A social network balance optimization method and system based on dynamic weight adjustment

Abstract

This invention discloses a social network balance optimization method and system based on dynamic weight adjustment, belonging to the field of social network analysis and optimization. The method includes the following steps: S1, constructing a directed graph social network model and dividing it into key edges and non-key edges; S2, introducing a virtual leader-follower structure to improve the cooperative benefits between individuals and the group; S3, constructing a Hamilton-Jacobi-Bellman (HJB) coupling equation and applying an optimal control strategy to dynamically adjust the weights of key edges; S4, implementing a weight adjustment mechanism to adjust the weights of non-key edges and ensure a strong network balance. Through the above approach, a social network balance optimization method based on dynamic weight adjustment is designed, fully considering the interaction between individuals and the group in the social network and ensuring global optimization of network cooperation. This invention introduces a novel weight adjustment mechanism, which significantly improves the overall cooperative efficiency and stability of the network while overcoming the local optimum trap.

Description

Technical Field

[0001] This invention belongs to the field of social network analysis and optimization, specifically relating to a social network balance optimization method and system based on dynamic weight adjustment. Background Technology

[0002] In recent years, with the rapid development and widespread application of social networks, people have increasingly higher expectations for the balance, efficiency, and stability of these networks. However, as social networks become more closely integrated with social life, users' demands for balance, efficiency, and stability are also increasing. Currently, dynamic balancing of social networks typically requires human intervention by adjusting the connection weights between users. While this approach can maintain balance to some extent, it often overlooks other potentially more effective weight adjustment strategies, thereby increasing the operational costs of the social network and reducing system performance. Furthermore, current methods for optimizing social network balance often employ static weight allocation. While this approach satisfies the basic requirements of network balance to some extent, it often ignores the dynamic changes in network structure and the diversity of user behavior, thus reducing the adaptability and efficiency of the social network.

[0003] In social networks, the connection weights between users determine the efficiency of information dissemination and the stability of the network. Therefore, choosing a suitable weight adjustment strategy is crucial for improving the efficiency and stability of social networks. Existing research shows that different weight adjustment strategies can significantly affect the behavior and performance of social networks. International researchers began studying weight adjustment strategies in social networks earlier, exploring the impact of weight adjustment on network performance from different perspectives. For example, some studies focus on improving information dissemination efficiency by enhancing the weights of key nodes (such as high-influence users or central nodes), which can significantly accelerate information diffusion and expand coverage. Furthermore, some studies have proposed trust-based weight adjustment strategies; users with high trust levels have more reliable information sources, and their connection weights are higher. This strategy helps filter out false information and improve the quality and credibility of information transmission in the network. Domestic research on social network weight adjustment strategies has also yielded rich results. Some researchers have deeply analyzed the complex structure of social networks and proposed a community detection-based weight adjustment strategy. By identifying closely connected groups in the network, this strategy optimizes the connection strength within and between groups, improving the overall network connectivity and information flow efficiency. In addition, researchers have developed a social network weight adjustment model that comprehensively considers user behavior and content characteristics. This model analyzes user interaction behaviors (such as likes, comments, and reposts) and delves into the attributes of the content itself (such as topic popularity and sentiment). Based on this, it adjusts the weight of social relationships to more accurately reflect the actual influence and interest similarity between users.

[0004] While existing weighting strategies have achieved some success in improving information dissemination efficiency and network stability, they still have some shortcomings: centralized strategies can rapidly spread information, but when key nodes fail, the overall network's transmission capacity will significantly decrease; the measurement of trust is often subjective and difficult to quantify, and the trust relationship between different users may change over time, making this strategy perform poorly in dynamic environments; community-based weighting strategies ignore subtle changes in relationships between individual users and cannot fully utilize the potential connectivity advantages of the entire network; comprehensively considering user behavior and content characteristics relies on a large amount of data, requiring complex calculations during processing, resulting in low efficiency in large-scale social networks. Summary of the Invention

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

[0006] To solve the technical problem, the technical solution of the present invention is as follows:

[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 it into key edges and non-key edges;

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

[0010] The Hamilton-Jacobi-Bellman (HJB) coupling equation is constructed, and the weights of the key edges are dynamically adjusted using the optimal control strategy.

