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This paper mainly discusses the problem of fast fixed-time bipartite synchronization in the complex networks with signed graph that is based on TS fuzzy system. By designing suitable and effective controller, the synchronization of the considered complex networks has been achieved successfully in this paper, whose convergence rate is superior to the great majority of existing results. With the assistance of a comparison system being built and using the theory of Lyapunov stability, this paper has established sufficient criteria successfully that are able to achieve fast fixed-time bipartite synchronization. And a numerical simulation example displays the performance of the obtained new results at the end of this paper. [ABSTRACT FROM AUTHOR]

With the increasing complexity and demand for transportation networks, effective routing planning has attracted more and more attention. Different modes of transportation, such as the airplane, railway and so on, work together, forming a multi-modal transportation network. Therefore, this paper studies the routing and congestion problems in the multi-modal transportation network, and shows how to increase the network capacity as much as possible while saving time and economic costs, so as to avoid congestion and realize the effective use of different modes of transportation. This paper simulates the influence of two main factors on the network capacity, the parameter which shows the importance between time costs and economic costs, and the difference between different transportation modes. The results show the change of the network capacity when the time cost and economic cost are of different importance. There exists a critical point that can balance time costs and economic costs, so as to maximize network capacity. Then this paper further finds out the method of estimating the condition when the network takes the maximum capacity through theoretical analysis. [ABSTRACT FROM AUTHOR]

The development of Econophysics is studied from the perspective of scientific communication networks. Papers in Econophysics published from 1992 to 2003 are collected. Then a weighted and directed network of scientific communication, including collaboration, citation and personal discussion, is constructed. Its static geometrical properties, including degree distribution, weight distribution, weight per degree, and betweenness centrality, give a nice overall description of the research works. The way we introduced here to measure the weight of connections can be used as a general one to construct weighted network. [ABSTRACT FROM AUTHOR]

To discern the role social and cultural networks play in the emergence of preeminent historical figures and ideas in History, we use a method based on complex networks analysis to reveal emergent interactions in Wikipedia. We built a network constituted by derivative links, where nodes are connected if they are co-linked by other papers or co-link other papers within Wikipedia. We apply this method, focused on the structural distance, to three significant individuals associated with the Italian Renaissance: Copernicus, Michelangelo, and Pico della Mirandola. The results point to the effectiveness of this approach for discovering new knowledge about the interdisciplinary transactions between people and ideas coming from artistic, scientific and philosophical domains during this period. The emergent network reflects the apparently strong network-level interactions between Michelangelo and Mirandola's clusters; the importance of Hermeticism across the three clusters; and how the so-called "knowledge dealers" related to Neoplatonism contribute to the depiction of the period by future historians. Finally, we advance the notion of "focus reading", in which complex networks analysis allows us to build bridges between close and distant forms of reading historical evidence. [ABSTRACT FROM AUTHOR]

This paper investigates the factors influencing the spread of popular topic competition from the perspective of propagation dynamics. The popularity of a topic is directly influenced by the level of people's interest in it. The rarity, deviation and type can influence the level of interest in such topics. In addition, the topic publisher also has an impact on the competitive dissemination of the topic. The higher the rank of the original publisher is, the easier it spreads. Compared with small bloggers without fans, it is easier to attract people's attention, and the heat of the topic will rise faster. The results show that the rarer the topic, the greater the deviation from reality, and the more followers the originator has, the more competitive it is. [ABSTRACT FROM AUTHOR]

Link prediction plays an important role in information filtering and numerous research works have been made in this field. However, traditional link prediction algorithms mainly focus on overall prediction accuracy, ignoring the heterogeneity of the prediction accuracy for different links. In this paper, we analyzed the prediction accuracy of each link in networks and found that the prediction accuracy for different links is severely polarized. Further analysis shows that the accuracy of edges with low edge betweenness is consistently high while that of edges with high edge betweenness is consistently low, i.e. AUC follows a bimodal distribution with one peak around 0.5 and the other peak around 1. Our results indicate that link prediction algorithms should focus more on edges with high betweenness instead of edges with low betweenness. To improve the accuracy of edges with high betweenness, we proposed an improved algorithm called RA_LP which takes advantage of resource transfer of the second-order and third-order paths of local path. Results show that this algorithm can improve the link prediction accuracy for edges with high betweenness as well as the overall accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we construct an infinite family of weighted growing complex networks, namely, weighted neighborhood networks (WNN) which are constructed in an iterative way by using a base network and a sequence of growing weighted networks. We determine the weighted Laplacian spectra of WNN which is expressed in terms of the spectra of base network and the sequence of weighted regular networks. Using the weighted Laplacian spectra, we obtain the Kirchhoff index, the entire mean weighted first-passage time and the number of spanning trees of WNN. Also, we compute the weighted normalized Laplacian spectra of these networks which is expressed in terms of the spectra of regular base network and the sequence of weighted regular networks and from that, we derive the multiplicative Kirchhoff index, Kemeny's constant and the number of spanning trees in terms of the weighted normalized Laplacian spectra. [ABSTRACT FROM AUTHOR]

