Small Average Path Length Research Articles

Exploring evolutionary features of directed weighted hazard network in the subway construction**Project supported by the Co-Funding of National Natural Science Foundation of China and Shenhua Group Corporation Ltd (Grant No. U1261212) and the Program of Major Achievements Transformation and Industrialization of Beijing Education Commission, China (Grant No. ZDZH20141141301).

A better understanding of previous accidents is an effective way to reduce the occurrence of similar accidents in the future. In this paper, a complex network approach is adopted to construct a directed weighted hazard network (DWHN) to analyze topological features and evolution of accidents in the subway construction. The nodes are hazards and accidents, the edges are multiple relationships of these nodes and the weight of edges are occurrence times of repetitive relationships. The results indicate that the DWHN possesses the property of small-world with small average path length and large clustering coefficient, indicating that hazards have better connectivity and will spread widely and quickly in the network. Moreover, the DWHN has the property of scale-free network for the cumulative degree distribution follows a power-law distribution. It makes DWHN more vulnerable to target attacks. Controlling key nodes with higher degree, strength and betweenness centrality will destroy the connectivity of DWHN and mitigate the spreading of accidents in the network. This study is helpful for discovering inner relationships and evolutionary features of hazards and accidents in the subway construction.

The Polynomial Volume Law of Complex Networks in the Context of Local and Global Optimization

Many complex networks expose global hub structures: for some nodes, the number of incident edges far exceeds the average, leading to a small average shortest path length. Such ‘small-world properties’ are often guided by a scale-free power-law distribution of the node degrees, and self-organization inside the network has been identified as a reason driving the emergence of this structure. Small-world networks have recently raised lots of interest, because they capture the global topology of the World-Wide Web, metabolic, and social networks. While small-world networks reflect global structures, little attention is paid to the local structure of complex networks. In this article neighbourhoods are demonstrated to share a common local structure in many real complex networks, manifested by a polynomial volume law. This law can, in case of networks that are embedded in space, be explained in terms of the embedding and the properties of Euclidean space. A model of hierarchical spatial networks is introduced to examine the effect of global structures, in particular of hierarchies, on the polynomial volume law. It turns out that the law is robust against the coexistence of such global structures. The local structure of space and global optimization can both be found in transport, brain, and communication networks, which suggests the polynomial volume law, often in combination with hierarchies or other global optimization principles, to be a generic property inherent to many networks.

Co-occurrence patterns of soybean rhizosphere microbiome at a continental scale

Rhizosphere microorganisms play important roles in plant health and growth. The diversity and composition of rhizosphere microbial communities have been well studied, but little is known about their co-occurrence patterns, especially at a continental scale. Herein, we performed a network-based analysis using integrated bacterial and fungal community datasets to delineate the co-occurrence patterns of bulk soil and rhizosphere microbiome and the geographic patterns of network topological features in 51 soybean fields across China. Results showed that the microbial networks differed between bulk soil and rhizosphere in terms of structure and composition. Compared with the bulk soil networks, the rhizosphere networks had fewer links between bacteria and fungi, lower modularity, and smaller average path length; the global, southern and northern networks of rhizosphere showed similar, higher and lower complexity, respectively. The southern-specific networks of both bulk soil and soybean rhizosphere had more links between bacteria and fungi compared with the northern-specific networks. Additionally, the geographic patterns of network topological features differed between bulk soil and rhizosphere habitats, northern and southern regions. Bacterial sub-networks of both bulk soil and rhizosphere were most influenced by soil pH; fungal sub-networks were related to fewer environmental factors and most influenced by soil Mg content. Given that microbial networks may reflect interactions or niches shared among microorganisms, these results provide new insights into the organization of rhizosphere microbial communities.

