Deep reinforcement learning and graph neural network driven dynamic social network competition influence maximization method and system

Abstract

The invention discloses a dynamic social network competition influence maximization method and system based on deep reinforcement learning and graph neural network driving, relates to the field of social network competition influence maximization, and aims to solve the problem that an existing method cannot fully capture complex dynamic characteristics of an actual propagation situation of a real social network. According to the technical key points, the method comprises the following steps: S100, collecting a dynamic social network data set; s200, a Q network based on StateGNN and InfGNN is constructed, the StateGNN is used for capturing and updating state information of nodes, the InfGNN is used for modeling influence features of the nodes, multi-head attention is introduced for feature extraction and fusion, and the nodes are guided to perform selective operation according to time information when neighborhood features are aggregated in the out direction and the in direction; s300, training a Q network model based on DDQN; s400, inputting the dynamic social network into the trained Q network to calculate a Q value of a node, and constructing a target seed set; and S500, inputting the target seed set into the DCIC model for propagation to complete an influence maximization process.

Description

Technical Field

[0001] This invention relates to the field of competitive influence maximization technology in social networks, and more specifically, to a method and system for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks. Background Technology

[0002] The influence maximization (IM) problem originated in an important area of ​​social network analytics. Its core objective is to identify and activate k key nodes (or users) within a social network, aiming to maximize the reach of influence through the spread of these nodes' influence. The IM problem has wide applications in real-world scenarios such as viral marketing, public opinion monitoring, and public health interventions. For example, businesses may want to reach the widest possible user base with minimal cost, or government departments may need to quickly identify key nodes to curb the spread of rumors.

[0003] In recent years, although some research [7-10] Attempts have been made to extend the influence maximization problem to dynamic network environments with single-entity competition, or to explore the multi-entity maximization competition problem on traditional static networks. [11-15] However, current research is mostly confined to the traditional static network framework, failing to fully capture the complex dynamic characteristics of real-world social networks. Furthermore, traditional methods often focus on the diffusion process of a single entity, similarly neglecting the complexity of actual propagation scenarios. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing methods have failed to fully capture the complex dynamic characteristics of real-world social network propagation scenarios.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks, comprising the following steps:

[0008] S100, Collect dynamic social network datasets;

[0009] S200. Construct the DDQN deep reinforcement learning neural network model Q network. The Q network model is based on two collaborative graph neural networks, StateGNN and InfGNN. StateGNN is used to capture and update the state information of nodes, and InfGNN is used to model the influence features of nodes. Multi-head attention is introduced to further extract and fuse features to obtain more accurate influence features of nodes. A time-based aggregation mechanism is introduced into the network to guide nodes to perform selective operations based on time information when aggregating neighborhood features in the outgoing and incoming directions, respectively.

[0010] S300, Q-network model trained based on DDQN;

[0011] S400. Input the dynamic social network into the trained Q-network model to calculate the Q value of each node, select seed nodes based on the seed selection strategy, and obtain the target seed set.

[0012] S500: The target seed set is input into the Dynamic Competitive Independent Cascaded Propagation (DCIC) model for propagation to simulate the complex dynamic changes in real networks and the competitive influence between different entities, thereby maximizing the influence process.

[0013] The present invention also provides a competitive influence maximization system for dynamic social networks driven by deep reinforcement learning and graph neural networks. The system has program modules corresponding to the steps of the method described above, and executes the steps in the above-described method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks when running.

[0014] The present invention also provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps in the method for maximizing competitive influence in a dynamic social network driven by deep reinforcement learning and graph neural networks as described in the above technical solution.