The robustness of complex networks to various kinds of attacks that could trigger cascading failures has attracted increasing attention. Most existing studies fail to consider that the cost to attack each network component (node or edge) may be unequal. Therefore, in this paper, we explore the network robustness to cascaded attacks based on heterogeneous costs. We introduce an attack cost model with both cost-sensitive and budget-constraint parameters. On this basis, three attack strategies are considered, including hub strategy, average degree strategy, and leaf strategy. Their cascaded attack effects are compared by considering the load local preferential redistribution rule. Both the fraction of failed nodes and the value of a new robustness metric, i.e. the budget-constraint threshold, are monitored in different complex networks. Numerical experiments indicate that as the attack cost changes from homogeneity to heterogeneity, the performance of the classic hub strategy decreases gradually. For the situation of weak heterogeneity of attack cost of each node, leaf strategy achieves the maximum attack performance gradually. Moreover, the budget, network structure, and robustness metrics may all affect the selection of the optimal attack strategy. [ABSTRACT FROM AUTHOR]

This paper shows how a new theory of epidemics can be developed for viral pandemics in a globally interconnected world. The study of the in-host dynamics and, in parallel, the spatial diffusion of epidemics defines the goal of our work, which looks ahead to new mathematical tools to model epidemics beyond the traditional approach of population dynamics. The approach takes into account the evolutionary nature of the virus, which can generate pseudo-Darwinian mutations and selection, while learning the presence of the virus and activating adaptive immunity. The study of immune competition plays a key role in both the in-host dynamics and the contagion dynamics. [ABSTRACT FROM AUTHOR]

Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. Node and link residual closeness are novel sensitive graph based characteristics for network vulnerability analysis. Node and link residual closeness measure the vulnerability even when the removal of nodes or links does not disconnect the network. Node and link residual closeness are of great theoretical and practical significance to network design and optimization. In this paper, vulnerabilities of multipartite network type topologies to the failure of individual nodes and links are computed via node and link residual closeness which provides a much fuller characterization of the network. Then, how multipartite network type topologies perform when they suffer a node or a link failure is analyzed. [ABSTRACT FROM AUTHOR]

Wikipedia is a widely used tool people use to gather knowledge about the world, causing it to have a vast impact on the way individuals perceive the reality they live in. It is then of paramount importance that the picture of the world Wikipedia provides is accurate. We cannot afford such an important tool to eschew inclusiveness or a fair representation of reality: an inaccurate picture of the world in such a tool can be used to claim unjust and unfair positions — such as that women are inferior to men — as if they were facts, because they are enshrined on an encyclopedia. In this paper, we study issues of fair gender representations for people in history noted by multiple language editions of Wikipedia: are women underrepresented on Wikipedia? We do so via a combination of natural language processing and network science. Our results indicate that there is indeed a higher bar for women to have their own biographical page on Wikipedia: women are only included when they have more significant connections than men to the rest of the network. There are visible effects of the initiatives Wikipedia is taking to fix this issue, showing that the gap is narrowing, which validates our interpretation of the data. [ABSTRACT FROM AUTHOR]

In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors: vigorousness and dormancy. Based on this idea, a citation network model is proposed, in which a node has two discrete stage: vigorous and dormant. Vigorous nodes can be deactivated and dormant nodes may be activated and become vigorous. The evolution of the network couples addition of new nodes and state transitions of old ones. Both analytical calculation and numerical simulation show that the degree distribution of nodes in generated networks displays a good right-skewed behavior. Particularly, scale-free networks are obtained as the deactivated vertex is target selected and exponential networks are realized for the random-selected case. Moreover, the measurement of four real-world citation networks achieves a good agreement with the stochastic model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks’ nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model. [ABSTRACT FROM AUTHOR]

Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoretical and applied points of view. [ABSTRACT FROM AUTHOR]

The idea of discovering a few nodes with potential to impact an entire network, is known as Influence Maximization (IM) and has many real-world applications which make it one of well-studied research problems in the domain of network analysis. IM typically requires a fixed criteria of budget (number of influential nodes to be identified) as input. The fundamental premise of this research is that the budget is not the sole criteria for real-world applications. This study challenges the conventional method to identify influential nodes, and proves that it requires specification of the stoppage criteria and the model used to quantify influence. We analyze the complex interplay of various criteria that can be used to solve IM problem, and prove that changing the criterion also changes the algorithm determined as the top performer. A number of criteria are presented in this paper apart from budget, such as the spread achieved by the algorithm (in terms of number of nodes influenced) and absolute time. The proposed IMine framework provides an interface to apply influence problem on various stoppage criteria, while also providing customization option to change the model of quantifying influence spread. [ABSTRACT FROM AUTHOR]