Spatial structural pattern and vulnerability of China-Japan-Korea shipping network

The economies of China-Japan-Korea (CJK) are complementary, with their proximity resulting in the three countries having a high degree of interdependence with respect to trade. Currently, trade among these countries relies mainly on port-centered shipping. The development of the shipping network is integral for in-depth integration of CJK trade. This paper analyzes the overall characteristics, centrality, spatial structure, and vulnerability of the CJK shipping network using the methods of complex network analysis, blocking flow theory, and interruption and deletion of hub ports. The main findings are as follows: 1) The CJK shipping network has a small average path length and clustering coefficient, and its degree distribution follows a power-law distribution, which make the network present obvious characteristics of a Barabasi-Albert scale-free. 2) The characteristics of the multi-center point of the CJK shipping network can alleviate traffic pressure. At the same time, the network shows a clear hierarchy in the port transportation system, with cargo transport relying mainly on the ‘hub port-hub port’ connection. 3) The CJK shipping network is relatively stable. Compared with ports in Japan and Korea, the main hub ports in China have a greater impact on the stability of the shipping network, in particular those ports of the central coastal region, including Shanghai, Ningbo, and Lianyungang.

Characteristics of Information Dissemination of Agricultural Safety Emergencies Based on Complex Network

Information dissemination of agricultural safety emergencies on the Internet has drawn wide attention of academia and industry. Topological properties of information dissemination network of agricultural safety emergency on the news websites based on complex network theory, such as degree distribution, diameter, average path length, centrality and betweenness centrality of network, is studied in this paper. The result shows that the information dissemination network of agricultural safety emergency on the news websites presents small world feature, which means the dissemination network has relative small average path length and high betweenness centrality.

Causal relationship between the global foreign exchange market based on complex networks and entropy theory

The foreign exchange (FX) market is a typical complex dynamic system under the background of exchange rate marketization reform and is an important part of the financial market. This study aims to generate an international FX network based on complex network theory. This study employs the mutual information method to judge the nonlinear characteristics of 54 major currencies in international FX markets. Through this method, we find that the FX network possesses a small average path length and a large clustering coefficient under different thresholds and that it exhibits small-world characteristics as a whole. Results show that the relationship between FX rates is close. Volatility can quickly transfer in the whole market, and the FX volatility of influential individual states transfers at a fast pace and a large scale. The period from July 21, 2005 to March 31, 2015 is subdivided into three sub-periods (i.e., before, during, and after the US sub-prime crisis) to analyze the topology evolution of FX markets using the maximum spanning tree approach. Results show that the USD gradually lost its core position, EUR remained a stable center, and the center of the Asian cluster became unstable. Liang's entropy theory is used to analyze the causal relationship between the four large clusters of the world.

An Approach for Understanding and Promoting Coal Mine Safety by Exploring Coal Mine Risk Network

Capturing the interrelations among risks is essential to thoroughly understand and promote coal mining safety. From this standpoint, 105 risks and 135 interrelations among risks had been identified from 126 typical accidents, which were also the foundation of constructing coal mine risk network (CMRN). Based on the complex network theory and Pajek, six parameters (i.e., network diameter, network density, average path length, degree, betweenness, and clustering coefficient) were employed to reveal the topological properties of CMRN. As indicated by the results, CMRN possesses scale-free network property because its cumulative degree distribution obeys power-law distribution. This means that CMRN is robust to random hazard and vulnerable to deliberate attack. CMRN is also a small-world network due to its relatively small average path length as well as high clustering coefficient, implying that accident propagation in CMRN is faster than regular network. Furthermore, the effect of risk control is explored. According to the result, it shows that roof collapse, fire, and gas concentration exceeding limit refer to three most valuable targets for risk control among all the risks. This study will help offer recommendations and proposals for making beforehand strategies that can restrain original risks and reduce accidents.

A Novel Neighbor-Preferential Growth Scale-Free Network Model and its Properties

In this paper, we propose a novel neighbor-preferential growth (NPG) network model. Theoretical analysis and numerical simulations indicate the new model can reproduce not only a scale-free degree distribution and its power exponent is related to the edge-adding number m, but also a small-world effect which has large clustering coefficient and small average path length. Interestingly, the clustering coefficient of the model is close to that of globally coupled network, and the average path length is close to that of star coupled network. Meanwhile, the synchronizability of the NPG model is much stronger than that of BA scale-free network, even stronger than that of synchronization-optimal growth network.

Coevolution of Cooperation and Partner Rewiring Range in Spatial Social Networks.

