The Analysis of the Power Law Feature in Complex Networks

Consensus about the universality of the power law feature in complex networks is experiencing widespread challenges. In this paper, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that are more common than BA networks in the real world, and then we calculate their degree distributions; the results show that the tails of their degree distributions exhibit a distinct power law feature. Second, we suggest that in the real world two important factors—network size and node disappearance probability—will affect the analysis of power law characteristics in observation networks. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behavior of the degree distribution within its effective intervals.     

Synchronization and Bifurcation of General Complex Dynamical Networks

In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.     

Computing Influential Nodes Using the Nearest Neighborhood Trust Value and PageRank in Complex Networks

Computing influential nodes gets a lot of attention from many researchers for information spreading in complex networks. It has vast applications, such as viral marketing, social leader creation, rumor control, and opinion monitoring. The information-spreading ability of influential nodes is greater compared with other nodes in the network. Several researchers proposed centrality measures to compute the influential nodes in a complex network, such as degree, betweenness, closeness, semi-local centralities, and PageRank. These centrality methods are defined based on the local and/or global information of nodes in the network. However, due to their high time complexity, centrality measures based on the global information of nodes have become unsuitable for large-scale networks. Very few centrality measures exist that are based on the attributes between nodes and the structure of the network. We propose the nearest neighborhood trust PageRank (NTPR) based on the structural attributes of neighbors and nearest neighbors of nodes. We define the measure based on the degree ratio, the similarity between nodes, the trust values of neighbors, and the nearest neighbors. We computed the influential nodes in various real-world networks using the proposed centrality method. We found the maximum influence by using influential nodes with SIR and independent cascade methods. We also compare the maximum influence of our centrality measure with the existing basic centrality measures.     

Link Prediction in Complex Networks Using Recursive Feature Elimination and Stacking Ensemble Learning

Link prediction is an important task in the field of network analysis and modeling, and predicts missing links in current networks and new links in future networks. In order to improve the performance of link prediction, we integrate global, local, and quasi-local topological information of networks. Here, a novel stacking ensemble framework is proposed for link prediction in this paper. Our approach employs random forest-based recursive feature elimination to select relevant structural features associated with networks and constructs a two-level stacking ensemble model involving various machine learning methods for link prediction. The lower level is composed of three base classifiers, i.e., logistic regression, gradient boosting decision tree, and XGBoost, and their outputs are then integrated with an XGBoost model in the upper level. Extensive experiments were conducted on six networks. Comparison results show that the proposed method can obtain better prediction results and applicability robustness.     

复杂换热网络MINLP中的非线性特性分析

针对复杂换热网络MINLP问题,本文应用多维函数渐变法探索和分析了连续变量和整型变量引起的网络性能非线性和非凸特性。研究表明,当系统规模增大时,不但连续变量的叠加效应将增加系统的非线性,整型变量将使得非线性特性更为严重。     

An Efficient Partition-Based Approach to Identify and Scatter Multiple Relevant Spreaders in Complex Networks

One of the main problems in graph analysis is the correct identification of relevant nodes for spreading processes. Spreaders are crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases, rumors, and more. Correct identification of spreaders in graph analysis is a relevant task to optimally use the network structure and ensure a more efficient flow of information. Additionally, network topology has proven to play a relevant role in the spreading processes. In this sense, more of the existing methods based on local, global, or hybrid centrality measures only select relevant nodes based on their ranking values, but they do not intentionally focus on their distribution on the graph. In this paper, we propose a simple yet effective method that takes advantage of the underlying graph topology to guarantee that the selected nodes are not only relevant but also well-scattered. Our proposal also suggests how to define the number of spreaders to select. The approach is composed of two phases: first, graph partitioning; and second, identification and distribution of relevant nodes. We have tested our approach by applying the SIR spreading model over nine real complex networks. The experimental results showed more influential and scattered values for the set of relevant nodes identified by our approach than several reference algorithms, including degree, closeness, Betweenness, VoteRank, HybridRank, and IKS. The results further showed an improvement in the propagation influence value when combining our distribution strategy with classical metrics, such as degree, outperforming computationally more complex strategies. Moreover, our proposal shows a good computational complexity and can be applied to large-scale networks.     

Reliability and Efficiency of Generalized Rumor Spreading Model on Complex Social Networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader (SS) and the spreader-stifler (SR) interactions have the same rate α, we define α(1) and α(2) for SS and SR interactions, respectively. The effect of variation of α(1) and α(2) on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.     

Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

We analyze the correlation properties of the Erdos-Rényi random graph (RG) and the Barabási-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre.     

