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Conformity is a common phenomenon among people in social networks. In this paper, we focus on customers’ conformity behaviors in a symmetry market where customers are located in a social network. We establish a conformity model and analyze it in ring network, random network, small-world network, and scale-free network. Our simulations shown that topology structure, network size, and initial market share have significant effects on the evolution of customers’ conformity behaviors. The market will likely converge to a monopoly state in small-world networks but will form a duopoly market in scale networks. As the size of the network increases, there is a greater possibility of forming a dominant group of preferences in small-world network, and the market will converge to the monopoly of the product which has the initial selector in the market. Also, network density will become gradually significant in small-world networks.

This paper aims to study the combined impact of countermeasure and network topology on virus diffusion and optimal dynamic countermeasure. A novel heterogenous propagation model and its optimal control problem are proposed and analyzed. Qualitative analysis shows that the unique equilibrium of the proposed model is globally attractive and the optimal control problem has an optimal control. Some simulation experiments are also performed. Specifically, it is found that our obtained results are contrary to some previous results and countermeasure dissemination to higher-degree nodes is more effective than that to lower-degree nodes. The related explanations are also made. This indicates that countermeasures and network topology play an important role in suppressing viral spread. [ABSTRACT FROM AUTHOR]

The aim of the paper is to show how the transition from the emergence of a technology to its development phase impacts the evolution of the structure of the collaboration network. In order to identify these first phases of the life cycle of the technology a method is developed based on the International Patent Classification. Using this method, we identify when a technology transitions from an emerging technology to a stage in which applications of the technology are found. We then compare the moment at which this transition occurs to the evolution of the collaboration network for the same technology and show that there is a significant change in the structure of the network when this transition occurs. [ABSTRACT FROM AUTHOR]

Quarantine strategies are frequently used to control or reduce the transmission risks of epidemic diseases such as SARS, tuberculosis and cholera. In this paper, we formulate a susceptible-exposed-infected-quarantined-recovered model on a scale-free network incorporating the births and deaths of individuals. Considering that the infectivity is related to the degrees of infectious nodes, we introduce quarantined rate as a function of degree into the model, and quantify the basic reproduction number, which is shown to be dependent on some parameters, such as quarantined rate, infectivity and network structures. A theoretical result further indicates the heterogeneity of networks and higher infectivity will raise the disease transmission risk while quarantine measure will contribute to the prevention of epidemic spreading. Meanwhile, the contact assumption between susceptibles and infectives may impact the disease transmission. Furthermore, we prove that the basic reproduction number serves as a threshold value for the global stability of the disease-free and endemic equilibria and the uniform persistence of the disease on the network by constructing appropriate Lyapunov functions. Finally, some numerical simulations are illustrated to perform and complement our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the effect of neighbors on the infection of packets by computer virus in the SI and SIR models using the minimal traffic routing protocol. We have applied this model to the Barabasi-Albert network to determine how intrasite and extrasite infection rates affect virus propagation through the traffic flow of information packets in both the free-flow and the congested phases. The numerical results show that when we change the intrasite infection rate while keeping constant the extrasite infection rate , we get normal behavior in the congested phase: in the network, the proportion of infected packets increases to reach a peak and then decreases resulting in a simultaneous increase of the recovered packets. In contrast, when the intrasite infection rate is kept fixed, an increase of the extrasite infection rate results in two regimes: The first one is characterized by an increase of the proportion of infected packets until reaching some peak value and then decreases smoothly. The second regime is characterized by an increase of infected packets to some stationary value. [ABSTRACT FROM AUTHOR]

In this paper, we study the effect of channel noise on the temporal coherence of scale-free Hodgkin-Huxley neuronal networks with time delay. It is found that the temporal coherence of the neuronal networks changes as channel noise intensity is varied in different ways depending on the range of channel noise intensity. The temporal coherence monotonically decreases with the increase of channel noise intensity for too small or too big channel noise intensity. However, for intermediate channel noise intensity it intermittently and rapidly becomes high and low as channel noise intensity is varied, exhibiting temporal coherence transitions. Moreover, this phenomenon is dependent on coupling strength and network average degree and becomes strongest when they are optimal. This result shows that channel noise has a regulation effect on the temporal coherence of the delayed neuronal networks by inducing temporal coherence transitions. This provides a new insight into channel noise for the information processing and transmission in neural systems. [ABSTRACT FROM AUTHOR]