In recent years, there has been growing interest in the study of coevolutionary games on networks. Despite much progress, little attention has been paid to spatially embedded networks, where the underlying geographic distance, rather than the graph distance, is an important and relevant aspect of the partner rewiring process. It thus remains largely unclear how individual partner rewiring range preference, local vs. global, emerges and affects cooperation. Here we explicitly address this issue using a coevolutionary model of cooperation and partner rewiring range preference in spatially embedded social networks. In contrast to local rewiring, global rewiring has no distance restriction but incurs a one-time cost upon establishing any long range link. We find that under a wide range of model parameters, global partner switching preference can coevolve with cooperation. Moreover, the resulting partner network is highly degree-heterogeneous with small average shortest path length while maintaining high clustering, thereby possessing small-world properties. We also discover an optimum availability of reputation information for the emergence of global cooperators, who form distant partnerships at a cost to themselves. From the coevolutionary perspective, our work may help explain the ubiquity of small-world topologies arising alongside cooperation in the real world.

A study on small-world characteristics of Chinaäó»s high-speed railway networks

The small-world model provides a useful perspective and method to study the topological structure and intrinsic characteristics of high-speed rail networks (HRNs). In this paper, the P-space method is used to examine global and local HRNs in China, meanwhile the adjacency matrix is developed, then the social network analysis and visualization tool UCINET is used to calculate the spatial and attribute data of HRNs at national and local levels in China. The small-world characteristics of whole HRNs are discussed, three networks which have different properties are determined, and a comparative analysis of the small-world effect is detected. Then, the relationship between the construction of high-speed rail and regional development of China is analysed. The results show that: 1) China's HRNs have small average path length ( L ) and large clustering coefficient (C ), representing a typical small-world network; 2) Local HRNs have a certain correlation with economic development. The reasons for the difference of HRNs with respect to characteristics among regions are eventually discussed.

Construction of protein interaction network involved in lung adenocarcinomas using a novel algorithm.

Studies that only assess differentially-expressed (DE) genes do not contain the information required to investigate the mechanisms of diseases. A complete knowledge of all the direct and indirect interactions between proteins may act as a significant benchmark in the process of forming a comprehensive description of cellular mechanisms and functions. The results of protein interaction network studies are often inconsistent and are based on various methods. In the present study, a combined network was constructed using selected gene pairs, following the conversion and combination of the scores of gene pairs that were obtained across multiple approaches by a novel algorithm. Samples from patients with and without lung adenocarcinoma were compared, and the RankProd package was used to identify DE genes. The empirical Bayesian (EB) meta-analysis approach, the search tool for the retrieval of interacting genes/proteins database (STRING), the weighted gene coexpression network analysis (WGCNA) package and the differentially-coexpressed genes and links package (DCGL) were used for network construction. A combined network was also constructed with a novel rank-based algorithm using a combined score. The topological features of the 5 networks were analyzed and compared. A total of 941 DE genes were screened. The topological analysis indicated that the gene interaction network constructed using the WGCNA method was more likely to produce a small-world property, which has a small average shortest path length and a large clustering coefficient, whereas the combined network was confirmed to be a scale-free network. Gene pairs that were identified using the novel combined method were mostly enriched in the cell cycle and p53 signaling pathway. The present study provided a novel perspective to the network-based analysis. Each method has advantages and disadvantages. Compared with single methods, the combined algorithm used in the present study may provide a novel method to analyze gene interactions, with increased credibility.

A new small-world network created by Cellular Automata

In this paper, we generate small-world networks by the Cellular Automaton based on starting with one-dimensional regular networks. Besides the common properties of small-world networks with small average shortest path length and large clustering coefficient, the small-world networks generated in this way have other properties: (i) The edges which are cut in the regular network can be controlled that whether the edges are reconnected or not, and (ii) the number of the edges of the small-world network model equals the number of the edges of the original regular network. In other words, the average degree of the small-world network model equals to the average degree of the original regular network.