基于复杂网络的时间序列双变量联动波动

选择伦敦金与Au9999下午收盘价格作为样本数据研究时间序列双变量之间的联动波动规律.依据粗粒化方法,将伦敦金与Au9999价格的联动波动状态转化为由5个{P,N,M}字符组成的字符串,每个字符串代表5天的价格联动波动模态.将模态作为节点,模态之间的转化为边,构建价格联动波动复杂网络.运用复杂网络理论对时间序列双变量联动波动模态的统计、变化规律和演化机制进行分析.结果表明:时间序列双变量联动波动模态分布具有幂律性、群簇性和周期性,其联动波动模态主要通过少数几种模态进行转换与演化.本方法不仅可以研究不同类型时间序列双变量联动波动,同时可为多变量联动波动研究提供思路.     

Identifying Influential Nodes in Complex Networks Based on Multiple Local Attributes and Information Entropy

Identifying influential nodes in complex networks has attracted the attention of many researchers in recent years. However, due to the high time complexity, methods based on global attributes have become unsuitable for large-scale complex networks. In addition, compared with methods considering only a single attribute, considering multiple attributes can enhance the performance of the method used. Therefore, this paper proposes a new multiple local attributes-weighted centrality (LWC) based on information entropy, combining degree and clustering coefficient; both one-step and two-step neighborhood information are considered for evaluating the influence of nodes and identifying influential nodes in complex networks. Firstly, the influence of a node in a complex network is divided into direct influence and indirect influence. The degree and clustering coefficient are selected as direct influence measures. Secondly, based on the two direct influence measures, we define two indirect influence measures: two-hop degree and two-hop clustering coefficient. Then, the information entropy is used to weight the above four influence measures, and the LWC of each node is obtained by calculating the weighted sum of these measures. Finally, all the nodes are ranked based on the value of the LWC, and the influential nodes can be identified. The proposed LWC method is applied to identify influential nodes in four real-world networks and is compared with five well-known methods. The experimental results demonstrate the good performance of the proposed method on discrimination capability and accuracy.     

Evolution of Cohesion between USA Financial Sector Companies before,during, and Post-Economic Crisis: Complex Networks Approach

Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system’s constituents and the emergence of a crisis is of great importance. In this paper, we propose a novel method for the inference of economic systems’ structures based on complex networks theory utilizing the time series of prices. Our network is obtained from the correlation matrix between the time series of companies’ prices by imposing a threshold on the values of the correlation coefficients. The optimal value of the threshold is determined by comparing the spectral properties of the threshold network and the correlation matrix. We analyze the community structure of the obtained networks and the relation between communities’ inter and intra-connectivity as indicators of systemic risk. Our results show how an economic system’s behavior is related to its structure and how the crisis is reflected in changes in the structure. We show how regulation and deregulation affect the structure of the system. We demonstrate that our method can identify high systemic risks and measure the impact of the actions taken to increase the system’s stability.     

Synchronization and Bifurcation Analysis in Coupled Networks of Discrete-Time Systems

Synchronization and bifurcation analysis in coupled networks of discrete-time systems are investigated in the present paper. We mainly focus on some special coupling matrix, i.e., the sum of each row equals a nonzero constant u and the network connection is directed. A result that the network can reach a new synchronous state, which is not the asymptotic limit set determined by the node state equation, is derived. It is interesting that the network exhibits bifurcation if we regard the constant u as a bifurcation parameter at the synchronous state. Numerical simulations are given to show the efficiency of our derived conclusions.     

Analysis of the Structure and Dynamics of European Flight Networks

We analyze structure and dynamics of flight networks of 50 airlines active in the European airspace in 2017. Our analysis shows that the concentration of the degree of nodes of different flight networks of airlines is markedly heterogeneous among airlines reflecting heterogeneity of the airline business models. We obtain an unsupervised classification of airlines by performing a hierarchical clustering that uses a correlation coefficient computed between the average occurrence profiles of 4-motifs of airline networks as similarity measure. The hierarchical tree is highly informative with respect to properties of the different airlines (for example, the number of main hubs, airline participation to intercontinental flights, regional coverage, nature of commercial, cargo, leisure or rental airline). The 4-motif patterns are therefore distinctive of each airline and reflect information about the main determinants of different airlines. This information is different from what can be found looking at the overlap of directed links.     

Sensing Enhancement on Social Networks: The Role of Network Topology

Sensing and processing information from dynamically changing environments is essential for the survival of animal collectives and the functioning of human society. In this context, previous work has shown that communication between networked agents with some preference towards adopting the majority opinion can enhance the quality of error-prone individual sensing from dynamic environments. In this paper, we compare the potential of different types of complex networks for such sensing enhancement. Numerical simulations on complex networks are complemented by a mean-field approach for limited connectivity that captures essential trends in dependencies. Our results show that, whilst bestowing advantages on a small group of agents, degree heterogeneity tends to impede overall sensing enhancement. In contrast, clustering and spatial structure play a more nuanced role depending on overall connectivity. We find that ring graphs exhibit superior enhancement for large connectivity and that random graphs outperform for small connectivity. Further exploring the role of clustering and path lengths in small-world models, we find that sensing enhancement tends to be boosted in the small-world regime.     