In traffic networks, it is quite important to assign proper packet delivering capacities to the routers with minimum cost. In this respect, many allocation models based on static and dynamic properties have been proposed. In this paper, we are interested in the impact of limiting the packet delivering capacities already allocated to the routers; each node is assigned a packet delivering capacity limited by the maximal capacity of the routers. To study the limitation effect, we use two basic delivering capacity allocation models; static delivering capacity allocation (SDCA) and dynamic delivering capacity allocation (DDCA). In the SDCA, the capacity allocated is proportional to the node degree, and for DDCA, it is proportional to its queue length. We have studied and compared the limitation of both allocation models under the shortest path (SP) routing strategy as well as the efficient path (EP) routing protocol. In the SP case, we noted a similarity in the results; the network capacity increases with increasing . For the EP scheme, the network capacity stops increasing for relatively small packet delivering capability limit for both allocation strategies. However, it reaches high values under the limited DDCA before the saturation. We also find that in the DDCA case, the network capacity remains constant when the traffic information available to each router was updated after long period times . [ABSTRACT FROM AUTHOR]

Micro-RNA (miRNA or miR) regulates at least 60% of the genes in the human genome through their target sites at mRNA 3'-untranslated regions (UTR), and defects in miRNA expression regulation and target sites are frequently observed in cancers. We report here a systematic analysis of the distribution of miRNA target sites. Using the evolutionarily conserved miRNA binding sites in the TargetScan gfdatabase (release 7.1), we constructed a miRNA co-regulation network by connecting genes sharing common miRNA target sites. The network possesses characteristics of the ubiquitous small-world network. Non-hub genes in the network--those sharing miRNA target sites with small numbers of genes--tend to form small cliques with their neighboring genes, while hub genes exhibit high levels of promiscuousness in their neighboring genes. Additionally, miRNA target site distribution is extremely uneven. Among the miRNAs, the distribution concentrates on a small number of miRNAs, in that their target sites occur in an extraordinarily large number of genes, that is, they have large numbers of target genes. The distribution across the genes follows a similar pattern; the mRNAs of a small proportion of the genes contain extraordinarily large numbers of miRNA binding sites. Quantitatively, the patterns fit into the P(K) ∝ K∝ relationship (P(K): the number of miRNAs with K target genes or genes with K miRNA sites; ∝: a positive constant), the mathematical description of connection distribution among the nodes and a defining characteristic of the so-called scale-free networks--a subset of small-world networks. Notably, well-known tumor-suppressive miRNAs (Let-7, miR-15/16, 26, 29, 31, 34, 145, 200, 203-205, 223, and 375) collectively have more than expected target genes, and well-known cancer genes contain more than expected miRNA binding sites. In summary, miRNA target site distribution exhibits characteristics of the small-world network. The potential to use this pattern to better understand miRNA function and their oncological roles is discussed. [ABSTRACT FROM AUTHOR]

In order to efficiently fortify the robustness of a scale-free network against cascading failure, a model of this phenomenon is proposed based on defining the load of a node with respect to both degree and betweenness centrality. Simultaneously, when the load is redistributed, an allocation proportion is ascertained according to both the loads and the energies of the nodes. After that, we obtain the relationship between the model parameters and the robustness of the network against the cascading failure with theoretical analysis, which also helps us determine the influence of the average network degree on cascading failure. Finally, the results of theoretical analysis are verified with simulation experiments. [ABSTRACT FROM AUTHOR]