[0011] Based on the strong equilibrium 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 directed graph social network model is constructed, including nodes and edges. Then, strongly connected components are determined, and edges contained in strongly connected components are marked as key edges; edges not in any strongly connected components are marked as non-key edges.

[0013] The weights of critical edges and non-critical edges are iteratively updated until the weights of all edges are the same, the cooperation state of each node no longer changes, 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] It is an adjacency matrix;

[0017] Edge set From key edge set and non-critical edge set composition;

[0018] Node v of a directed graph G i Representing users, edge weights This represents the strength of influence between users;

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

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

[0021]

[0022] Where x i Represents node v i The cooperative status, x j Represents node v j The state of cooperation Indicates the relationship with node v i The number of neighboring nodes with interactive relationships, m ij are the elements of the adjacency matrix, where c and b represent the loss and gain parameters of node fitness, respectively;

[0023] Edge weight Calculate using the following formula:

[0024]

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

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

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

[0028]

[0029] Where x i For individual users v i The cooperative state is defined as follows: x0 represents the state of the virtual leader, and t represents the current iteration number.

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

[0031] Assuming that all nodes in a social network have the same dynamic model, it can be represented as:

[0032]

[0033] Where A is the state transition matrix and B is the control input matrix. Indicates the input to the control strategy;

[0034] Define the state tracking error δ between followers and virtual leaders. i as follows:

[0035]

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

[0037]

[0038] Where x0 represents the state of the virtual leader, x i For the follower's state, u0 is the control input for the virtual leader;

[0039] The follower's performance function is designed as follows:

[0040]

[0041] Where, δ i For the state tracking error between followers and virtual leaders, This represents the change in the weight 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 V of the follower. i (δ i (t));

[0043]

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

[0045] Differentiating the value function V0(x0(t)) of the virtual leader yields the Hamiltonian equation for the virtual leader, and solving it provides the optimal control strategy for the virtual leader.

[0046] Value function V for followers i (δ i Differentiating (t) yields the Hamiltonian equation for the follower, which in turn provides the optimal control strategy for the follower.

[0047] Will and Substituting the Hamilton equation into the follower's equation and rearranging, we obtain the coupled Hamilton-Jacobi-Bellman HJB equation. By solving the coupled Hamilton-Jacobi-Bellman HJB equation, we obtain the optimal control strategy of the virtual leader and the optimal control strategy of each follower.

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

[0049] Furthermore, by differentiating the value function V0(x0(t)) of the virtual leader, we obtain the Hamiltonian equation for the virtual leader as follows:

[0050]

[0051] in make The optimal control strategy for the virtual leader can be obtained by solving the problem.

[0052] Value function V for followers i (δ i Taking the derivative of (t), we obtain the Hamiltonian equation for the follower as follows:

[0053]

[0054] in make Solving for the optimal control strategy of the follower yields the solution. in

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

[0056]

[0057] The optimal control strategies for the leader and followers are obtained by solving the coupled Hamilton-Jacobi-Bellman (HJB) equations.

[0058] Furthermore, adjusting the weights of non-critical edges ensures a strong balance in the network, including:

[0059] Calculate the in-degree difference of each user node in a social network.

[0060]

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

[0063]

[0064] If the difference between in and out degrees If the difference between in-degree and out-degree is greater than zero, then reduce the weight of the outgoing edges; if the difference is less than zero, then reduce the weight of the outgoing edges. If the value is less than 0, reduce the weight of the incoming edges; continue until the difference between the in-degree and out-degree is reached.

[0065] Update node status.

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

[0067] The directed graph construction and edge partitioning module is used to construct a social network model of a directed graph and partition it into key edges and non-key edges.

[0068] The Virtual Leader-Follower Structure Building Module is used to construct a virtual leader-follower structure based on the constructed directed graph social network model to optimize the cooperative benefits between individuals and groups.

[0069] The HJB coupling equation construction and optimal control module is used to construct the Hamilton-Jacobi-Bellman (HJB) coupling equation and dynamically adjust the weights of key edges using an optimal control strategy.

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

[0071] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a social network balancing optimization method based on dynamic weight adjustment as described above.

[0072] A computer-readable storage medium storing a computer program that, when executed by a processor, implements a social network balancing optimization method based on dynamic weight adjustment as described above.

