BA Scale-free Network Research Articles

A Weibo local network growth model constructed from the perspective of following-followed

Abstract In order to explore the evolution process of the Weibo local network, this study first defines four factors influencing the evolution of the Weibo network. On this basis, the BA scale-free network model was enhanced by incorporating these four factors and accounting for directionality, resulting in a Weibo local network evolution model based on user attributes and behavioral similarity. The model's validity was validated by comparing simulation results with real data. The findings indicate that the Weibo local network exhibits both small-world characteristics and distinctive features. The results show that the Weibo local network exhibits both small-world characteristics and distinctive properties. The in-degree distribution follows a mixed pattern of exponential and power-law distributions, the degree-degree shows isomatching, and both the in-degree centrality and eigenvector centrality values are relatively low. This research contributes to our understanding of user behaviour in the Weibo network, and provides a structural basis for exploring the impact of Weibo network structure on information dissemination.

Diffusion model of multi-agent collaborative behavior in public crisis governance network based on complex network evolutionary game

In order to explore the phenomenon of diffusion of group decision making formed by the emergence of decision-making behaviors of governance agents in public crisis governance systems, this research uses a complex network evolutionary game approach, considers BA scale-free networks as network vectors of public crisis governance systems, and develops a diffusion model of collaborative governance decision making behaviors. Simulation experiments are also conducted to show the macro-level impact of micro-subjects’ decision-making behavior on group “Emergence-Diffusion”. The results of this study show that the cost of collaborative governance has the most significant effect on the depth and breadth of the spread of collaborative behavior in governance networks. The size of the network determines the speed of network diffusion. The smaller the network size, the more sensitive it is to the spillover benefits of collaborative governance, and the larger the network size, the more sensitive it is to the penalties of non-compliance. The findings of the study have implications for the collaborative behavior of multiple agents in public crisis governance. The main findings are that (1) in order to ensure the stability of the collaborative governance system, decision making options should be selected according to the size of the network. (2) A reasonable penalty mechanism for breach of contract should be set up to avoid the phenomenon of “free-riding” in collaborative governance. (3) Reasonable allocation of collaboration benefits and maintenance of cooperative relationships between nodes in the neighborhood. (4) External regulators should ensure that information in the network is disseminated without barriers and reduce the phenomenon of information asymmetry.

A Multi-Information Spreading Model for One-Time Retweet Information in Complex Networks.

In the realm of online social networks, the spreading of information is influenced by a complex interplay of factors. To explore the dynamics of one-time retweet information spreading, we propose a Susceptible-Infected-Completed (SIC) multi-information spreading model. This model captures how multiple pieces of information interact in online social networks by introducing inhibiting and enhancement factors. The SIC model considers the completed state, where nodes cease to spread a particular piece of information after transmitting it. It also takes into account the impact of past and present information received from neighboring nodes, dynamically calculating the probability of nodes spreading each piece of information at any given moment. To analyze the dynamics of multiple information pieces in various scenarios, such as mutual enhancement, partial competition, complete competition, and coexistence of competition and enhancement, we conduct experiments on BA scale-free networks and the Twitter network. Our findings reveal that competing information decreases the likelihood of its spread while cooperating information amplifies the spreading of mutually beneficial content. Furthermore, the strength of the enhancement factor between different information pieces determines their spread when competition and cooperation coexist. These insights offer a fresh perspective for understanding the patterns of information propagation in multiple contexts.

Effect of network topologies and attacking strategies on cascading failure model with power-law load redistribution

Various traffic networks play an important role in daily life and have different topological characteristics such as small-world and scale-free. The factors of traffic congestion, natural disasters and traffic accidents may induce cascading failure in which the load redistribution usually has the characteristic of power-law (that is to say, when a station is broken, the great majority of passengers would evacuate to the nearby stations, but the very few would evacuate to further). Based on them, this paper studies the load-capacity cascading failure model with power-law load redistribution using three kinds of attacking strategies (removing a single node according to the load, removing multiple nodes according to the load and removing multiple nodes randomly) for different network structures (random networks, WS small-world networks and BA scale-free networks). We confirm the robustness of our results by further performing simulations on real-world traffic networks. A quantitative description of network topologies and attacking strategies vs. the cascading failure model with power-law load redistribution is obtained by computer simulation. The results demonstrate that in contrast to removing the node according to the load, network robustness increases with the increase of the load control parameter α when randomly removing the node; when θ is small, the load tolerance parameter β is sensitive to the network robustness in random networks and WS small-world networks when removing a single node according to the load.