We discuss a novel epidemic SIRS model with time delay on a scale-free network in this paper. We give an equation of the basic reproductive number $R_{0}$ for the model and prove that the disease-free equilibrium is globally attractive and that the disease dies out when $R_{0}<1$ , while the disease is uniformly persistent when $R_{0}>1$ . In addition, by using a suitable Lyapunov function, we establish a set of sufficient conditions on the global attractiveness of the endemic equilibrium of the system. [ABSTRACT FROM AUTHOR]

The scale-free topology of power communication network leads to more data flow in less hub nodes, which can cause local congestion. Considering the differences of the nodes' delivery capacity and cache capacity, an integrated routing based on the communication service classification is proposed to reduce network congestion. In the power communication network, packets can be classified as key operational services (I-level) and affairs management services (II-level). The shortest routing, which selects the path of the least hops, is adopted to transmit I-level packets. The load-balanced global dynamic routing, which uses the node's queue length and delivery capacity to establish the cost function and chooses the path with minimal cost, is adopted to transmit II-level packets. The simulation results show that the integrated routing has a larger critical packet generation rate and can effectively reduce congestion. [ABSTRACT FROM AUTHOR]

Network theoretic approach has been used to model and study the flow of ecological information, growth and connectivity on landscape level of anemochory (wind dispersal) of Himalayan moist temperate forest species in the Western Himalaya region. A network is formally defined and derived for seed dispersion model of target floral species where vertices represent habitat patches which are connected by an edge if the distance between the patches is less than a threshold distance. We define centrality of a network and computationally identify the habitat patches that are central to the process of seed dispersion to occur across the network. These central patches are located on map and geographical regions critically important for the flow of ecological information across the network are identified as Gharwal region and eastern Himachal Pradesh of Indian Himalaya. We find that the network of habitat patches is a scale-free network and at the same time it also displays small-world property characterized by high clustering and low average shortest path length. As a result, ecological information propagates rapidly and evenly on a local scale. Hubs in the network are identified as important centres for dissemination of ecological information (seeds) and need to be conserved against a potential attack by malicious agents and also ecological shocks. The network showcase a well-formed community structure. As a consequence of these structural properties of the network, anemochory floral species studied in this work are likely to thrive across the ecological network of forest patches in the Western Himalaya region over time. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of models for generating spatial versions of three classic networks: Erdös-Rényi (ER), Watts-Strogatz (WS), and Barabási-Albert (BA). We assume that nodes have geographical coordinates, are uniformly distributed over an m × m Cartesian space, and long-distance connections are penalized. Our computational results show higher clustering coefficient, assortativity, and transitivity in all three spatial networks, and imperfect power law degree distribution in the BA network. Furthermore, we analyze a special case with geographically clustered coordinates, resembling real human communities, in which points are clustered over k centers. Comparison between the uniformly and geographically clustered versions of the proposed spatial networks show an increase in values of the clustering coefficient, assortativity, and transitivity, and a lognormal degree distribution for spatially clustered ER, taller degree distribution and higher average path length for spatially clustered WS, and higher clustering coefficient and transitivity for the spatially clustered BA networks. [ABSTRACT FROM AUTHOR]

This paper is intended to investigate the effect of network topology on the spread of computer viruses in the presence of removable storage media. For that purpose, a novel network-based computer virus spreading model is proposed. Both theoretically and experimentally, it is shown that, under proper conditions, viruses on a scale-free network would tend to extinction. Experimental results show that either smaller maximum node degree or larger power-law exponent is conducive to the containment of virus spreading. To our knowledge, this is the first time the effect of network topology on virus spreading is investigated in this context. [ABSTRACT FROM AUTHOR]