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

[0074] To address the shortcomings of existing weight adjustment strategies, this invention proposes a social network balancing optimization method based on dynamic weight adjustment. By optimizing the information flow propagation mechanism, the reliance on key nodes is reduced, improving network robustness. Furthermore, a learning intensity-based measure of trust is adopted instead of a learning intensity-based measure between nodes, enabling synchronized updates based on node behavior over time and more accurately capturing state changes between nodes. Finally, a weight reduction strategy is employed, eliminating the weights of unimportant edges during iteration to reduce the computational load of the network.

[0075] This invention possesses broad application potential, particularly in the field of social networks, such as Weibo, Facebook, and Instagram. By optimizing the information flow dissemination mechanism, this invention can significantly enhance user engagement on social platforms. Furthermore, the implementation of this invention is not limited to existing social platforms; it also has the capability to extend 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, this invention will drive the development of social network platforms towards a more intelligent, efficient, and user-friendly direction, providing a superior social experience for users worldwide. Attached Figure Description

[0076] Figure 1 A flowchart of the social network balance optimization method based on dynamic weight adjustment of the present invention;

[0077] Figure 2 A graph showing the changes in node states in a social network after applying the method of this invention;

[0078] Figure 3 A trend diagram of edge weight changes in a social network after applying the method of this invention;

[0079] Figure 4 The diagram illustrates the process by which a network gradually evolves from an initial unbalanced state to a balanced state through adjustments made by the strategy of this invention. Detailed Implementation

[0080] The specific implementation of the present invention is described below with reference to embodiments:

[0081] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0082] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0083] Example 1:

[0084] Please refer to the instruction manual appendix. Figure 1-4 A social network balance optimization method based on dynamic weight adjustment includes the following steps:

[0085] S1. Construct a directed graph social network model, dividing it into critical edges and non-critical edges, specifically including:

[0086] Directed graphs: In a directed graph, vertices represent individual users, and directed edges represent asymmetric relationships between users, such as following or friend requests, to accurately depict the structure and information flow of interpersonal networks. Each directed edge points from one user to another, representing the relationship between the former and the latter, or the direction of information flow. Based on the interaction relationships between individual users, a directed graph model is built, quantifying the interaction relationships between each node and its neighbors, and initially setting the weights of each edge.

[0087] In this example, consider a social network consisting of N=10 users, and model it using a directed graph G. Let be the adjacency matrix and edge set. From key edge set and non-critical edge set Composition, a directed graph G consisting of nodes v i Representing users, edge weights This represents the strength of influence between users. In the initial state, the cooperation status of each node and the influence weight of the edge are randomly set between 0 and 1.

[0088] Key edges and non-key edges: Based on the directed graph model constructed above, edges containing strongly connected components are designated as key edges to ensure network connectivity. Other edges are designated as non-key edges. The weights of key edges are updated based on the node states in the network, while the weights of non-key edges can be directly adjusted.

[0089] Strongly connected components: A strongly connected component is a strongly connected graph in which no other nodes can be added to maintain its strong connection. In other words, a strongly connected component is a strongly connected graph that cannot be further expanded.

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

[0091] In this example, a sequence is defined. Let G be the largest connected component of the directed graph G, which is the set of edges consisting of key edges, and the other edges are non-key edges.

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

[0093]

[0094] Where x i x j Representing node v respectively i v j The state of cooperation Indicates the relationship with node v i The number of neighboring nodes with interactive relationships, m ij are elements of the adjacency matrix, where c and b represent the loss and gain parameters of node fitness, respectively.

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

[0096] In this example, the edge weights Calculate using 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 emanating from that node (i.e., the relationships between the user and other users), while the in-degree is the sum of the weights of all edges pointing to that node (i.e., the relationships between other users and that user). Out-degree and in-degree reflect a 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 emanating from that node, i.e. The in-degree is the sum of the weights of all edges pointing to that node, i.e.

