Social network balance optimization method and system based on dynamic weight adjustment

Abstract

The invention discloses a social network balance optimization method and system based on dynamic weight adjustment, and belongs to the field of social network analysis and optimization, and the method comprises the following steps: S1, constructing a social network model of a directed graph, and dividing key edges and non-key edges; s2, a virtual leader-follower structure is introduced to improve the cooperation income of individuals and collections; s3, constructing a Hamilton-Jacobian-Bellman (HJB) coupling equation, and dynamically adjusting the weight of the key edge by applying an optimal control strategy; and S4, implementing a weight adjustment mechanism to adjust the weight of the non-critical edge and ensure the strong balance state of the network. Through the above mode, the social network balance optimization method based on dynamic weight adjustment is designed, interaction between individuals and collections in the social network is fully considered, and global optimization of network cooperation is ensured. According to the method, a brand new weight adjustment mechanism is introduced, and the overall cooperation efficiency and stability of the network are remarkably improved on the premise of overcoming a local optimal trap.

Description

Technical Field

[0001] The present invention belongs to the field of social network analysis and optimization, and in particular relates to a social network balance optimization method and system based on dynamic weight adjustment. Background Art

[0002] In recent years, with the rapid development and widespread application of social networks, people have higher and higher expectations for the balance, efficiency and stability of social networks. However, with the close integration of social networks with social life, users' requirements for the balance, efficiency and stability of social networks are also increasing. However, the dynamic balance of social networks usually requires human intervention, which is achieved by adjusting the connection weights between users. Although such an approach can maintain the balance of social networks to a certain extent, it often ignores other weight adjustment strategies that may be more effective, thereby increasing the operating cost of social networks and reducing system performance. However, the current balance optimization methods of social networks often use static weight allocation. Although such behavior meets the basic requirements of network balance to a certain extent, it often ignores the dynamic changes of network structure and the diversity of user behavior, thereby reducing the adaptability and efficiency of social networks.

[0003] In social networks, the connection weights between users can determine the efficiency of information dissemination and the stability of the network. Therefore, choosing a suitable weight adjustment strategy is of great significance for improving the efficiency and stability of social networks. Existing studies have shown that different weight adjustment strategies can significantly affect the behavior and performance of social networks. Foreign researchers started early in the study of weight adjustment strategies in social networks, and they explored the impact of weight adjustment on network performance from different perspectives. For example, some studies focus on improving the efficiency of information dissemination by enhancing the weights of key nodes (such as highly influential users or central nodes), which can significantly accelerate the speed of information diffusion and expand the coverage. In addition, some studies have proposed a weight adjustment strategy based on trust. Users with high trust have more reliable sources of information and their connection weights will be higher. This strategy helps to filter false information and improve the quality and credibility of information transmission in the network. Domestic research on social network weight adjustment strategies has also achieved rich results. Some researchers have deeply analyzed the complex structure of social networks and proposed a weight adjustment strategy based on community detection. By identifying closely connected groups in the network, optimizing the connection strength within and between groups, and improving the connectivity and information flow efficiency of the overall network. In addition, researchers have also developed a social network weight adjustment model that comprehensively considers user behavior and content characteristics. The model analyzes the interactive behaviors between users (such as likes, comments, reposts, etc.), and deeply explores the attributes of the content itself (such as topic popularity, emotional tendencies, etc.), and adjusts the weights of social relationships based on this, thereby more accurately reflecting the actual influence and interest similarities between users.

[0004] Although existing weight adjustment strategies have achieved certain results in improving information dissemination efficiency and network stability, they still have some shortcomings: although centralized strategies can quickly spread information, when key nodes fail, the transmission capacity of the entire network will drop significantly; the trust measurement criteria are often subjective and difficult to quantify, and the trust relationship between different users may also change over time. This strategy performs poorly in a dynamic environment; the weight adjustment strategy based on community detection ignores the subtle changes in relationships between individual users and cannot fully utilize the potential connection advantages of the entire network; comprehensive consideration of user behavior and content characteristics relies on a large amount of data, which requires complex calculations when processing, and is less efficient in large-scale social networks. Summary of the invention

[0005] In order to solve the technical problems existing in the background technology, the present invention aims to provide a social network balance optimization method and system based on dynamic weight adjustment, which realizes the balance between information dissemination and user interaction in the social network through an algorithm.