For decades, centrality has been one of the most studied concepts in the case of complex networks. It addresses the problem of identification of the most influential nodes in the network. Despite the large number of the proposed methods for measuring centrality, each method takes different characteristics of the networks into account while identifying the "vital" nodes, and for the same reason, each has its advantages and drawbacks. To resolve this problem, the TOPSIS method combined with relative entropy can be used. Several of the already existing centrality measures have been developed to be effective in the case of static networks, however, there is an ever-increasing interest to determine crucial nodes in dynamic networks. In this paper, we are investigating the performance of a new method that identifies influential nodes based on relative entropy, in the case of dynamic networks. To classify the effectiveness, the Suspected-Infected model is used as an information diffusion process. We are investigating the average infection capacity of ranked nodes, the Time-Constrained Coverage as well as the Cover Time. [ABSTRACT FROM AUTHOR]

When transporting data packets on communication networks, the local routing protocols are often preferred because of the large-scale and complicated property of many realistic network structures such as Internet. Based on a local routing protocol with a navigation parameter proposed in a previous paper [W. X. Wang et al., Phys. Rev. E73, 026111 (2006)], this paper numerically investigates the distribution of travel time for transporting data packets from the origin to the destination in complex networks, including random networks, small-world networks and scale-free networks. Numerical results show that exponential distributions of travel time with various values of exponent in complex networks are obtained. Furthermore, the different values of the exponent can also intuitively prove the previous result for the optimal local routing strategy. Finally, violations of the First-Departure-First-Arrival situation in complex networks are discussed. [ABSTRACT FROM AUTHOR]

In order to study the stability of the ecosystem under external attack, we regard the ecosystem as a complex network and the species disturbance after the attack as an infectious disease. We establish an ecological network disturbance propagation model based on the infectious disease model, and analyze its dynamics with the above ideas. In this paper, the species are regarded as nodes in the network, and the predator–prey relationship is regarded as the edge of the network. When the ecosystem is attacked by external forces, the disturbance can be transmitted from a species to its predator or prey through the food chain, and the disturbed species can recover themselves and then return to a stable state. At the same time, we consider adding human quarantine and protection of disturbed species. In this way, all species in the ecosystem are divided into four states: undisturbed, disturbed, quarantine and recovered. By analyzing the dynamics of disturbance propagation, the critical threshold and equilibrium point of disturbance diffusion are determined, and the local and global stability of disease-free equilibrium and endemic equilibrium are analyzed. The results show that the existence of endemic equilibrium depends on the critical threshold of disturbance propagation, which is related to the structure of food web, the propagation proportion of disturbance and the recovery proportion of species after being attacked. The larger the propagation proportion is, the weaker the resistance stability is, and the easier the disturbance propagates in the system. The higher the recovery proportion of the disturbed species, the stronger the stability of the recovery rate, and the more difficult it is for the disturbance to propagate in the system. Then we regard human protection of species as species immunity, and choose the most effective species protection measures by comparing and analyzing the threshold changes under the three protection strategies. The results show that the moderately large neighbor nodes of the disturbed species should be protected. This kind of protection measure is the most effective and it is easier to restrain the propagation of disturbance. Finally, the food webs of 85 species in a pine forest in Otago, New Zealand is selected to analyze the propagation process of disturbance by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper proposed a novel routing strategy with two tunable parameters, α 1 , β , based on the dynamic local information in a finite buffer network. The system behaves differently from that with a local routing strategy based on the degree with an adjustable parameter α 2 . Simulations show that, under dynamic local strategy, the maximal capacity of the network system increases with β whereas it increases with the decrement of α 1 in the case of all the nodes having identical delivering ability. The dynamic local routing performs much better than the local routing, which is demonstrated by a larger value of the critical packet generation rate. We found that buffer coefficient has a limited impact on the performance of network system. We also demonstrate that a smaller α 1 would be better if we want to have an excellent traffic capacity considering the travel time, average path length and waiting time. Our study will be helpful to improve traffic performance in finite buffer networks. [ABSTRACT FROM AUTHOR]

Many factors can lead to ship collision accidents, and identifying the importance of these factors is crucial for marine safety management and risk assessment. Are there rooted factors that are responsible for the presence of other factors? Notably, it is hard to analyze the causal relationship between these factors, due to the diversity and the interwoven of factors, especially when the size of the accident sample is small. To address this problem, an accident-cause network and a cause-inducing chain network are constructed in this paper by extracting 98 causes from 300 ship collision accidents. Our results show that there are six hidden rooted causes, i.e. the captain did not give any orders of night, the navigation alarm on the bridge was not on, communication failure between the officer on duty and the sailor on duty, no vessel traffic service was established, the shipping company does not fully grasp the navigation management regulations which is important to ship safety, and defects in bridge resource management, responsible for the presence of others among 98 causes. Our findings may shed some new lights on how to avoid ship collision accidents. [ABSTRACT FROM AUTHOR]

