that people, using only local information, are very effective at finding short paths in a network of social contacts. In this paper we argue that the underlying key to finding short paths is scale invariance. In order to appreciate scale invariance we suggest a continuum setting, since true scale invariance happens at all scales, something which cannot be observed in a discrete model. We introduce a random-connection model that is related to continuum percolation, and we prove the existence of a unique scale-free model, among a large class of models, that allows the construction, with high probability, of short paths between pairs of points separated by any distance.
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Song, Xiao, and Wen Shi. "Impact of Informal Network on Opinion Dynamics in Command and Control Network." Applied Mechanics and Materials 764-765 (May 2015): 919–23. http://dx.doi.org/10.4028/www.scientific.net/amm.764-765.919.
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This paper aims to study the opinion dynamics in military command and control (C2) network with the impact of informal network. The authors reviewed recent opinion dynamics models and explored the relationships between formal and informal networks in detail. Then the opinion dynamics model in C2 network was introduced and a hybrid network based on small-world or scale-free network was proposed. Afterwards, the authors studied the opinion dynamics based on the formal C2 network and hybrid network by computer simulations, and found that opinion dynamics with the impact of informal network is almost independent on the network properties (including small-world, scale-free and rewiring probability) but dependent on the scale of the informal network. And it is concluded that the larger the size of informal network is, the better it can facilitate convergence of opinions in formal C2 network.
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BAO, ZHE-JING, WEN-JUN YAN, and CHUANG-XIN GUO. "RISK ASSESSMENT OF ATTACK-INDUCED CASCADE IN COMPLEX NETWORKS." International Journal of Modern Physics C 22, no. 08 (August 2011): 765–73. http://dx.doi.org/10.1142/s0129183111016579.
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For the complex networks, including scale-free, small-world, local-world and random networks, the global quantitative evaluation of attack-induced cascade is investigated in this paper by introducing the risk assessment, which integrates the probability of occurrence with the damage size of attacks on nodes. It is discovered by simulations, among the several kinds of networks, that the small-world network has the largest risk assessment of attack-induced cascade; the risk assessment of three other networks are all very low and the most protection against attack should be given to the small-world network accordingly. Furthermore, the percentage of the most fragile nodes in the scale-free network is very low, compared with that in the small-world network.
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WU, ZHENGPING, and ZHI-HONG GUAN. "TIME-DELAY ROBUSTNESS OF CONSENSUS PROBLEMS IN REGULAR AND COMPLEX NETWORKS." International Journal of Modern Physics C 18, no. 08 (August 2007): 1339–50. http://dx.doi.org/10.1142/s0129183107011364.
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Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.