[0101] S2. Introduce a virtual leader-follower structure to enhance the benefits of cooperation between individuals and the group, specifically including:

[0102] Virtual Leader-Follower Structure: The main responsibility of the virtual leader is to improve the overall cooperation efficiency while minimizing direct intervention in the followers; all users in the directed graph G are 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 generally refer to the positive effects gained through cooperation or interaction between individuals, such as information sharing, resource exchange, or social support. The higher the willingness to cooperate, the greater the potential gains for participants (all users in the network). Losses, on the other hand, refer to the reduction in value caused by negative factors such as conflict, misunderstanding, or resource depletion. The concepts of gains and losses help in understanding the dynamics and stability of interpersonal relationships in social networks.

[0104] In this example, to ensure the highest overall cooperation state across all nodes, the virtual leader is selected as the user individual with the highest cooperation state in each iteration. The cooperation state refers to the node state, i.e.:

[0105]

[0106] Where, x i For individual users v i The cooperative state is defined as follows: x0 represents the state of the virtual leader, and t represents the current iteration number.

[0107] S3. Construct the Hamilton-Jacobi-Bellman (HJB) coupling equation and apply the optimal control strategy to dynamically adjust the weights of the key edges.

[0108] Optimal Control Strategy: Optimal control theory is a method applied to mathematics and engineering that uses mathematical models to find the optimal strategy or decision to achieve a certain goal under given conditions. In social networks, the strategy adjustments of virtual leaders and followers can be viewed as a dynamic system, where the behavior of the virtual leader can influence 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, propagation efficiency, or stability. Simultaneously, followers can also use this theory to optimize their behavior to adapt to or respond to the leader's strategies, thereby achieving optimal individual or collective interests within the social network.

[0109] In this example, we first consider a social network consisting of a set of identical nodes, where identical nodes are those with the same dynamic model (node ​​attributes). The network dynamic model is given by the following equation:

[0110]

[0111] Where A is the state transition matrix and B is the control input matrix. This represents the input to the control strategy.

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

[0113]

[0114] To construct the Hamilton-Jacobi-Bellman (HJB) coupling equation, its performance function is constructed based on the characteristics of the virtual leader and followers as follows:

[0115]

[0116] Where J0 represents the performance function of the virtual leader, J i The performance functions of the followers are S0 and S... i Q i R i It is a positive definite matrix, δ i For node state tracking error, This represents the change in the weight of the key edge. For node v i The set of connected critical edges.

[0117] The value functions for the virtual leader and followers are then constructed as follows:

[0118]

[0119] To find the optimal control strategy (optimal weight change), the derivative of the virtual leader's value function V0 is taken, yielding the Hamiltonian equation for the virtual leader:

[0120]

[0121] in make The optimal control strategy for the virtual leader can be obtained by solving the problem.

[0122] Similarly, the value function V for the follower i Differentiating, we obtain the Hamiltonian equation for the follower:

[0123]

[0124] in make Solving for the optimal control strategy of the follower yields the solution. in

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

[0126]

[0127] The optimal control strategy for the virtual leader and the optimal control strategy for each follower can be obtained by solving the coupled HJB equations. This is referred to as the optimal control strategy, which adjusts the weights of 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 network balance.

[0129] Adjusting the weights of non-critical edges involves the following steps:

[0130] Step S41: Calculate the difference between the in-degree and out-degree of each individual user node in the social network.

[0131] In this example, for each node, node v is calculated using the following formula. i In-degree difference:

[0132]

[0133] Step S42: If the difference is greater than zero, reduce the weight of the outgoing edge; if the difference is less than zero, reduce the weight of the incoming edge.

[0134] Step S43: Update node status.

[0135] Figure 2 The evolution trend of cooperation strategies in a social network with 10 nodes is presented. Initially, the cooperation state of each node is a random value between 0 and 1, where 0 represents no cooperation and 1 represents full 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 states of the nodes fluctuate greatly, reflecting the uncertainty and exploration process of the nodes in the early stages regarding cooperation strategies. Subsequently, by applying steps S3 and S4 of this invention, namely the weight adjustment strategy, these fluctuations gradually decrease, and the cooperation states of the nodes begin to stabilize. Further scaling up... Figure 2 The details reveal that the state of all nodes stabilizes within 10 iterations. This rapid stabilization process is crucial for understanding and designing effective social network cooperation mechanisms. It not only demonstrates 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 trend of edge weight changes among 10 nodes in a social network, with different colored lines representing the dynamic weights of different edges. In the initial iteration steps, Figure 3 The enlarged illustration reveals the significant changes in edge weights. Lines of different colors represent the dynamic weights of different edges in the network. These weight fluctuations demonstrate the instability of relationships between nodes and their adjustments in the process of finding the optimal cooperation strategy. As iterations proceed, the edge weights gradually stabilize, eventually converging to a constant value of 0.5, indicating that the interactive learning relationships between nodes have reached a state of equilibrium.