The robustness is an important functionality of networks because it manifests the ability of networks to resist failures or attacks. Many robustness measures have been proposed from different aspects, which provide us various ways to evaluate the network robustness. However, whether these measures can properly evaluate the network robustness and which aspects of network robustness these measures can evaluate are still open questions. Therefore, in this paper, a thorough introduction over attacks and robustness measures is first given, and then nine widely used robustness measures are comparatively studied. To validate whether a robustness measure can evaluate the network robustness properly, the sensitivity of robustness measures is first studied on both initial and optimized networks. Then, the performance of robustness measures in guiding the optimization process is studied, where both the optimization process and the obtained optimized networks are studied. The experimental results show that, first, the robustness measures are more sensitive to the changes in initial networks than to those in optimized networks; second, an optimized network may not be useful in practical situations because some useful functionalities, such as the shortest path length and communication efficiency, are sacrificed too much to improve the robustness; third, the robustness of networks in terms of closely correlated robustness measures can often be improved together. These results indicate that it is not wise to just apply the optimized networks obtained by optimizing over one certain robustness measure into practical situations. Practical requirements should be considered, and optimizing over two or more Received February 22, 2016; accepted September 29, 2016 E-mail: neouma@163.com suitable robustnessmeasures simultaneously is also a promising way. [ABSTRACT FROM AUTHOR]

In recent years, China's urbanization has developed very quickly. Many scholars have conducted China's urbanization research (CUR) and have published a large number of articles. With CUR as a case, we construct the dynamic co-word network to analyze the characteristics of development about the knowledge system (KS). We draw several conclusions from this research. (1) The development of CUR possesses small-world characteristics and scale-free effects. The co-word network of CUR increases significantly to a large-scale network. (2) Betweenness centrality and eigenvector centrality of the dynamic co-word networks positively correlate with node degree. The popular nodes connecting with a large number of topics are also the nodes that occur in the critical paths. The popular keywords in CUR also bridge distant clusters of the related topics. (3) The clustering coefficients indicate that a number of topics with low degrees tend to relate to the adjacent topics more directly to form 'conglobation' clusters. The network is a hierarchical clustered structure. The hub keywords play a crucial role in bridging distinct clusters of highly associated keywords and make them form an integrated network. (4) Since 2003, the CUR has begun to develop systematically. From 1998 to 2015, the hotspots in CUR varied diversely, which are highly correlated with social issues and public concerns. (5) We proposed several practical implications on the development of CUR from the dynamic co-word network measures. Beyond the case of CUR's KS, we hope the versatility of methods in this research also provides enlightenment for other KS studies. [ABSTRACT FROM AUTHOR]

The minimum dominating set (MDS) problem is a fundamental subject of theoretical computer science, and has found vast applications in different areas, including sensor networks, protein interaction networks, and structural controllability. However, the determination of the size of a MDS and the number of all MDSs in a general network is NP-hard, and it thus makes sense to seek particular graphs for which the MDS problem can be solved analytically. In this paper, we study the MDS problem in the pseudofractal scale-free web and the Sierpiński graph, which have the same number of vertices and edges. For both networks, we determine explicitly the domination number, as well as the number of distinct MDSs. We show that the pseudofractal scale-free web has a unique MDS, and its domination number is only half of that for the Sierpiński graph, which has many MDSs. We argue that the scale-free topology is responsible for the difference of the size and number of MDSs between the two studied graphs, which in turn indicates that power-law degree distribution plays an important role in the MDS problem and its applications in scale-free networks. [ABSTRACT FROM AUTHOR]

The size and number of maximum matchings in a network have found a large variety of applications in many fields. As a ubiquitous property of diverse real systems, power-law degree distribution was shown to have a profound influence on size of maximum matchings in scale-free networks, where the size of maximum matchings is small and a perfect matching often does not exist. In this paper, we study analytically the maximum matchings in two scale-free networks with identical degree sequence, and show that the first network has no perfect matchings, while the second one has many. For the first network, we determine explicitly the size of maximum matchings, and provide an exact recursive solution for the number of maximum matchings. For the second one, we design an orientation and prove that it is Pfaffian, based on which we derive a closed-form expression for the number of perfect matchings. Moreover, we demonstrate that the entropy for perfect matchings is equal to that corresponding to the extended Sierpiński graph with the same average degree as both studied scale-free networks. Our results indicate that power-law degree distribution alone is not sufficient to characterize the size and number of maximum matchings in scale-free networks. [ABSTRACT FROM AUTHOR]