[0006] In order to solve the technical problem, the technical solution of the present invention is:

[0007] A social network balance optimization method based on dynamic weight adjustment, the method comprising:

[0008] Construct a social network model based on a directed graph and divide the key edges into non-key edges;

[0009] Based on the constructed directed graph social network model, a virtual leader-follower structure is constructed to optimize the cooperation benefits between individuals and the collective;

[0010] The Hamilton-Jacobi-Bellman (HJB) coupling equations are constructed and the key edge weights are dynamically adjusted using the optimal control strategy;

[0011] Based on the strong balance state of the network, a weight adjustment mechanism is implemented to adjust the weights of non-critical edges, and then the weights are iteratively updated to achieve the overall optimization goal of the network.

[0012] Furthermore, a social network model of a directed graph is constructed, including nodes and edges, and then the strongly connected components are determined, and the edges contained in the strongly connected components are marked as key edges; the edges not in any strongly connected components are marked as non-key edges;

[0013] The key edge weights and non-key edge weights are iteratively updated until the weights of all edges are the same or the cooperation status of each node does not change or the set number of iterations is reached.

[0014] Furthermore, the construction of the directed graph social network model includes:

[0015] A social network consisting of N users is modeled using a directed graph G;

[0016] is the adjacency matrix;

[0017] Edge Set By key edge set With non-critical edge set composition;

[0018] Node v of directed graph G i Represents the user, the weight of the edge Represents the influence strength between users;

[0019] In the initial state, the cooperation state of each node and the weight of the edge are randomly set between 0 and 1;

[0020] The following node fitness function fi(x) is introduced into the social network model of the directed graph:

[0021]

[0022] where x i Represents node v i The cooperation status, x j Represents node v j The status of cooperation, Represents the node v i The number of neighbor nodes with interactive relationships, m ij is the element of the adjacency matrix, c and b represent the loss and gain parameters of the node fitness respectively;

[0023] Edge weight Calculated by the following formula:

[0024]

[0025] where p ij =sigmoid(β|Δf ji |), Δf ji =f(x j )-f(x i ), β is an adjustable parameter.

[0026] Furthermore, a virtual leader-follower structure is introduced to improve the cooperation benefits of individuals and the collective, including:

[0027] The virtual leader is the user with the highest cooperation status in each iteration, and other users are followers. The cooperation status of the virtual leader is expressed as:

[0028]

[0029] where x i For individual user v i The cooperation state of x0 is the state of the virtual leader, and t is the current iteration number.

[0030] Furthermore, the Hamilton-Jacobi-Bellman (HJB) coupling equation is constructed, and the optimal control strategy is used to dynamically adjust the key edge weights, including:

[0031] Assume that the dynamic model of each node in the social network is the same, expressed as:

[0032]

[0033] Where A is the state transition matrix, B is the control input matrix, represents the input of the control strategy;

[0034] Define the state tracking error δ between the follower and the virtual leader i as follows:

[0035]

[0036] The performance function of the virtual leader is designed as follows:

[0037]

[0038] Among them, x0 is the state of the virtual leader, x i is the state of the follower, and u0 is the control input item of the virtual leader;

[0039] The performance function of the follower is designed as follows:

[0040]

[0041] Among them, δ i is the state tracking error between the follower and the virtual leader, is the weight change of the key edge, For node v i The set of connected critical edges;

[0042] Construct the value function V0(x0(t)) of the virtual leader and the value function V0(x0(t)) of the follower i (δ i (t));

[0043]

[0044] S0, S i , Q i , R i is a positive definite matrix, is the weight change of the key edge, For node v i The set of connected critical edges;

[0045] Derivative the value function V0(x0(t)) of the virtual leader, obtain the Hamiltonian equation of the virtual leader, and solve it to obtain the optimal control strategy of the virtual leader

[0046] The value function V for the follower i (δ i (t)) to obtain the Hamiltonian equation of the follower, and solve it to obtain the optimal control strategy of the follower

[0047] Will and Substitute the Hamiltonian equation of the follower into the equation and get the coupled Hamilton-Jacobi-Bellman HJB equation. By solving the coupled Hamilton-Jacobi-Bellman HJB equation, the optimal control strategy of the virtual leader and the optimal control strategy of each follower are obtained.

[0048] The weights of key edges in the social network are adjusted according to the optimal control strategy of the virtual leader and the optimal control strategy of each follower described above.