Link prediction is a significant and fundamental research issue in the field of network science. Numerous similarity-based algorithms have been widely applied due to low computational cost and high prediction accuracy. The topological features of networks like community structure are beneficial to link prediction. In this paper, we first introduce a Weighted Two-level Neighborhood Similarity (WTNS) index that integrates the resource allocation index and local path index. Then we define the Strength of Community Link (SCL) as a quantitative index to evaluate the close relationship among communities. Based on this, the connection likelihood between two nodes can be calculated and a new link prediction algorithm called SCL-WTNS is presented. The proposed algorithm has been compared with nine popular similarity methods on 12 real-world networks to verify the performance. SCL-WTNS is also compared with two groups of community-based link prediction methods. Experiments indicate that the proposed algorithm is better than comparison algorithms both in prediction accuracy and stability. [ABSTRACT FROM AUTHOR]

As COVID-19 spread globally in 2020, the interaction between the traffic dynamics and the spread of the epidemic has attracted much attention. However, controlling the spread of the epidemic remains a challenging issue. In this paper, we have investigated the relationships between link-closure strategies and the traffic-driven epidemic spreading. It is found that the epidemic spreading can be suppressed by the targeted closing of links between small-degree nodes. In contrast, closing links between large-degree nodes can accelerate the outbreak of the epidemic. These findings have significance for controlling the spread of the epidemic. [ABSTRACT FROM AUTHOR]

Several real-world directed networks do not have multiple links. For example, in a paper citation network a paper does not cite two identical references, and in a network of friends there exists only a single link between two individuals. This suggest that the growth and evolution models of complex networks should take into account such feature in order to approximate the topological properties of this class of networks. The aim of this paper is to propose a growth model of directed complex networks that takes into account the prohibition of the existence multiple links. It is shown through numerical experiments that when multiple links are forbidden, the exponent γ of the in-degree connectivity distribution, , takes values ranging from 1 to ∞. In particular, the proposed multi-link free (MLF) model is able to predict exponents occurring in real-world complex networks, which range 1.05 < γ < 3.51. As an example, the MLF reproduces somxe topological properties exhibited by the network of flights between airports of the world (NFAW); i.e. γ ≈ 1.74. With this result, we believe that the multiple links prohibition might be one of the local processes accounting for the existence of exponents γ < 2 found in some real complex networks. [ABSTRACT FROM AUTHOR]

In this paper, we construct evolving networks from n -dimensional Sierpinski cube. Using the self-similarity of Sierpinski cube, we show the evolving networks have scale-free and small-world properties. [ABSTRACT FROM AUTHOR]

Community structure is a common characteristic of complex networks and community detection is an important methodology to reveal the structure of real-world networks. In recent years, many algorithms have been proposed to detect the high-quality communities in real-world networks. However, these algorithms have shortcomings of performing calculation on the whole network or defining objective function and the number of commonties in advance, which affects the performance and complexity of community detection algorithms. In this paper, a novel algorithm has been proposed to detect communities in networks by belonging intensity analysis of intermediate nodes, named BIAS, which is inspired from the interactive behavior in human communication networks. More specifically, intermediate nodes are middlemen between different groups in social networks. BIAS algorithm defines belonging intensity using local interactions and metrics between nodes, and the belonging intensity of intermediate node in different communities is analyzed to distinguish which community the intermediate node belongs to. The experiments of our algorithm with other state-of-the-art algorithms on synthetic networks and real-world networks have shown that BIAS algorithm has better accuracy and can significantly improve the quality of community detection without prior information. [ABSTRACT FROM AUTHOR]

Community detection is a pivotal part of network analysis and is classified as an NP-hard problem. In this paper, a novel community detection algorithm is proposed, which probabilistically predicts communities' diameter using the local information of random seed nodes. The gravitation method is then applied to discover communities surrounding the seed nodes. The individual communities are combined to get the community structure of the whole network. The proposed algorithm, named as Local Gravitational community detection algorithm (LGCDA), can also work with overlapping communities. LGCDA algorithm is evaluated based on quality metrics and ground-truth data by comparing it with some of the widely used community detection algorithms using synthetic and real-world networks. [ABSTRACT FROM AUTHOR]

Ranging from computer network to traffic network, complex networks are ubiquitous in our lives. How to control congestion to make network operate more effectively is one of the most essential issues in complex network research. At present, a large number of studies on traffic dynamics mainly focus on single-layer networks. However, in fact, many complex systems are coupled by multiple networks. In this paper, we propose a resource allocation strategy for three-layer network with which the limited total delivery capacity can be reasonably allocated to each node of physical layer based on the degree of nodes in two logical layers. Compared with the average allocation of delivery capacity, the traffic capacity is improved and the network has better transmission performance in average traveling time and average throughput with our strategy. [ABSTRACT FROM AUTHOR]