Analysis of the factors influencing the promotion of stone sculpture art based on social media communication dynamics

Abstract This paper first focuses on the design elements and digital platforms of stone carving art and then discusses the dissemination of stone carving art on social media platforms. Secondly, a social media propagation dynamics modeling of stone sculpture art promotion is proposed, and the degree distribution of stone sculpture art promotion in the BA scale-free network is calculated by the social media network model and propagation evolution model. Finally, the kinetic analysis of social media on stone carving art promotion by different influencing factors and information dissemination stages is explored. The results show that when the user recognizes stone carving art as Ii (0) = 0.7 the larger the value Ii = (0), the greater the user’s propensity to spread stone carving art promotion information and the greater the rate of stone carving art promotion information dissemination. Through the in-depth combination of social media and stone carving art, this paper has important practice and significance for the protection and inheritance of stone carving art and for improving its influence and popularity.

Aged Care Projects Evaluation Research Based on the Self-Adaptive Consensus Emergence Model Driven by the Social Learning Mechanism

In recent years, the accelerated aging process in China has brought enormous pressure on the traditional aged care system. The private family-based aged care mode cannot resolve the contradiction between the insufficient labor force and a large elderly population. The public community-based aged care mode could effectively integrate various social resources such as housing, healthcare, land, education, etc., which may better meet diverse elderly care demands. The senior residents' evaluation of public aged care services is essential for local pension policy making, determining the local government's investment direction to some extent. Therefore, this research organizes a decision group to conduct the evaluation of alternative aged care service projects with Maslow's hierarchy-based evaluation framework. The decision group consists of senior citizens from the Xiaolingwei community in Nanjing, which is a deeply aging metropolis with the flourishing aged care service market and demand. Considering the aged residents' inherent preference differences rooted in living habits, cultural background, and risk attitude, it is essential to introduce an effective consensus model into the group evaluation to control opinion conflict and reach consensus. The current consensus models still have the following limitations: consensus models depend on the preset empirical consensus threshold, hardly reflecting the spontaneous consensus emergence; the inconsistency of group consensus opinion harms the reliability and effectiveness of group decision; the existing methods generally identify the non-cooperative behavior passively, lacking the adaptive and active management. Therefore, this paper develops the consensus emergence model driven by the social learning mechanism based on the BA scale-free network and the Bayesian learning rule, guiding the self-adaptive opinion evolution and the spontaneous consensus convergence. The novel consensus model includes three crucial parts: the environment network construction, the private cognition formation, and the individual preference modification. The proposed consensus emergence model has outstanding advantages in consensus consistency through spontaneous opinion evolution, the adaptive consensus emergence with greater consensus efficiency, and the consensus robustness under non-cooperators disturbance.

Epidemic spreading dynamics on two-layer complex networks

Recent studies have shown that many real-world systems can be described by multi-layer complex networks. In this paper, the concept of layers is introduced to construct a traffic-driven SIR epidemic spreading model on “logical-physical” layered network. Based on the peak density of infected nodes and the ultimate density of recovered nodes, we investigate the features of epidemic spreading on layered network. Through numerical simulations, it is shown that traffic flow greatly influences the intensity and scope of epidemic spreading. By comparing the effects of four kinds of two-layer networks generated by ER random network model and BA scale-free network model on epidemic spreading, we found that the homogeneity of logical or physical network structure can promote the spread of epidemic more than heterogeneous networks. This work may be of service to design traffic-driven epidemic prevention and control strategies.