[0015] Compared with the prior art, the beneficial effects of the present invention are:

[0016] This invention proposes a Dynamic Competitive Independent Cascaded Propagation (DCIC) model, aiming to accurately simulate the complex dynamic competitive scenario of maximizing influence in real social networks, and defines the Competitive Influence Maximization (DCIM) problem in dynamic social networks. For the DCIM problem, this invention constructs an end-to-end model architecture, D2G-DCIM, which can efficiently solve this challenging task. In D2G-DCIM, a time-based aggregation mechanism is designed to conform to the information propagation process of DCIC. This mechanism guides nodes to perform selective operations based on time information when aggregating neighborhood features, thereby more effectively learning the node's embedded representation. Furthermore, two collaborative graph neural networks (GNNs) are used to model the node's influence features, and multi-head attention is used to further learn these features to obtain more accurate node influence features. Attached Figure Description

[0017] Figure 1 This is an example diagram of the DCIC propagation process in an embodiment of the present invention;

[0018] Figure 2 This is a general framework diagram of D2G-DCIM in an embodiment of the present invention;

[0019] Figure 3 This is a diagram of the Q-network structure in an embodiment of the present invention;

[0020] Figure 4 This is an example diagram of a time-based aggregation mechanism in an embodiment of the present invention;

[0021] Figure 5 As described in the embodiments of the present invention Structural diagram;

[0022] Figure 6 As described in the embodiments of the present invention Structural diagram;

[0023] Figure 7 This is a diagram showing the propagation range under different seed selection strategies in embodiments of the present invention;

[0024] Figure 8 A comparison chart showing the time required to select 50 nodes on different datasets using different strategies in this embodiment of the invention;

[0025] Figure 9 The different algorithms in the embodiments of the present invention are in the competitive seed set. / A diagram showing the propagation range under different conditions;

[0026] Figure 10 The different algorithms in the embodiments of the present invention are in the competitive seed set. / A diagram showing the propagation range under different conditions;

[0027] Figure 11 This is a runtime graph of different algorithms in the embodiments of the present invention. Detailed Implementation

[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0029] 1. Construction of DCIC Model

[0030] First, let's define dynamic social networks: given a dynamic directed graph... ,in, Represents a set of nodes. Let n represent the set of edges, where n and m are the number of nodes and edges, respectively. Each edge... , and Let these represent the starting and ending nodes of the edge, respectively. It is a discrete time set representing edges Existing in the graph at these specific moments middle.

[0031] In the DCIC model, two competing entities, A and B, vie for the opportunity to activate nodes within the network. Each edge in the network... There is an activation probability. This reflects the probability that node v will be activated by node u. Once a node is successfully activated by A or B, it will permanently belong to that entity, can only propagate the influence of that entity, and remains unchanged throughout the propagation process. In the DCIC model, each node has an activation time. The information dissemination process must be based on The existence time of the edges is determined together. Given the seed sets of two entities A and B. and ( The propagation process is as follows:

[0032] (1) At t=0, all nodes The activation time is set to The remaining nodes The activation time is set to This indicates that they have not yet been activated.

[0033] (2) At each time step, each newly activated node u has one and only one chance to try to activate its inactive neighbor node v. If u will try to apply probability to v Activate. If v is successfully activated, the activation time of v is set to... Specifically, if node v receives activation requests from entities A and B simultaneously and is successfully activated, it will randomly choose to accept one of the requests.

[0034] (3) This process will continue until no new activated nodes appear.

[0035] like Figure 1 The diagram provides an intuitive and concise example of the DCIC propagation process. Therefore, there is =0. At t=0, node 2 successfully activated node 6 first: Node 4 attempted to activate node 7 but failed. Node 2 and Node 4 jointly attempted to activate node 3 and both successfully activated it. According to the random principle, Node 3 accepted the activation from Node 4 and joined its entity B. At t=1, the newly activated node 6 attempted to activate node 5, but due to... The conditions were not met, so node 6 could not activate node 5. Node 6 attempted to activate node 7 and successfully activated it. Since node 7 can no longer activate other nodes, the entire influence propagation process ends here. Entity A ultimately influenced the node set {2, 6, 7}, while entity B included nodes {3, 4}.