This paper presents a study of the bounded confidence model applied to the complex networks. Two different cases were examined: opinion formation process in the Barabási--Albert network and corruption spreading in a hierarchical network. For both cases, the value of the bounded confidence parameter s was assumed as a constant, or its value was dependent on the degree of a node in the network. To measure the opinion formation and corruption spreading processes, we introduced the order parameter related to the number of interfaces in the system. As a results of numerical simulations, the influence of the values of t on the final opinions in the population, as well as, the influence of an initial source of corruption in the company structure on the corruption spreading process, were obtained and discussed. [ABSTRACT FROM AUTHOR]

Identifying multiple key spreaders in a network can effectively control the diffusion of information and optimize the use of available resources, which can be also called the influence maximization problem in sociology domains. In order to maximize collective influence in complex networks, multiple spreaders must have both large single influence and small overlapping influence, but it is rather difficult to satisfy these two conditions simultaneously. In this paper, we try to achieve the best compromise between importance and dispersibility for multiple spreaders through clustering. The cluster centers are surrounded by nodes with lower influence, and the distance among different cluster centers is relatively far. In addition, the initial centers selection directly affects the efficiency of clustering and the realization of global optimization. Consequently, we present an initial centers selection algorithm combining H-index and minimum distance. The experimental results on four actual datasets show that the proposed method has better performance than the traditional benchmark methods in terms of transmission speed, diffusion scale and structural characteristics. [ABSTRACT FROM AUTHOR]

In recent years, because complex networks can be used to model real-world complex systems, such as the Internet, urban infrastructure networks, and gene interaction networks, such research has been widely applied in engineering, social sciences, and life sciences and has caused widespread concern. Fractal dimension, as a concept concerning the filling ability and complexity of an object space, has great significance for the study of the robustness of complex networks. This paper studies the relationship between fractal dimension and the robustness of different types of complex networks from the perspective of network structure and network scale. We find that fractal dimension is strongly correlated with robustness under certain conditions and can be used as an important index to evaluate the robustness of complex networks. [ABSTRACT FROM AUTHOR]

This paper presents an internal public subsidy mechanism, in which the population themselves subsidize the vaccinated individuals, to study the evolutionary vaccination dynamics in the epidemic spreading process. By means of theoretical analysis and extensive computer simulations, we show that the mechanism can effectively enhance the vaccine coverage and significantly make many persons still choose vaccination when the vaccination cost is nearly or even more than the infection cost. In addition, we prove that there exists a lower bound of vaccine coverage controlled by our proposed mechanism. The overall results are robust to the typical synthetic and real-world networks. [ABSTRACT FROM AUTHOR]

Cluster modified projective synchronization (CMPS) between two topologically distinct community networks is studied in this paper. Each cluster here has a unique dynamics at least with respect to the parameter sets. Using an adaptive feedback control gain and a matrix scaling factor, we show that CMPS between two community networks can be realized with considering minimum assumptions and imposing just few restrictions on the configuration set. We use Lyapunov stability theory for the proof and employ computer simulation to confirm our result on randomly generated community networks. Simulations also show the possibility of having hybrid synchronization between the two networks. [ABSTRACT FROM AUTHOR]

Local processes exert influence on the growth and evolution of complex networks, which in turn shape the topological and dynamic properties of these networks. Some local processes have been researched, for example: Addition of nodes and links, rewiring of links between nodes, accelerated growth, link removal, aging, copying and multiple links prohibition. These processes impact directly into the topological and dynamical properties of complex networks. This paper introduces a new model for growth of directed complex networks which incorporates the prohibition of multiple links, addition of nodes and links, and rewiring of links. This paper also reports on the impact that these processes have in the topological properties of the networks generated with the proposed model. Numerical simulation shows that, when the frequency of rewiring increases in the proposed model, the γ exponent of the in-degree distribution approaches a value of 1.1. When the frequency of adding new links increases, the γ exponent approaches 1. That is the proposed model is able to generate all exponent values documented in real-world networks which range 1.05 < γ < 8.94. [ABSTRACT FROM AUTHOR]

Multiplex networks have proven to be valuable tools for modeling and analyzing real complex system. Extensive work has been done on the traffic dynamics on multiplex networks, but there remains a lack of sufficient attention towards studying routing strategies for the purpose of suppressing epidemic spreading. In this paper, the impact of global awareness routing (GAR), improved global awareness routing (IGAR), and improved active routing (IAR) strategies on traffic-driven epidemic spreading are investigated. Our findings indicate that in the case of infinite node-delivery capacity and no traffic congestion in the network, adjusting routing parameters can effectively suppress epidemic spreading. In this context, these three strategies show better abilities on the multiplex network built by WS or ER model to minimize the density of infected nodes, thus contributing to the overall inhibition of the epidemic spread. However, in the multiplex network constructed by BA model, GAR strategy has a promoting effect on epidemic spreading compared with the shortest routing strategy. In addition, by controlling traffic flow, limiting node delivery capabilities can contain outbreaks. Our results suggest that adopting appropriate routing strategies in multiplex networks can play a proactive role in controlling epidemic spreading. This is crucial for formulating effective prevention and control measures and improving public health security. [ABSTRACT FROM AUTHOR]