Strategically positioning non-competitive individuals can rescue cooperation in scale-free networks

Cooperation rescue in populations has long been a challenging problem, and previous studies have suggested that strategically placing cooperators in important positions in structured populations at the initial moment can obtain the opportunity of cooperation expansion. How to effectively lay out the location and place personalized nodes occupies a very important position in solving social dilemmas. However, most previous studies have focused on how the distribution of initial cooperators or defectors in homogeneous groups affects evolutionary outcomes, and relatively few studies have examined the placement of individuals with invariant heterogeneous characteristics. To enrich this research, we extend the cooperation rescue model to investigate the importance of the positional layout of two types of individuals with heterogeneous social value orientation characteristics in BA scale-free networks. Our study specifically investigates the impact of the distribution of non-competitive individuals on cooperation. We introduce non-competitive individuals into a BA scale-free network with only competitive individuals using different ranking rules. Our findings demonstrate that the presence of non-competitive individuals can promote cooperation. Furthermore, we determine the minimum number of nodes required to sustain cooperation under different ranking rules. In summary, our study emphasizes the importance of non-competitive individuals being placed in positions of importance for cooperation to flourish.

Complexity of networks: A structural heterogeneity approach

The complexity measurement of networks is one of the hot topics in complex networks. How to accurately describe the complexity difference between networks is helpful to the study of network structure. This paper proposes a method for measuring the network complexity considering the local and global structural heterogeneity. This method introduces the k-order neighbors to examine the local structural heterogeneity. Besides, the standard deviation is used to evaluate the global structural heterogeneity. Based on this, the complexity measurement model is established. In order to testify the efficiency of the method, the ER random networks, BA scale-free networks and real networks (including four social networks and two infrastructure networks) are used for experiments. The results show that the proposed method is sensitive and can effectively describe the subtle difference of structure complexity between networks.

Control-capacity analysis and optimized construction for controlled interdependent networks

In order to obtain interdependent networks with stronger control-capacity, in this paper, based on Kalman’s rank theory, a widely used and improved index of control-capacity for controlled interdependent networks is firstly analyzed and proposed theoretically, and two examples are employed to show the feasibility and effectiveness of this presented index. Secondly, with this index, the influence of the intra-couplings, network scale, inter-coupling strength, inter-couplings, and controllers on the control-capacity of sixteen controlled interdependent networks with two subnets, which are any combination of BA scale-free network, WS small-world network, NW small-world network and ER random network, are analyzed and discussed, as well as their optimal structures and various parameters for best control-capacity. Finally, with this index proposed, a novel algorithm is put forward to build up interdependencies or inter-couplings to enhance the control-capacity of controlled interdependent networks. The simulations show that the algorithm designed in this paper is feasible and effective, and can achieve interdependent networks with stronger control-capacity.

Novel payoff calculation resolves social dilemmas in networks

Standing in others’ shoes is usually describing the phenomenon that individuals switch their position and think about others’ benefits. This common saying can also stimulate the cooperation behavior, no matter in natural system or human society. In fact, Scholars have conducted abundant of researches to explore human behaviors in evolutionary game theory to discover how to improve cooperation among individualist. Results clearly showed that players can achieve the highest payoff when they choose cooperation strategy. However, selfishness among individuals results in that cooperation is not guaranteed every time, and how to improve cooperative behavior still remains a challenge in literature. Nevertheless, we analyzed the notion of “Standing in others’ shoes” through mathematical method, and analyzed this idea by introducing evolutionary game theory. The results indicate that the cooperation can be promoted significantly when players take opponents’ payoff into account. Here, a parameter of u was introduced into the simulation process representing when different strategies are applied by the focal player x and its neighbor, the focal player x will calculate its own payoff at possibilities u, and with the possibilities of 1−u considering its neighbor yi’s payoff. The Monte Carlo simulation is conducted on spatial-lattice network, BA scale-free network and small-world network respectively. The results reveal that the frequency of cooperation can be improved dramatically when parameter u reached a certain threshold.