[0137] Figure 4 This demonstrates the process by which a network gradually evolves from an initial unbalanced state to a balanced state through adjustments made using the strategy of this invention. Figure 4 (a) Uneven weight distribution of nodes and edges in the network leads to an unbalanced network structure. By applying the weight adjustment strategy proposed in this invention, the following can be obtained: Figure 4 (b) At this point, each node in the network has the same in-out degree, and the weights of all edges become consistent, forming a balanced network structure. The strategy of this invention, by continuously adjusting the edge weights, not only balances the in-out degree of each node but also promotes the transformation of the network from an unbalanced state to a strongly connected balanced state. This adjustment method effectively optimizes the overall performance of the network, ensuring a balanced distribution of influence among each node in the network.

[0138] Example 2:

[0139] This embodiment provides a terminal device, which includes a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes 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 (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or function. The processor described in this embodiment can be used to operate a social network balancing optimization method based on dynamic weight adjustment, including the following steps:

[0140] Construct a directed graph social network model and divide it into critical edges and non-critical edges;

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

[0142] Construct the Hamilton-Jacobi-Bellman HJB coupling equation and dynamically adjust the key edge weights using an optimal control strategy;

[0143] Based on the strong equilibrium 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] Example 3:

[0145] This embodiment provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

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

[0147] Construct a directed graph social network model and divide it into critical edges and non-critical edges;

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

[0149] Construct the Hamilton-Jacobi-Bellman HJB coupling equation and dynamically adjust the key edge weights using an optimal control strategy;

[0150] Based on the strong equilibrium 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 understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied 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] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0153] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0154] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0155] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

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

Claims

1. A social network balancing optimization method based on dynamic weight adjustment, characterized in that, The method comprises: constructing a social network model based on a directed graph, dividing key edges and non-key edges; based on the constructed social network model of the directed graph, constructing a virtual leader-follower structure to optimize the cooperation benefits of individuals and groups; constructing Hamilton-Jacobi-Bellman (HJB) coupled equations, and dynamically adjusting the weights of key edges by using optimal control strategies; based on the strong equilibrium state of the network, adjusting the weights of non-key edges by implementing a weight adjustment mechanism, and then iteratively updating the weights to achieve the overall optimization goal of the network; introducing a virtual leader-follower structure to improve the cooperation benefits of individuals and groups, which specifically includes: the state of the virtual leader is the user individual with the highest cooperation state in each iteration process, and the other users are followers, and the cooperation state of the virtual leader is represented as: ； wherein is the state of the user individual, is the state of the cooperation, is the state of the virtual leader, is the current iteration number; constructing Hamilton-Jacobi-Bellman (HJB) coupled equations, and dynamically adjusting the weights of key edges by using optimal control strategies, which specifically includes: assuming that the dynamic model of each node in the social network is the same, which is represented as: ； wherein is a state transition matrix, is a control input matrix, denotes an input of the control strategy; Defining a state tracking error between a follower and a virtual leader As follows: ； the performance function of the virtual leader is designed as follows: ； ； wherein, a state of being a virtual leader, a state of being a follower, a control input for the virtual leader; the performance function of the follower is designed as follows: ； ； wherein, is a state tracking error between the follower and the virtual leader, is a weight change amount of the critical edge, is a set of critical edges connected to the node ; Constructing value function for virtual leader Value function for follower ; ； , , , is a positive definite matrix, is a weight change of a key edge, is a set of key edges connected to node . Value function for virtual leader Taking the derivative, we obtain the Hamiltonian equations for the virtual leader, which are solved to obtain the optimal control policy for the virtual leader ; Value function for follower Derive the Hamiltonian equations for the follower, and solve for the optimal control policy for the follower ; Will and Substituting the Hamilton equation into the follower's equation and rearranging, we obtain the coupled Hamilton-Jacobi-Bellman HJB equation. By solving the coupled Hamilton-Jacobi-Bellman HJB equation, we obtain the optimal control strategy of the virtual leader and the optimal control strategy of each follower. adjusting the weights of key edges in the social network according to the optimal control strategy of the virtual leader and the optimal control strategy of each follower. 2.The social network balancing optimization method based on dynamic weight adjustment of claim 1, wherein, constructing a social network model based on a directed graph, including nodes and edges, and then determining strongly connected components, marking the edges contained in the strongly connected components as key edges; the edges not in any strongly connected component are marked as non-key edges; iteratively updating the weights of key edges and non-key edges respectively until the weights of all edges are the same or the cooperation states of each node no longer change or reach a set number of iterations.