Topology evolution model for ad hoc‐cellular hybrid networks based on complex network theory

SummarySwitching and routing are two important issues in the ad hoc‐cellular hybrid network. Frequently switching between different network modes will lead to the increase of time delay, and unreasonable routing will reduce information transmission efficiency and shorten the network life. In order to reduce the influence of these problems to the network, in this paper, we proposed a robust and efficient ad hoc network topology evolution model, which can reduce the switching probability and establish efficient transmission paths. In this model, the mobile users' residual energy, available channel quality, and the importance are taken into account. The model is based on Barrat, Barthelemy, and Vespignani model and the triad formation mechanism, which ensures the network topology have scale‐free and small‐world features. The topology construction process of the ad hoc network is composed of three parts: (i) new users join the network; (ii) new users establish connections with existing users; (iii) the connections between existing users were deleted because of the network optimization and the interference of cellular network. Simulation results show that the network built by this model with small‐world and scale‐free features has small average shortest path length and the robustness against random nodes failure, which will significantly improve the transmission efficiency and reduce the probability of switching between different transmission model. Copyright © 2016 John Wiley & Sons, Ltd.

A toward cost-effective scale-free coupling network construction method

Large network average path length will cause large network delay which brings difficulty in supporting the time sensitive services and applications. Large hop distance between source node and destination node in traditional network leads to significant network delay. By adding long-ranged links, path length from source node to destiny node will be reduced and original network can be transformed into a scale-free network with a small network average path length. The network delay is optimized by minimizing hop distance, in which information can transfer more efficiently and rapidly. Adding links can lower network delay effectively, but on the other hand, it will increase its cost. Common network construction methods focus on separating networks that are very different from each other and mostly unaware of each other, such as fixed and mobile networks planning. But in many real networks, networks are dependent on each other; therefore ignoring these network interactions cannot become more efficient. Cost and effectiveness play a key role in real network construction and layering network is an effective way to analyze coupling network especially in heterogeneous network. In this paper, the model of a toward cost-effective scale-free coupling network construction method is proposed. It combines the advantages of layered network and cost-effective network. A layered coupling network model is established in which network is divided into several networks based on link property. Links in the same layer have the same property and the upper layer capability is higher than lower layer capability. The nodes in the upper network are selected from the lower layer network coupling with the corresponding nodes with the same spatial location. Based on the network optimization and evolving network researches, the increases of node degree and local network radius are supposed to be continuous, moreover cost-effective indicator is introduced which characterizes the costs and effectiveness of adding links. Based on continuum, links are added to upper layer network with a certain probability by two continuous processes and thus network evolves into a scale-free network. The two continuous processes include node degree increasing process and local network radius increasing process. In the previous processes, cost-effective indicator is introduced and only the links satisfied cost-effectiveness are added. Cost-effective indicator characterizes the cost and effectiveness of network construction. Cost is proportional to Euclidean distance and effectiveness includes revenue of network average path length decreasing and link property benefit. In the coupling network, traffic prefers to transmit in the upper layer network for reducing network latency, and consequently leading to traffic congestion in upper layer. In the simulation, network topology evolution and dynamic traffic performance are evaluated. The simulation result shows that this method can effectively reduce the network latency within cost-effective requirement and initial network characteristics are maintained. The results also show that the network average path length declines slowly when network average path length is small because lower average path length needs higher cost when average path length is small. To investigate the traffic behaviors in the coupled layered networks, the traffic dynamic transition model is taken and dynamic traffic performance is given in this evolved scale-free network. Moreover, the cooperation between the two layers can be used to optimize network traffic performance by adjusting the link capacity to satisfy the requirements for the network congestion.

지식 전파에 있어 네트워크 구조와 지식 탐색의 상호작용

This paper models knowledge diffusion on an inter-organizational network. Based on literatures related to knowledge diffusion, the model considers critical factors that affect diffusion behavior including nodal property, relational property, and environmental property. We examine the relationships among network structure, knowledge search, and diffusion performance. Through a massive simulation runs based on the agent-based model, we find that the average path length of a network decreases a firm's cumulative knowledge stock, whereas the clustering coefficient of a firm has no significant relationship with the firm's knowledge. We also find that there is an interaction effect of network structure and the range of knowledge search on knowledge diffusion. Specifically, in a network of a larger average path length (APL) the marginal effect of search conduct is significantly greater than in that of a smaller APL.