Control Meets Inference: Using Network Control to Uncover the Behaviour of Opponents

Using observational data to infer the coupling structure or parameters in dynamical systems is important in many real-world applications. In this paper, we propose a framework of strategically influencing a dynamical process that generates observations with the aim of making hidden parameters more easily inferable. More specifically, we consider a model of networked agents who exchange opinions subject to voting dynamics. Agent dynamics are subject to peer influence and to the influence of two controllers. One of these controllers is treated as passive and we presume its influence is unknown. We then consider a scenario in which the other active controller attempts to infer the passive controller’s influence from observations. Moreover, we explore how the active controller can strategically deploy its own influence to manipulate the dynamics with the aim of accelerating the convergence of its estimates of the opponent. Along with benchmark cases we propose two heuristic algorithms for designing optimal influence allocations. We establish that the proposed algorithms accelerate the inference process by strategically interacting with the network dynamics. Investigating configurations in which optimal control is deployed. We first find that agents with higher degrees and larger opponent allocations are harder to predict. Second, even factoring in strategical allocations, opponent’s influence is typically the harder to predict the more degree-heterogeneous the social network.     

Joint Detection of Community and Structural Hole Spanner of Networks in Hyperbolic Space

Community detection and structural hole spanner (the node bridging different communities) identification, revealing the mesoscopic and microscopic structural properties of complex networks, have drawn much attention in recent years. As the determinant of mesoscopic structure, communities and structural hole spanners discover the clustering and hierarchy of networks, which has a key impact on transmission phenomena such as epidemic transmission, information diffusion, etc. However, most existing studies address the two tasks independently, which ignores the structural correlation between mesoscale and microscale and suffers from high computational costs. In this article, we propose an algorithm for simultaneously detecting communities and structural hole spanners via hyperbolic embedding (SDHE). Specifically, we first embed networks into a hyperbolic plane, in which, the angular distribution of the nodes reveals community structures of the embedded network. Then, we analyze the critical gap to detect communities and the angular region where structural hole spanners may exist. Finally, we identify structural hole spanners via two-step connectivity. Experimental results on synthetic networks and real networks demonstrate the effectiveness of our proposed algorithm compared with several state-of-the-art methods.     

On the Possibility of Glucose Sensing Using Boronic Acid and a Luminescent Ruthenium Metal-Ligand Complex

We describe a new approach to optical sensing of glucose based on the competitive interactions between a ruthenium metal ligand complex, a boronic acid derivative and glucose. The metal-ligand complex [Ru(2,2-bipyridine)₂(5,6-dihydroxy-1,10-phenanthroline)](PF₆)₂ at pH 8 forms a reversible complex with 2-toluylboronic acid or 2-methoxyphenyl boronic acid. Complexation is accompanied by a several-fold increase in the luminescent intensity of the ruthenium complex. Addition of glucose results in decreased luminescent intensity, which appears to be the result of decreased binding between the metal-ligand complex and the boronic acid. Ruthenium metal-ligand complexes are convenient for optical sensing because their long luminescent decay times allow lifetime-based sensing with simple instrumentation.     

Assigning Degrees of Stochasticity to Blazar Light Curves in the Radio Band Using Complex Networks

We focus on characterizing the high-energy emission mechanisms of blazars by analyzing the variability in the radio band of the light curves of more than a thousand sources. We are interested in assigning complexity parameters to these sources, modeling the time series of the light curves with the method of the Horizontal Visibility Graph (HVG), which allows us to obtain properties from degree distributions, such as a characteristic exponent to describe its stochasticity and the Kullback–Leibler Divergence (KLD), presenting a new perspective to the methods commonly used to study Active Galactic Nuclei (AGN). We contrast these parameters with the excess variance, which is an astronomical measurement of variability in light curves; at the same time, we use the spectral classification of the sources. While it is not possible to find significant correlations with the excess variance, the degree distributions extracted from the network are detecting differences related to the spectral classification of blazars. These differences suggest a chaotic behavior in the time series for the BL Lac sources and a correlated stochastic behavior in the time series for the FSRQ sources. Our results show that complex networks may be a valuable alternative tool to study AGNs according to the variability of their energy output.     

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations

Recently, there has been enormous development due to advancements in technology. Industries and enterprises are moving towards a digital system, and the oil and gas industries are no exception. There are several threats and risks in digital systems, which are controlled through cyber-security. For the first time in the theory of fuzzy sets, this research analyzes the relationships between cyber-security and cyber-crimes in the oil and gas sectors. The novel concepts of complex intuitionistic fuzzy relations (CIFRs) are introduced. Moreover, the types of CIFRs are defined and their properties are discussed. In addition, an application is presented that uses the Hasse diagram to make a decision regarding the most suitable cyber-security techniques to implement in an industry. Furthermore, the omnipotence of the proposed methods is explained by a comparative study.     

Evolution of the Photon-number Probability Distribution in the System of a Three Level Atom with an Added Kerr-like Medium

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