Existing routing strategies such as the global dynamic routing [X. Ling, M. B. Hu, R. Jiang and Q. S. Wu, Phys. Rev. E 81, 016113 (2010)] can achieve very high traffic capacity at the cost of extremely long packet traveling delay. In many real complex networks, especially for real-time applications such as the instant communication software, extremely long packet traveling time is unacceptable. In this work, we propose to assign a finite Time-to-Live (TTL) parameter for each packet. To guarantee every packet to arrive at its destination within its TTL, we assume that a packet is retransmitted by its source once its TTL expires. We employ source routing mechanisms in the traffic model to avoid the routing-flaps induced by the global dynamic routing. We compose extensive simulations to verify our proposed mechanisms. With small TTL, the effects of packet retransmission on network traffic capacity are obvious, and the phase transition from flow free state to congested state occurs. For the purpose of reducing the computation frequency of the routing table, we employ a computing cycle within which the routing table is recomputed once. The simulation results show that the traffic capacity decreases with increasing . Our work provides a good insight into the understanding of effects of packet retransmission with finite packet lifetime on traffic capacity in scale-free networks. [ABSTRACT FROM AUTHOR]

We modify sliding mode control technique from the synchronization of a single dynamic system to the synchronization of complex network. Projective synchronization of uncertain scale-free network is investigated based on modified sliding mode control technique. Further, the sliding surfaces, the identification laws of uncertain parameters and the control inputs are designed, and the condition of realizing projective synchronization of uncertain scale-free network is obtained. Finally, the Logistic systems with chaotic behavior are taken as nodes to constitute the scale-free network and the synchronization target. The simulation results show that the synchronization mechanism is effective. [ABSTRACT FROM AUTHOR]

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach. [ABSTRACT FROM AUTHOR]

A novel epidemic spreading model with distributed delay on complex heterogeneous network is presented. The formula of the basic reproductive number is presented to the model. It is proven that the disease dies out if the basic reproductive number is less than unity, while if the basic reproductive number is more than unity, the disease is uniformly persistent. The results enrich the previous results. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid queuing strategy (HQS) is proposed in traffic dynamics model on scale-free networks, where the delivery priority of packets in the queue is related to their distance to destination and the queue length of next jump. We compare the performance of the proposed HQS with that of the traditional first-in-first-out (FIFO) queuing strategy and the shortest-remaining-path-first (SRPF) queuing strategy proposed by Du et al. It is observed that the network traffic efficiency utilizing HQS with suitable value of parameter h can be further improved in the congestion state. Our work provides new insights for the understanding of the networked-traffic systems. [ABSTRACT FROM AUTHOR]

In many real complex artificial networks, a navigation route between a pair of source and destination is often desired to pass through at least a specified node called check-in node for doing check-in like services, such as gas fuel supplement for vehicles, GPS recording for express packages and so on. However, currently, there is a lack of routing study for complex networks equipped with check-in nodes. In this work, we first propose a general routing mechanism called check-in based routing (CBR) which can guarantee that every efficient path must include at least one check-in node. With a finite fraction of check-in nodes in the network, it can be observed that the higher the degrees of check-in nodes, the higher the network traffic capacity will be by employing the shortest path routing into CBR (namely CBR-SP). It is a great challenge on routing optimization for a network with a fraction of check-in nodes of the lowest degrees. We then employ the degree-based efficient routing (ER) into the CBR to efficiently redistribute heavy traffic from hub nodes to non-hub nodes. Under the CBR-ER, the traffic capacity can be significantly enhanced at the cost of a little network diameter and average path lengthening. The extensive simulations in scale-free networks can well confirm the effectiveness of CBR-ER. [ABSTRACT FROM AUTHOR]