Finding vital vertices is an important issue in complex network analysis, which has wide applications in disease control, information diffusion, etc. This topic has attracted increasing attention from various disciplines. In this paper, we propose a new algorithm called Vertex–Edge algorithm to find vital vertices. This algorithm takes both the incident edges and also its neighbors into consideration when evaluating a vertex's importance, and the importance of vertices and edges construct a mutually updated iterative framework. We also give convergence conditions for the iterative framework. Besides, we verify the stability, effectiveness, accuracy, and superiority of this new Vertex–Edge algorithm by applying it on lots of networks (unweighted or weighted) and comparing the results with other 10 more existing methods. This new method is expected to have promising applications in the future. [ABSTRACT FROM AUTHOR]

Many realistic networked systems may face sustained attack over a sequence of time. In this paper, we propose a cascading failure model in coupled map lattices (CMLs) with sustained attack, where a number of crucial nodes will be attacked one by one at each time step. The effects of four attacking strategies: high-degree strategy (HDS), high-clustering coefficient strategy, high-closeness strategy and high-betweenness strategy are compared. This shows that the performance of HDS is better than that of other attacking strategies when the value of the outside attack is small. The effectiveness of HDS on Watts–Strogatz (WS) small-world networks and two real-world networks is extensively investigated. The results indicate that increasing the value of the rewiring probability of WS networks can make the network more robust to resist sustained attack. The sparser the network structure is, the faster the diffusion velocity of cascading failures is. A smaller coupling strength in CMLs can restrain the diffusion velocity of cascades. We also extend our CML-based model with sustained attack from one node strategy (ONS) to two nodes strategy (TNS) and compare the effect of ONS and TNS with different values of the outside attack. It is found that ONS outperforms TNS for small values of the outside attack, but TNS would be a better choice when the outside attack and the time step are all large. Our work will provide new insights into the problem of protecting complex networks against cascading failures with respect to malicious attack. [ABSTRACT FROM AUTHOR]

The volatility is one of the essential characteristics of financial time series, which is vital for the knowledge acquisition from financial data. However, since the high noise and nonsteady features, the volatility identification of financial time series is still a challenging problem. In this paper, from a perspective of granule complex network, a novel approach is proposed to study this problem. First, numeric time series is structured into fuzzy information granules (FIGs), where the segments of time series in each granule would own similar volatility features. Second, by using the transfer relations among granules, granule complex network is to be constructed, which intuitively describes the transfer processes among the different volatility patterns. Third, a novel community detection algorithm is applied to divide the granule complex networks, where granules with frequent mutual transfers would belong to the same granule community. Finally, Markov chain model is carried out to analyze the higher level of transfer processes among different granule communities, which would further describe the larger-scale transitions of volatility in overall financial time series. An empirical study of the proposed system is applied in the Shanghai stock index market, where volatility patterns of financial data can be effectively acquired and the corresponding transfer processes can be analyzed by means of the granule communities. [ABSTRACT FROM AUTHOR]

It is significant to assign reputation scores to users and identify spammers in the bipartite rating networks. In this paper, we propose an Iterative Group-based and Difference Ranking (IGDR) method, which is based on the original Iterative Group-based Ranking (IGR) method. The IGR method considers users grouping behaviors, but it ignores the characteristics of the individual ratings. It is discovered that individual rating characteristics could also contribute to the redistribution of reputation scores of users. The user with a smaller rating deviation will be given a higher reputation score. The proposed method outperforms IGR method ranging from 8% to 163% tested on three real datasets. It also can be applied to deal with big data in a short time. [ABSTRACT FROM AUTHOR]

Computer networks are prone to targeted attacks and random failures. Robustness is a measure of an ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. The study of network robustness is a critical tool in the characterization and understanding of complex interconnected systems. There are several proposed graph metrics that predicates network resilience against such attacks. Isolated rupture degree is a novel graph-theoretic concept defined as a measure of network vulnerability. Isolated rupture degree is argued as an appropriate measure for modelling the robustness of network topologies in the face of possible node destruction. In this paper, the relationships between isolated rupture degree and some other graph parameters such as connectivity, covering number, minimum vertex degree are established. The isolated rupture degrees of 2 K 2 -free graphs, middle graphs, corona graphs of a middle graph and a complete graph K 2 on two vertices are evaluated, then compared and the more stable graph types are reported. A sharp upper bound for the isolated rupture degree of middle graphs is established. [ABSTRACT FROM AUTHOR]