Assessing Graph Robustness through Modified Zagreb Index

Graph robustness or network robustness is the ability that a graph or a network preserves its connectivity or other properties after the loss of vertices and edges, which has been a central problem in the research of complex networks. In this paper, we introduce the Modified Zagreb index and Modified Zagreb index centrality as novel measures to study graph robustness. We theoretically find some relationships between these novel measures and some other graph measures. Then, we use Modified Zagreb index centrality to analyze the robustness of BA scale-free networks, ER random graphs and WS small world networks under deliberate or random vertex attacks. We also study the correlations between this new measure and some other existed measures. Finally, we use Modified Zagreb index centrality to study the robustness of two real world networks. All these results demonstrate the efficiency of Modified Zagreb index centrality for assessing the graph robustness.

The impact of information dissemination on vaccination in multiplex networks

The impact of information dissemination on epidemic control is essentially subject to individual behaviors. Vaccination is one of the most effective strategies against the epidemic spread, whose correlation with the information dissemination should be better understood. To this end, we propose an evolutionary vaccination game model in multiplex networks by integrating an information-epidemic spreading process into the vaccination dynamics, and explore how information dissemination influences vaccination. The spreading process is described by a two-layer coupled susceptible-alert-infected-susceptible (SAIS) model, where the strength coefficient between two layers characterizes the tendency and intensity of information dissemination. We find that the impact of information dissemination on vaccination decision-making depends on not only the vaccination cost and network topology, but also the stage of the system evolution. For instance, in a two-layer BA scale-free network, information dissemination helps to improve vaccination density only at the early stage of the system evolution, as well as when the vaccination cost is smaller. A counter-intuitive conclusion that more information transmission cannot promote vaccination is obtained when the vaccination cost is larger. Moreover, we study the impact of the strength coefficient and individual sensitivity on the fraction of infected individuals and social cost, and unveil the role of information dissemination in controlling the epidemic.

Information dimension based on [formula omitted] entropy

Information dimension is applied to quantify fractal, and the current methods are improved on the basis of information entropy. Although information entropy is always used to measure the information volume, it fails when dealing with complex and uncertain information. To solve this problem, in this paper, the information dimension is defined by using Deng entropy, due to the reason that Deng entropy as the extension of information entropy has the characteristic of being able to measure uncertain information better. In our method, Deng entropy is considered to measure the information volume in the information dimension. Besides, box coverage is also combined in the process of the box covering to define box coverage Deng entropy information dimension. In addition, the classical information dimension and box dimension of BA scale-free networks, WS and NW small-world networks and four real networks are calculated to compare with the proposed information dimension. The results show that the values of Deng entropy information dimension and box coverage Deng entropy information dimension are bigger than the classical information dimension and box dimension for the same network. Moreover, the information dimension of the networks does not increase linearly with the increase of nodes.

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored. From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.

Identifying influential spreaders in complex networks for disease spread and control

Identifying influential spreaders is an important task in controlling the spread of information and epidemic diseases in complex networks. Many recent studies have indicated that the identification of influential spreaders is dependent on the spreading dynamics. Finding a general optimal order of node importance ranking is difficult because of the complexity of network structures and the physical background of dynamics. In this paper, we use four metrics, namely, betweenness, degree, H-index, and coreness, to measure the central attributes of nodes for constructing the disease spreading models and target immunization strategies. Numerical simulations show that spreading processes based on betweenness centrality lead to the widest range of propagation and the smallest epidemic threshold for all six networks (including four real networks and two BA scale-free networks generated according to Barabasi–Albert algorithm). The target immunization strategy based on the betweenness centrality of nodes is the most effective for BA scale-free networks but displays poor immune effect for real networks in identifying the most important spreaders for disease control. The immunization strategy based on node degrees is the most effective for the four real networks. Findings show that the target immune strategy based on the betweenness centrality of nodes works best for standard scale-free networks, whereas that based on node degrees works best for other nonstandard scale-free networks. The results can provide insights into understanding the different metrics of measuring node importance in disease transmission and control.