3. The social network balancing optimization method based on dynamic weight adjustment according to claim 1, characterized in that, The construction of the social network model based on the directed graph comprises: a social network of users, employing a directed graph modeling the social network; is an adjacency matrix; edge set consisting of key edge sets and non-key edge sets consisting; directed graph of nodes representing users, weights of edges representing strength of influence between users; initial state, the cooperation state of each node and the weight of the edge are randomly set to 0-1; In the social network model of the directed graph, a node fitness function is introduced as follows : ； wherein represents the cooperation state of a node , represents the cooperation state of a node , represents the number of neighbor nodes that have an interaction relationship with a node , is an element of the adjacency matrix, , respectively represent the loss and gain parameters of the node fitness. weight of an edge is calculated by the following equation: ； wherein , , are adjustable parameters.

4. The social network balancing optimization method based on dynamic weight adjustment according to claim 1, characterized in that, Value function for virtual leader Taking the derivative, the Hamiltonian equations for the virtual leader are given by ； wherein , let , solve for the optimal control policy of the virtual leader ; Value function for follower Taking the derivative, we obtain the Hamiltonian equations for the follower as follows: ； wherein , let , solve for the optimal control strategy of the follower wherein ; Substitute the Hamiltonian into the follower's Hamiltonian equation, organize and simplify, and obtain the coupled Hamilton-Jacobi-Bellman (HJB) equation as follows: and Substitute the Hamiltonian into the follower's Hamiltonian equation, organize and simplify, and obtain the coupled Hamilton-Jacobi-Bellman (HJB) equation as follows: ； solving the coupled Hamilton-Jacobi-Bellman (HJB) equations to obtain the optimal control strategy of the leader and the optimal control strategy of the follower.

5. The social network balancing optimization method based on dynamic weight adjustment according to claim 1, characterized in that, adjusting the weights of non-key edges to ensure the strong equilibrium state of the network, including: Computing the out-degree minus in-degree of each user individual node in a social network ; ； wherein, out-degree of a node , is the sum of the weights of all edges emanating from the node , denoted as: ; in-degree of a node The in-degree of a node, denoted by di, is the sum of the weights of all edges pointing to the node, denoted as: ； If the out-in degree difference is greater than zero, reduce the out edge weight; if the out-in degree difference is less than 0, reduce the in edge weight; until the out-in degree difference =0; updating the node state.

6. A social network balancing optimization system based on dynamic weight adjustment, the system comprising: The system is used to perform the method of any one of claims 1-5, and the system comprises: a directed graph construction and edge division module for constructing a social network model based on a directed graph, dividing key edges and non-key edges; a virtual leader-follower structure construction module for constructing a virtual leader-follower structure based on the constructed social network model of the directed graph to optimize the cooperation benefits of individuals and groups; an HJB coupled equation construction and optimal control module for constructing Hamilton-Jacobi-Bellman (HJB) coupled equations and dynamically adjusting the weights of key edges by using optimal control strategies; a weight adjustment and iterative update module for adjusting the weights of non-key edges by implementing a weight adjustment mechanism based on the strong equilibrium state of the network, and then iteratively updating the weights to achieve the overall optimization goal of the network.

7. A computer device, comprising: a computer program stored on a memory and executable on a processor, wherein the processor executes the program to implement the social network balance optimization method based on dynamic weight adjustment of any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is executed by the processor to implement the social network balancing optimization method based on dynamic weight adjustment in any one of claims 1 to 5.

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