Some of the nodes of complex social networks may support for a given proposal, while the rest of the nodes may be against the given proposal. Even though all the nodes support for or are against the given proposal, the decision certitudes of individual nodes may be different. In this case, the steady state values of the decision certitudes of the majority of the nodes are either higher than or lower than a threshold value. Deriving the near consensus property is a key to the analysis of the behaviors of complex social networks. So far, no result on the behaviors of the complex social networks satisfying the near consensus property has been reported. Hence, it is useful to extend the definition of the exact consensus property to that of a near consensus property and investigate the behaviors of the complex social networks satisfying the near consensus property. This paper extends the definition of exact consensus complex social networks to that of near consensus complex social networks. For complex linear social networks, this paper investigates the relationships among the vectors representing the steady state values of the decision certitudes of the nodes, the influence weight matrix and the set of vectors representing the initial state values of the decision certitudes of the nodes under a given near consensus specification. The above analysis is based on the Eigen theory. For complex nonlinear social networks with certain types of nonlinearities, the relationship between the influence weight matrix and the vectors representing the steady state values of the decision certitudes of the nodes is studied. When a complex nonlinear social network does not achieve the exact consensus property, the optimal near consensus condition that the complex social network can achieve is derived. This problem is formulated as an optimization problem. The total number of nodes that the decision certitudes of the nodes are either higher than or lower than a threshold value is maximized subject to the corresponding near consensus specification. The optimization problem is a nonsmooth optimization problem. The nonsmooth constraints are first approximated by smooth constraints. Then, the approximated optimization problem is solved via a conventional smooth optimization approach. Computer numerical simulation results as well as the comparisons of the behaviors of complex nonlinear social networks to those of the complex linear social networks are presented. The obtained results demonstrate that some complex social networks can satisfy the near consensus property but not the exact consensus property. Also, the conditions for the near consensus property are dependent on the types of nonlinearities, the influence weight matrix and the vectors representing the initial state values of the decision certitudes of the nodes. [ABSTRACT FROM AUTHOR]

Based on the analysis of evolutionary characteristics of public opinion in social networking services (SNS), in the paper we propose a dynamic evolution model, in which opinions are coupled with topology. This model shows the clustering phenomenon of opinions in dynamic network evolution. The simulation results show that the model can fit the data from a social network site. The dynamic evolution of networks accelerates the opinion, separation and aggregation. The scale and the number of clusters are influenced by confidence limit and rewiring probability. Dynamic changes of the topology reduce the number of isolated nodes, while the increased confidence limit allows nodes to communicate more sufficiently. The two effects make the distribution of opinion more neutral. The dynamic evolution of networks generates central clusters with high connectivity and high betweenness, which make it difficult to control public opinions in SNS. [ABSTRACT FROM AUTHOR]

In this paper, we present a growing complex network model, namely, the generalized corona network (GCN) which is built on a base network and a sequence of networks by using corona product of graphs. This construction generalizes several existing complex network models. We study the structural properties of the special classes of generalized corona networks and show that these networks have small diameter, the cumulative betweenness distribution follows a power-law distribution, the degree distribution decay exponentially, small average path length with the network order, high clustering coefficient and small-world behavior. Further, we obtain the spectra of the adjacency matrix and the signless Laplacian matrix of GCN when the constituting networks are regular. Also, we obtain the Laplacian spectra for all generalized corona networks. In addition, explicitly give eigenvector corresponding to the adjacency and Laplacian eigenvalues. Finally, we derive the spectral radius and the algebraic connectivity of GCN. [ABSTRACT FROM AUTHOR]

Rumor is an unauthenticated statement that gives significant changes in the social life of the people, financial markets (stocks and trades), etc. By incorporating the dissemination of rumor through groups in social, mobile networks and by considering the people's cognitive factor (hesitate and forget), a new model on the rumor spreading process is presented in this paper. The spreading dynamics of rumor in homogeneous and heterogeneous networks is analyzed by using mean-field theory. The reproduction number is obtained by using the next-generation matrix. The global stability of the rumor-free equilibrium for the homogeneous and heterogeneous model is proved elaborately. An optimal control problem is developed to minimize the hesitators and infected persons and the existence of optimality is shown using Pontryagin's Minimum Principle. The hesitating and forgetting mechanism has a great impact on the model and is similar to the real-life. Further, the control parameters work superior in controlling the spreading of rumors. Finally, the numerical results are verified by the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm to select the relevant nodes — those that maintain the cohesion of the network — of the complex network is presented. The experiments on most of the real complex networks show that the proposed approach outperforms centrality measures as node degree, PageRank algorithm and betweenness centrality. The rationale of the algorithm for extracting relevant nodes is to discover the self-similarity of the network. As seen in the algorithm, throughout the extraction sequence of relevant nodes, differences are advised with node degree, PageRank algorithm and betweenness centrality. Finally, empirical evidence is considered to show that complex network robustness is a nonlinear function of the small-worldness measure. [ABSTRACT FROM AUTHOR]