[0049] Furthermore, by taking the derivative of the value function V0(x0(t)) of the virtual leader, the Hamiltonian equation of the virtual leader is obtained as follows:

[0050]

[0051] in make Solve to obtain the optimal control strategy of the virtual leader

[0052] The value function V for the follower i (δ i (t)) and the Hamiltonian equation of the follower is obtained as follows:

[0053]

[0054] in make Solve to obtain the optimal control strategy of the follower in

[0055] Will and Substituting into the follower's Hamiltonian equation, sorting and simplifying, we get the coupled Hamilton-Jacobi-Bellman HJB equation as follows:

[0056]

[0057] The optimal control strategy of the leader and the optimal control strategy of the follower are obtained by solving the coupled Hamilton-Jacobi-Bellman (HJB) equations.

[0058] Furthermore, the weights of non-critical edges are adjusted to ensure a strong balance of the network, including:

[0059] Calculate the in-degree difference of each user's individual node in the social network

[0060]

[0061] in, Represents node v i The out-degree of node v i The sum of the weights of all the outgoing edges is expressed as:

[0062] Represents node v i The in-degree of a node is the sum of the weights of all edges pointing to the node, expressed as:

[0063]

[0064] If the in-out difference is greater than zero, the outbound edge weight is reduced; if the inbound and outbound degree difference Less than 0, reduce the weight of the incoming edge; until the difference between the in- and out-degrees is

[0065] Update node status.

[0066] A social network balance optimization system based on dynamic weight adjustment, the system comprising:

[0067] Directed graph construction and edge division module, used to construct a social network model of directed graphs and divide key edges into non-key edges;

[0068] A virtual leader-follower structure building module is used to build a virtual leader-follower structure based on a social network model of a constructed directed graph to optimize the cooperation benefits of individuals and the collective;

[0069] HJB coupling equation construction and optimal control module, which is used to construct Hamilton-Jacobi-Bellman (HJB) coupling equations and dynamically adjust the key edge weights using the optimal control strategy;

[0070] The weight adjustment and iterative update module is used to implement the weight adjustment mechanism to adjust the weights of non-critical edges based on the strong balance state of the network, and then iteratively update the weights to achieve the overall optimization goal of the network.

[0071] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, any one of the above-mentioned methods for optimizing social network balance based on dynamic weight adjustment is implemented.

[0072] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any one of the above-mentioned social network balance optimization methods based on dynamic weight adjustment.

[0073] Compared with the prior art, the advantages of the present invention are:

[0074] In view of the shortcomings of the existing weight adjustment strategy, the present invention proposes a social network balance optimization method based on dynamic weight adjustment. By optimizing the propagation mechanism of information flow, the dependence on key nodes is reduced and the robustness of the network is improved; and the measurement standard based on the learning strength between nodes is replaced by the trust degree, which can be updated synchronously over time according to the behavior changes of nodes, and the state changes between nodes can be captured more accurately; the weight reduction strategy is adopted to reduce the amount of network calculation by eliminating the weights of unimportant edges in the iterative process.

[0075] The present invention has a wide range of application potentials, especially in the field of social networks, such as platforms such as Weibo, Facebook and Instagram. By optimizing the propagation mechanism of information flow, the present invention can significantly improve the user's participation on social platforms. In addition, the implementation of the present invention is not limited to existing social platforms, it also has the ability to expand to emerging social networks to adapt to the ever-changing network environment and user needs. Through continuous algorithm optimization and weight adjustment, this technology can ensure the efficiency and quality of information dissemination while maintaining the stability and sustainability of social networks. Ultimately, the present invention will promote the development of social network platforms in a more intelligent, efficient and humanized direction, and provide global users with a better social experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 , a flow chart of a social network balance optimization method based on dynamic weight adjustment of the present invention;

[0077] Figure 2 , a graph showing the change in node status in a social network after the method of the present invention is adopted;

[0078] Figure 3 , a weight change trend diagram of edges in a social network after adopting the method of the present invention;

[0079] Figure 4 , a process diagram of the network evolving from an initial unbalanced state to a balanced state through the strategy adjustment of the present invention. DETAILED DESCRIPTION

[0080] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0081] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0082] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0083] Embodiment 1:

[0084] Please refer to the instruction manual Figure 1-4 , a social network balance optimization method based on dynamic weight adjustment, comprising the following steps:

[0085] S1. Construct a social network model of a directed graph and divide key edges into non-key edges, including:

[0086] Directed graph: The vertices of a directed graph represent individual users, and the directed edges represent asymmetric relationships between users, such as attention or friend requests, to accurately depict the structure of the interpersonal network and the direction of information flow. Each directed edge points from one user to another, indicating the relationship between the former and the latter or the direction of information flow. Based on the interactive relationship between individual users, a directed graph model is established to quantify the interactive relationship between each node and its neighbors, and preliminarily set the initial weight of each edge.