Analysis of epidemic vaccination strategies by node importance and evolutionary game on complex networks

Currently, vaccination is the most effective means to prevent the spread of infectious diseases. In this paper, a novel SIRV-NI-EG (susceptible, infected, recovered, vaccinated - node importance - evolutionary game) model is established to analyze the evolution of vaccination strategy under the combination of mandatory vaccination and voluntary vaccination. For the mandatory vaccination, some nodes with high node importance are firstly vaccinated in a certain proportion according to the node importance ranking. The remaining nodes in the network voluntarily decide whether to vaccinate according to the surrounding situation based on the evolutionary game theory. And degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, PageRank, k-core, structural holes and WTOPSIS are used to evaluate the node importance in the network. In addition, the methods based on node deletion are used to further evaluate the importance of the initial vaccination nodes. Finally, vaccination evolutionary game analysis based on the SIRV-NI-EG model is performed on three complex networks, including USAir network, Facebook network and BA scale-free network. The results show that the performances of all evaluation indicators are better than random vaccination. Our conclusions can provide better vaccination strategies for government decision-making to control the spread of infectious diseases.

Study on Connectivity Mechanism and Robustness of Three-Dimensional Pore Network of Sandstone

As one of the most prevalent porous media, rock contains a large number of pore throats of varying size and shape. It is essential to analyze the complex pore network structure and to define the network structural features to reveal the microscopic mechanism of the rock permeability. In this paper, based on the complex network theory and CT scanning technology, sandstone is used as an example to study the structural characteristics of the rock network with different porosities. The results show that the structural characteristics of the sandstone seepage network are consistent with BA scale-free network, whose average path length increases with the size of the network. At the same time, the porosity of the sandstone is strongly influenced by the number of throat in the rock pore network. Furthermore, our analysis concludes that a few pores with a large number of connections contribute significantly to the overall connectivity of the sandstone seepage network. Removing the ‘hub’ pores increased the average path length of the entire network by 27.63-37.26%, which could not be achieved by randomly removing method. While the sandstone seepage network has better fault tolerance and robustness to external random attacks, this study provides a new approach to study the mechanisms of fluid storage and migration in porous media.

The behavior propagation and confrontation competition model based on information energy

In recent years, the influence of group behavior on individual behavior has been widely concerned by people. This paper takes the propagation of behavior-related information as the influencing medium, constructs the behavior propagation and confrontation competition model based on information energy, and studies the propagation of single behavior and confrontation behaviors in the network. In the model, the behavioral information energy on nodes is related to the information edge weight and the length of the reachable path between nodes, and we quantify the propagation probability of behaviors and the competition probability between the confrontation behaviors by the behavioral information energy. Through modeling and analyzing the change of node motivation and the behavior propagation rule, we carry out the simulation in small-world network and BA scale-free network, respectively. Experimental results show that the information energy has a promoting effect on the propagation of behaviors, and the behaviors that erupt in the network generally have an important information dissemination basis in the early stage and may be promoted by relevant information in the later stage. An open and tightly connected network environment is easier to promote the large-scale propagation of a new behavior. In addition, when two kinds of confrontation behaviors occur in the crowd network, the propagation of behavior-related information and the maintenance of people’s interest in the behavior are the key to the success of the behavioral competition.

Evolving complex networks with logistic property: Global versus local growth

Considering the retarding effect of natural resources, environmental conditions, and other factors on network growth, the capacity of network nodes to connect to new edges is generally limited. Inspired by this hindered growth of many real-world networks, two types of evolving network models are suggested with different logistic growth schemes. In the global and local logistic network, the total number of network edges and the number of edges added into the network at each step are in line with the Logistic growth, respectively. The most exciting feature of the Logistic growth network is that the growth rule of network edges is first fast, then slow and finally reaches the saturation value [Formula: see text]. Theoretical analysis and numerical simulation reveal that the node degrees of two new networks converge to the same results of the BA scale-free network, [Formula: see text], as the growth rate [Formula: see text] approaches to 0. The local logistic network follows a bilateral power-law degree distribution with a given value of [Formula: see text]. Meanwhile, for these two networks, it is found that the greater [Formula: see text] and [Formula: see text], the smaller the average shortest paths, the greater the clustering coefficients, and the weaker the disassortativity. Additionally, compared to the local logistic growth network, the clustering feature of the global logistic network is more obvious.