Considering some phenomena observed in the real world, we introduce a rational selecting mechanism based on radical evaluation into evolutionary snowdrift game. In the proposed model, players are endowed with a sense of rationality, which helps evaluate behaviors radically and select neighbors with different attractiveness. Those neighbors who made a preferable strategy and got more payoffs compared with the anti-strategy will have more attractiveness as references. It is found that the selection based on radical evaluation significantly enhances the level of cooperation on regular networks with large neighborhood size K and scale-free networks over a wide range of cost-to-benefit ratio r . Discussions for the transition of spatial patterns and strategy degree distribution at some critical values of the payoff parameter show the effects of the proposed selecting mechanism. The findings may be helpful in understanding cooperative behavior in natural and social systems consisting of rational selection with radical evaluation. [ABSTRACT FROM AUTHOR]

In order to study the influence of the preferential degree and the heterogeneity of underlying networks on the spread of preferential e-commerce information, we propose a novel susceptible–infected–beneficial model based on scale-free networks. The spreading dynamics of the preferential information are analyzed in detail using the mean-field theory. We determine the basic reproductive number and equilibria. The theoretical analysis indicates that the basic reproductive number depends mainly on the preferential degree and the topology of the underlying networks. We prove the global stability of the information-elimination equilibrium. The permanence of preferential information and the global attractivity of the information-prevailing equilibrium are also studied in detail. Some numerical simulations are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

The Ising model on a restricted scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form P (k) ∼ k − α , and is called restricted, because independently of the network size, we always have fixed the maximum k m and a minimum k 0 degree on distribution, being that for it, we only limit the minimum network size of the system. We calculated the thermodynamic quantities of the system, such as, the magnetization per spin m N , the magnetic susceptibility χ N , and the reduced fourth-order Binder cumulant U N , as a function of temperature T for several values of lattice size N and exponent 1 ≤ α ≤ 5. For the values of α , we have obtained the finite critical points due to we also have finite second and fourth moments in the degree distribution, and the phase diagram was constructed for the equilibrium states of the model in the plane T versus k 0 , k m , and α , showing a transition between the ferromagnetic F to paramagnetic P phases. Using the finite-size scaling (FSS) theory, we also have obtained the critical exponents for the system, and a mean-field critical behavior is observed. • Always convergent moments on a scale-free network degree distribution. • Ising model on a scale-free network with always finite critical temperature. • A finite critical temperature for any exponent on a power-law degree distribution. • Mean-field behavior for any exponent on a power-law degree distribution. • Degree–degree correlations affect the critical behavior of the system. [ABSTRACT FROM AUTHOR]

Background: Emerging infectious diseases are a class of diseases that are spreading rapidly and are highly contagious. It seriously affects social stability and poses a significant threat to human health, requiring urgent measures to deal with them. Its outbreak will very easily lead to the large-scale spread of the virus, causing social problems such as work stoppages and traffic control, thereby causing social panic and psychological unrest, affecting human activities and social stability, and even endangering lives. It is essential to prevent and control the spread of infectious diseases effectively., Purpose: We aim to propose an effective method to classify the risk level of a new epidemic region by using graph theory and risk classification methods to provide a theoretical reference for the comprehensive evaluation and determination of epidemic prevention and control, as well as risk level classification., Methods: Using the graph theory method, we first define the network structure of social groups and construct the risk transmission network of the new epidemic region. Then, combined with the risk classification method, the classification of high, medium, and low risk levels of the new epidemic region is discussed from two cases with common and looped graph nodes, respectively. Finally, the reasonableness of the classification method is verified by simulation data., Results: The directed weighted scale-free network can better describe the transmission law of an epidemic. Moreover, the proposed method of classifying the risk level of a region by using the correlation function between two regions and the risk value of the regional nodes can effectively evaluate the risk level of different regions in the new epidemic region. The experiments show that the number of medium and high risk nodes shows no increasing trend. The number of high-risk regions is relatively small compared to medium-risk regions, and the number of low-risk regions is the largest., Conclusions: It is necessary to distinguish scientifically between the risk level of the epidemic area and the neighboring regions so that the constructed social network model of the epidemic region's spread risk can better describe the spread of the epidemic risk in the social network relations., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Liu, Wang and Zhang.)