[0087] In this example, consider a social network consisting of N = 10 users, modeled by a directed graph G. is the adjacency matrix, the edge set By key edge set With non-critical edge set Composed of nodes v in the directed graph G i Represents the user, the weight of the edge Represents the influence strength between users. In the initial state, the cooperation state of each node and the influence weight of the edge are randomly set between 0 and 1.

[0088] Key edges and non-key edges: According to the directed graph model constructed above, the edges with strong connected components are set as key edges to ensure the connectivity of the network, and the other edges are non-key edges. The weight of the key edge is updated according to the node status in the network, and the weight of the non-key edge can be adjusted directly.

[0089] Strongly Connected Component: A strongly connected component is a strongly connected graph and no other nodes can be added so that the result is still a strongly connected graph. In other words, a strongly connected component is a strongly connected graph that cannot be expanded further.

[0090] Strongly connected graph: A strongly connected graph means that there is a bidirectional path between any two users (vertices) in the graph. For example, any user can directly or indirectly follow (or be followed by) all other users, forming a closely interconnected group.

[0091] In this example, define the sequence is the maximum connected component of the directed graph G, that is, the edge set consisting of key edges, and the other edges are non-key edges.

[0092] Node fitness: In order to facilitate the quantification of the influence of individual nodes in a social network, in this example, the following node fitness function is introduced:

[0093]

[0094] where x i 、x j Respectively represent the node v i 、v j The status of cooperation, Represents the node v i The number of neighbor nodes with interactive relationships, m ij are the elements of the adjacency matrix, c and b represent the loss and gain parameters of the node fitness respectively.

[0095] Edge weight: The edge weight indicates the intensity of the interaction between two individual users or the closeness of the relationship. The larger the weight, the closer the connection between the two or the more frequent the interaction.

[0096] In this example, the edge weight Calculated by the following formula:

[0097]

[0098] where p ij =sigmoid(β|Δf ji |), Δfji =f(x j )-f(x i ), 0<β≤1 is an adjustable parameter.

[0099] Out-degree and in-degree: The out-degree of a node is the sum of the weights of all edges sent from the node (i.e., the relationship of the user following other users), while the in-degree is the sum of the weights of all edges pointing to the node (i.e., the relationship of other users following the user). The out-degree and in-degree reflect the user's activity and influence in the network.

[0100] In this example, node v i The out-degree of a node is the sum of the weights of all edges emitted by the node, that is, The in-degree is the sum of the weights of all edges pointing to the node, that is

[0101] S2. Introduce a virtual leader-follower structure to improve the benefits of individual and collective cooperation, including:

[0102] Virtual leader-follower structure: The main responsibility of the virtual leader is to improve the overall cooperation efficiency while minimizing direct intervention on followers; the users in the directed graph G are all followers, and the goal of the followers is to maximize the overall benefits with minimal changes while following the leader's state.

[0103] Gains and losses: Gains usually refer to the positive effects obtained through cooperation or interaction between individuals, such as information sharing, resource exchange or social support. The higher the willingness to cooperate, the higher the benefits that participants (all users in the network) may obtain; while losses refer to the reduction in value caused by negative factors such as conflict, misunderstanding or resource consumption. The concepts of gains and losses help understand the dynamics and stability of interpersonal relationships in social networks.

[0104] In this example, in order to ensure that the overall cooperation status of all nodes is the highest, the virtual leader is selected as the user individual with the highest cooperation status in each iteration. The cooperation status refers to the node status, that is:

[0105]

[0106] Among them, x i For individual user v i The cooperation state of x0 is the state of the virtual leader, and t is the current iteration number.