The real-world network is heterogeneous, and it is an important and challenging task to effectively identify the influential nodes in complex networks. Identification of influential nodes is widely used in social, biological, transportation, information and other networks with complex structures to help us solve a variety of complex problems. In recent years, the identification of influence nodes has received a lot of attention, and scholars have proposed various methods based on different practical problems. This paper proposes a new method to identify influential nodes, namely Attraction based on Node and Community (ANC). By considering the attraction of nodes to nodes and nodes to community structure, this method quantifies the attraction of a node, and the attraction of a node is used to represent its influence. To illustrate the effectiveness of ANC, we did extensive experiments on six real-world networks and the results show that the ANC algorithm is superior to the representative algorithms in terms of the accuracy and has lower time complexity as well. [ABSTRACT FROM AUTHOR]

In this paper, we analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modeled as a heterogeneous network. We establish some stability results related to the behavior of the time-weighted average Basic Reproduction Number (BRN). Later, a Susceptible–Exposed–Infectious–Recovered (SEIR) model which describes the measles disease is proposed and we show that its dynamics is determined by a threshold value, below which the disease dies out. Moreover, compared with models without the Exposed compartment, we can find weaker stability results. A control strategy with an imperfect vaccine is applied, to determine how it could effect the size of the peak. Due to the periodic behavior of the switching rule, we compare the results with the BRN of the model. Some simulations are given, using a scale-free network, to illustrate the threshold conditions found. [ABSTRACT FROM AUTHOR]

The congestion control of traffic is one of the most important studies in complex networks. In the previous congestion algorithms, all the network traffic is assumed to have the same priority, and the privilege of traffic is ignored. In this paper, a privilege and common traffic congestion control routing strategy (PCR) based on the different priority of traffic is proposed, which can be devised to cope with the different traffic congestion situations. We introduce the concept of privilege traffic in traffic dynamics for the first time and construct a new traffic model which taking into account requirements with different priorities. Besides, a new factor is introduced by the theoretical derivation to characterize the interaction between different traffic routing selection, furthermore, is related to the network throughput. Since the joint optimization among different kinds of traffic is accomplished by PCR, the maximum value of can be significantly reduced and the network performance can be improved observably. The simulation results indicate that the network throughput with PCR has a better performance than the other strategies. Moreover, the network capacity is improved by 25% at least. Additionally, the network throughput is also influenced by privilege traffic number and traffic priority. [ABSTRACT FROM AUTHOR]

How can we uncover overlapping communities from complex networks to understand the inherent structures and functions? Chen et al. firstly proposed a community game (Game) to study this problem, and the overlapping communities have been discovered when the game is convergent. It is based on the assumption that each vertex of the underlying network is a rational game player to maximize its utility. In this paper, we investigate how similar vertices affect the formation of community game. The Adamic-Adar Index (AA Index) has been employed to define the new utility function. This novel method has been evaluated on both synthetic and real-world networks. Experimental study shows that it has significant improvement of accuracy (from 4.8% to 37.6%) compared with the Game on 10 real networks. It is more efficient on Facebook networks (FN) and Amazon co-purchasing networks than on other networks. This result implicates that 'friend circles of friends' of Facebook are valuable to understand the overlapping community division. [ABSTRACT FROM AUTHOR]

This paper concerns the outer synchronization problem between two complex delayed networks via the method of aperiodically intermittent pinning control. Apart from previous works, internal delay and coupling delay are both involved in this model, and the designed intermittent controllers can be aperiodic. The main work in this paper can be summarized as follows: First, two cases of aperiodically intermittent control with constant gain and adaptive gain are implemented, respectively. The intermittent control and pinning control are combined to reduce consumptions further. Then, based on the Lyapunov stability theory, synchronization protocols are given by strict derivation. Especially, the designed controllers are indeed simple and valid in application of theory to practice. Finally, numerical examples put the proposed control methods to the test. [ABSTRACT FROM AUTHOR]

Community detection and analysis have attracted wide public concerns over the recent years. Meanwhile, many related algorithms in complex networks have been proposed. However, most of them concentrate on undirected and unweighted networks. Concerning the significant theoretical value and potential application foreground for directed-weighted networks, in this paper, a novel hierarchical communities detection algorithm (termed as DCBAI) has been proposed on the basis of asymmetric intimacy between nodes. Community structures are effectively detected by node clustering algorithm in directed-weighted network, and a set of optimal communities are generated. In addition, a new and asymmetric parameter is adopted to measure the intimate relationship between nodes. We make some simulation using the proposed algorithm in real-world networks and artificial networks, and the result obtained proves that the parameter can describe the direct and indirect relationships between two nodes. Eventually, comparison with similar algorithms shows that our proposed algorithm has better performance. [ABSTRACT FROM AUTHOR]