Energy Efficient Wireless Sensor Network Modelling Based on Complex Networks

The power consumption and energy efficiency of wireless sensor network are the significant problems in Internet of Things network. In this paper, we consider the network topology optimization based on complex network theory to solve the energy efficiency problem of WSN. We propose the energy efficient model of WSN according to the basic principle of small world from complex networks. Small world network has clustering features that are similar to that of the rules of the network but also has similarity to random networks of small average path length. It can be utilized to optimize the energy efficiency of the whole network. Optimal number of multiple sink nodes of the WSN topology is proposed for optimizing energy efficiency. Then, the hierarchical clustering analysis is applied to implement this clustering of the sensor nodes and pick up the sink nodes from the sensor nodes as the clustering head. Meanwhile, the update method is proposed to determine the sink node when the death of certain sink node happened which can cause the paralysis of network. Simulation results verify the energy efficiency of the proposed model and validate the updating of the sink nodes to ensure the normal operation of the WSN.

A new method optimizing the subgraph centrality of large networks

Since many realistic networks such as wireless sensor/ad hoc networks usually do not agree very well with the basic network models such as small-word and scale-free models, we often need to obtain some expected structural features such as a small average path length and a regular degree distribution while optimizing the connectivity of these networks. Although a minor addition of links for optimizing network connectivity is not likely to change the structural properties of a network, it is necessary to investigate the impact of link addition on network properties as the number of the added links increases. However, to the best of our knowledge, the study of that problem has not been found so far. Furthermore, two closely related questions to that problem, i.e., how to measure and how to improve network connectivity, have not been studied carefully enough yet. To address the three problems above, the authors derive a better measure of network connectivity for large networks and a new strategy that can increase/decrease network connectivity the most, and propose a spectral density algorithm optimizing the connectivity of large networks, which is able to indicate the impact on the structural properties of a network while increasing/decreasing its connectivity, providing us a guided optimization of network connectivity. In other words, our algorithm can optimize not only the connectivity of a large network but also its structural features. Meanwhile, our new findings about spectral density are also concluded in this paper. In addition, we may also apply this algorithm to solve all eigenvalues of an N×N matrix, with a low complexity of O(N2) at most.

Nonlocal effects and countermeasures in cascading failures.

We study the propagation of cascading failures in complex supply networks with a focus on nonlocal effects occurring far away from the initial failure. It is shown that a high clustering and a small average path length of a network generally suppress nonlocal overloads. These properties are typical for many real-world networks, often called small-world networks, such that cascades propagate mostly locally in these networks. Furthermore, we analyze the spatial aspects of countermeasures based on the intentional removal of additional edges. Nonlocal actions are generally required in networks that have a low redundancy and are thus especially vulnerable to cascades.

Complex networks modeled on the Sierpinski gasket

In this paper, we use the Sierpinski gasket to construct evolving networks Gt whose node set is the solid regular triangles in the construction of the Sierpinski gasket up to the stage t and any two nodes are neighbors if and only if the corresponding solid triangles are in contact with each other on boundary. Using the encoding method, we show that our evolving networks are scale-free (power-law degree distribution) and have the small-world effect (small average path length and high clustering coefficient).

具有小世界特性的低能耗无线传感器网络簇级拓扑研究

The article proposes a cluster level topology algorithm of wireless sensor network and it is proposed to combine with UCR (unequal cluster-based routing）mechanism proposed by Professor Wu Jie. It reduces the cluster size near the base station and solves the hot problem of the high energy consumption. Using OPNET simulation software to simulate the cluster-level topology, when the super node number increased to 6 to 18, the average path length is reduced, the path length rate change is reduced, and energy decreases significantly. The simulation experiment indicates that the cluster level topology structure of wireless sensor network shows the strong robustness with good survivability. In the complex network, small world network has large aggregation coefficient and small average path length. By adding super nodes to the original network, it forms shortcuts of direct communication between the sink node, and decreases the average path length and energy consumption. Currently, the small world is used to the survey of WSN, which has not taken the hot spot problem near base station in consideration.