[0107] S3, construct Hamilton-Jacobi-Bellman (HJB) coupling equations and apply optimal control strategies to dynamically adjust the weights of key edges;

[0108] Optimal control strategy: Optimal control theory is a method in applied mathematics and engineering that uses mathematical models to find the optimal strategy or decision to achieve a certain goal under certain conditions. In social networks, the strategy adjustments of virtual leaders and followers can be regarded as a dynamic system, in which the behavior of virtual leaders can affect the dynamics of the entire network. Applying optimal control theory can help virtual leaders identify and implement the most effective strategies to maximize goals such as network influence, communication efficiency or stability. At the same time, followers can also use this theory to optimize their own behavior to adapt to or respond to the leader's strategy, thereby achieving the optimal interests of individuals or groups in social networks.

[0109] In this example, we first consider a social network consisting of a group of identical nodes. The identical nodes refer to nodes with the same dynamics model (node ​​attributes). The network dynamics model is given by the following formula:

[0110]

[0111] Where A is the state transition matrix, B is the control input matrix, Represents the input of the control strategy.

[0112] Afterwards, the state tracking error δ between the follower and the virtual leader is defined as i as follows:

[0113]

[0114] In order to construct the Hamilton-Jacobi-Bellman (HJB) coupling equation, the performance function is constructed according to the characteristics of the virtual leader and follower as follows:

[0115]

[0116] Among them, J0 represents the performance function of the virtual leader, J i represents the performance function of the follower, S0, S i , Q i , R i is a positive definite matrix, δ i is the node state tracking error, is the weight change of the key edge, For node v i The set of connected critical edges.

[0117] Afterwards, the value functions of the virtual leader and follower are constructed as follows:

[0118]

[0119] In order to find the optimal control strategy (optimal weight change), the value function V0 of the virtual leader is derived to obtain the Hamiltonian equation of the virtual leader:

[0120]

[0121] in make Solve to obtain the optimal control strategy of the virtual leader

[0122] Similarly, the value function V for the follower i Taking the derivative, we get the Hamiltonian equation for the follower:

[0123]

[0124] in make Solve to obtain the optimal control strategy of the follower in

[0125] Will and Substituting the above formula (Hamilton equation of the follower) and sorting and simplifying it, we get the coupled Hamilton-Jacobi-Bellman HJB equation as follows:

[0126]

[0127] By solving the coupled HJB equations, the optimal control strategy of the virtual leader and the optimal control strategy of each follower, referred to as the optimal control strategy, can be obtained to adjust the weights of the key edges in the social network.

[0128] S4. Implement a weight adjustment mechanism to adjust the weights of non-critical edges and ensure a strong balance state of the network;

[0129] Adjust the weight of non-critical edges, including the following steps:

[0130] Step S41: Calculate the in-degree difference of each user's individual node in the social network

[0131] In this example, for each node, the following formula is used to calculate the node v i In-out difference:

[0132]

[0133] Step S42: if the difference is greater than zero, reduce the outbound edge weight; if the difference is less than 0, reduce the inbound edge weight;

[0134] Step S43: Update node status.

[0135] Figure 2 The evolution trend of the cooperation strategy when there are 10 nodes in the social network is given. Initially, the cooperation state of each node is a random value between 0 and 1, where 0 represents complete non-cooperation and 1 represents complete cooperation. The thick red solid line represents the cooperation state of the virtual leader, and the rest are followers. At the beginning of the iteration, the cooperation state of the node fluctuates greatly. This fluctuation reflects the uncertainty and exploration process of the node for the cooperation strategy in the early stage. Afterwards, by applying steps S3 and S4 of the present invention, that is, the weight adjustment strategy, these fluctuations gradually decrease, and the cooperation state of the node begins to stabilize. Further zoom in Figure 2 From the details in the figure, we can find that the states of all nodes are stable within 10 iterations. This rapid stabilization process is crucial for understanding and designing effective social network cooperation mechanisms. It not only shows the dynamic evolution of cooperation strategies in social networks, but also provides valuable insights into how to promote cooperation in the real world.

[0136] Figure 3 The weight change trend of the edges between 10 nodes in the social network. Lines of different colors represent the weight dynamics of different edges. In the initial iteration step, Figure 3 The enlarged illustration of reveals the significant changes in edge weights. Lines of different colors represent the weight dynamics of different edges in the network. The fluctuations in edge weights show the instability of the relationship between nodes and their adjustments in the process of finding the optimal cooperation strategy. As the iterations proceed, the edge weights gradually stabilize and eventually converge to a constant value of 0.5, and the interactive learning relationship between nodes reaches a state of equilibrium.

[0137] Figure 4 The process of the network gradually evolving from an initial unbalanced state to a balanced state through the strategy adjustment of the present invention is demonstrated. Figure 4 (a), the weights of the nodes and edges of the network are unevenly distributed, resulting in an unbalanced network structure. By applying the weight adjustment strategy proposed in this invention, we can obtain Figure 4 (b), at this time, each node in the network has the same in- and out-degree, and the weights of all edges become consistent, forming a balanced network structure. The strategy of the present invention not only balances the in- and out-degrees of each node by continuously adjusting the weights of the edges, but also promotes the transition of the network from an unbalanced state to a strongly connected equilibrium state. This adjustment method effectively optimizes the overall performance of the network and ensures that the influence of each node in the network is evenly distributed.

[0138] Embodiment 2:

[0139] This embodiment provides a terminal device, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of a social network balance optimization method based on dynamic weight adjustment, including the following steps:

[0140] Construct a social network model of a directed graph and divide the key edges into non-key edges;

[0141] Based on the constructed directed graph social network model, a virtual leader-follower structure is constructed to optimize the cooperation benefits between individuals and the collective;

[0142] The Hamilton-Jacobi-Bellman HJB coupling equation is constructed and the key edge weights are dynamically adjusted using the optimal control strategy;

[0143] Based on the strong balance state of the network, a weight adjustment mechanism is implemented to adjust the weights of non-critical edges, and then the weights are iteratively updated to achieve the overall optimization goal of the network.

[0144] Embodiment 3:

[0145] This embodiment provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It is understandable that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory.

[0146] One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of a social network balance optimization method based on dynamic weight adjustment in the above embodiment; one or more instructions in the computer-readable storage medium are loaded and executed by a processor as follows:

[0147] Construct a social network model of a directed graph and divide the key edges into non-key edges;

[0148] Based on the constructed directed graph social network model, a virtual leader-follower structure is constructed to optimize the cooperation benefits between individuals and the collective;

[0149] The Hamilton-Jacobi-Bellman HJB coupling equation is constructed and the key edge weights are dynamically adjusted using the optimal control strategy;

[0150] Based on the strong balance state of the network, a weight adjustment mechanism is implemented to adjust the weights of non-critical edges, and then the weights are iteratively updated to achieve the overall optimization goal of the network.

[0151] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0152] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0153] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0154] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0155] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0156] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A social network balance optimization method based on dynamic weight adjustment, characterized in that: The method comprises: Construct a social network model based on a directed graph and divide the key edges into non-key edges; Based on the constructed directed graph social network model, a virtual leader-follower structure is constructed to optimize the cooperation benefits between individuals and the collective; The Hamilton-Jacobi-Bellman HJB coupling equation is constructed and the key edge weights are dynamically adjusted using the optimal control strategy; Based on the strong balance state of the network, a weight adjustment mechanism is implemented to adjust the weights of non-critical edges, and then the weights are iteratively updated to achieve the overall optimization goal of the network.

2. A social network balance optimization method based on dynamic weight adjustment according to claim 1, characterized in that: Construct a social network model based on a directed graph, including nodes and edges, and then determine the strongly connected components, and mark the edges contained in the strongly connected components as key edges; the edges not in any strongly connected components are marked as non-key edges; The key edge weights and non-key edge weights are iteratively updated separately until the weights of all edges are the same or the cooperation status of each node does not change or the set number of iterations is reached.

3. The social network balance optimization method based on dynamic weight adjustment according to claim 1, characterized in that: The social network model of the directed graph is constructed, comprising: A social network consisting of N users is modeled using a directed graph G; is the adjacency matrix; Edge Set By key edge set With non-critical edge set composition; Node v of directed graph G i Represents the user, the weight of the edge Represents the influence strength between users; In the initial state, the cooperation state of each node and the weight of the edge are randomly set between 0 and 1; The following node fitness function f is introduced into the social network model of the directed graph: i (x): where x i Represents node v i The cooperation status, x j Represents node v j The status of cooperation, Represents the node v i The number of neighbor nodes with interactive relationships, m ij is the element of the adjacency matrix, c and b represent the loss and gain parameters of the node fitness respectively; Edge weight Calculated by the following formula: where p ij =sigmoid(β|Δf ji |), Δf ji =f(x j )-f(x i ), β is an adjustable parameter.

4. The social network balance optimization method based on dynamic weight adjustment according to claim 1, characterized in that: Introducing a virtual leader-follower structure to improve the benefits of individual and collective cooperation, including: The state of the virtual leader is the user individual with the highest cooperation state in each iteration, and other users are followers. The cooperation state of the virtual leader is expressed as: where x i For individual user v i The cooperation state of x0 is the state of the virtual leader, and t is the current iteration number.

5. The social network balance optimization method based on dynamic weight adjustment according to claim 1, characterized in that: The Hamilton-Jacobi-Bellman HJB coupling equation is constructed, and the optimal control strategy is used to dynamically adjust the key edge weights, including: Assume that the dynamic model of each node in the social network is the same, expressed as: Where A is the state transition matrix, B is the control input matrix, represents the input of the control strategy; Define the state tracking error δ between the follower and the virtual leader i as follows: The performance function of the virtual leader is designed as follows: Among them, x0 is the state of the virtual leader, x i is the state of the follower, and u0 is the control input item of the virtual leader; The performance function of the follower is designed as follows: Among them, δ i is the state tracking error between the follower and the virtual leader, is the weight change of the key edge, For node v i The set of connected key edges; Construct the value function V0(x0(t)) of the virtual leader and the value function V0(x0(t)) of the follower i (δ i (t)); S0, S i , Q i , R i is a positive definite matrix, is the weight change of the key edge, For node v i The set of connected critical edges; Derivative the value function V0(x0(t)) of the virtual leader, obtain the Hamiltonian equation of the virtual leader, and solve it to obtain the optimal control strategy of the virtual leader The value function V for the follower i (δ i (t)) to obtain the Hamiltonian equation of the follower, and solve it to obtain the optimal control strategy of the follower Will and Substitute the Hamiltonian equation of the follower into the equation and get the coupled Hamilton-Jacobi-Bellman HJB equation. By solving the coupled Hamilton-Jacobi-Bellman HJB equation, the optimal control strategy of the virtual leader and the optimal control strategy of each follower are obtained. The weights of key edges in the social network are adjusted according to the optimal control strategy of the virtual leader and the optimal control strategy of each follower described above.

6. A social network balance optimization method based on dynamic weight adjustment according to claim 5, characterized in that: By taking the derivative of the value function V0(x0(t)) of the virtual leader, we get the Hamiltonian equation of the virtual leader as follows: in make Solve to obtain the optimal control strategy of the virtual leader The value function V for the follower i (δ i (t)) and the Hamiltonian equation of the follower is obtained as follows: in make Solve to obtain the optimal control strategy of the follower in Will and Substituting into the follower's Hamiltonian equation, sorting and simplifying, we get the coupled Hamilton-Jacobi-Bellman HJB equation as follows: The optimal control strategy of the leader and the optimal control strategy of the follower are obtained by solving the coupled Hamilton-Jacobi-Bellman HJB equations.

7. The social network balance optimization method based on dynamic weight adjustment according to claim 1, characterized in that: Adjust the weights of non-critical edges to ensure a strong balance of the network, including: Calculate the in-degree difference of each user's individual node in the social network in, Represents node v i The out-degree of node v i The sum of the weights of all the outgoing edges is expressed as: Represents node v i The in-degree of a node is the sum of the weights of all edges pointing to the node, expressed as: If the in-out difference is greater than zero, the outbound edge weight is reduced; if the inbound and outbound degree difference Less than 0, reduce the weight of the incoming edge; until the difference between the in- and out-degrees is Update node status.

8. A social network balance optimization system based on dynamic weight adjustment, characterized in that: The system comprises: Directed graph construction and edge division module, used to construct a social network model of directed graphs and divide key edges into non-key edges; A virtual leader-follower structure building module is used to build a virtual leader-follower structure based on a social network model of a constructed directed graph to optimize the cooperation benefits of individuals and the collective; HJB coupling equation construction and optimal control module, which is used to construct the Hamilton-Jacobi-Bellman HJB coupling equation and dynamically adjust the key edge weights using the optimal control strategy; The weight adjustment and iterative update module is used to implement the weight adjustment mechanism to adjust the weights of non-critical edges based on the strong balance state of the network, and then iteratively update the weights to achieve the overall optimization goal of the network.

9. A computer device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a social network balance optimization method based on dynamic weight adjustment according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, implements a social network balance optimization method based on dynamic weight adjustment according to any one of claims 1 to 7.

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