[0036] Dynamic Social Network Competitive Influence Maximization (DCIM) is defined as follows: Given a dynamic social network... The initial seed set of competing entities Given a positive integer k, the objective of the dynamic social network competitive influence maximization problem is to find a seed set containing k target entities under the DCIC model. , making In The number of activated nodes is maximized under competitive conditions, which affects the diffusion function. Maximum. Mathematically expressed as:

[0037]

[0038] in, This represents the influence diffusion function, i.e., the target seed set. In the competition seed The expected number of nodes to be activated under certain conditions.

[0039] 2. Construction of the D2G-DCIM Framework

[0040] like Figure 2As shown, the overall framework of D2G-DCIM (DRL and Dual GNNs for Dynamic CompetitiveInfluence Maximization) consists of two main phases: a training phase and a seed selection phase. In the training phase, a graph is randomly selected from a pre-defined training graph set as input. This graph, along with the initial state vector, is then fed into a Q-network. The Q-network calculates a Q-value for each node, reflecting its potential influence as a seed node. Next, based on these Q-values, a seed selection phase is adopted. A greedy strategy selects seed nodes and awards them a reward, along with an updated state. This process continues until the number of selected seed nodes reaches a preset size. Throughout the training phase, these steps are repeated multiple times, iteratively updating the parameters Θ of the Q-network to optimize its performance. In the seed selection phase, the trained Q-network is used to process the input test graph. This phase also calculates the Q-value of each node, but a more refined seed selection strategy P is used to select the seed node.

[0041] 2.1Q Network Design

[0042] Previous studies have often relied on extensive simulations or sampling to estimate the diffusion of effects, a time-consuming process that limits the model's generalization ability. Inspired by deep learning techniques, this invention introduces DRL technology to alleviate this problem of simulation and sampling intensity. First, the DCIM problem is defined as a DRL problem, with the components defined as follows:

[0043] State: State It is a |V|-dimensional vector, where V is the set of all nodes in the graph. It is composed of... and The composition of the graph, for each node If node v has been selected as the seed node of entity A (i.e., it has been added to the seed set), Then the elements in the corresponding state vector Otherwise, it is 0. Furthermore, for ,set up The state vector describes the current state of the seed set: 0 indicates that no selection has been made, 1 indicates that it has been selected by entity A, and 2 indicates that it belongs to entity B.

[0044] Action: A movement This means selecting a node from the set of nodes that have not yet been selected as a seed node and adding it to the seed set. In each step, the agent needs to select an action based on the current state.

[0045] In the context of the IM problem, the reward is defined as the reward in the current seed set. Next, select a new node v to add to the seed set. The marginal gain after that, i.e. .

[0046] Transition: When a node is selected to be added to the seed set back A change from 0 to 1 results in a new state. .

[0047] Policy: Based on the current state Determine the action the agent should take. In the DCIM problem, the goal of the strategy is to maximize the cumulative reward, that is, to find a seed set such that the number of nodes that can be affected through influence propagation is maximized.

[0048] In the DRL domain, DDQN

[16] As a classic algorithm, DDQN has been widely applied due to its excellent performance. Therefore, the DDQN architecture was chosen as the model training framework. In DDQN, the Q-network plays a central role. Designing a Q-network with an appropriate structure is crucial for different problems. The Q-network cleverly integrates two cooperating graph neural networks and multi-head attention to obtain the embedded representations of nodes. Subsequently, these embedded representations are used to compute the Q-value of each node, thus supporting seed selection in the decision-making process.

[0049] 2.1.1 Node Embedding Representation

[0050] Traditional graph embedding methods, such as DeepWalk

[17] node2vec

[18] These methods primarily rely on sequences generated by node traversal and Skip-Gram models to train multidimensional embedding representations of nodes. While these methods excel at capturing structural features of graphs, they suffer from two main drawbacks: first, they fail to effectively measure the influence range of nodes; and second, their generalization ability is limited, making them difficult to apply directly to different graph structures.

[0051] To overcome these limitations, this invention introduces a graph neural network (GNN) modeling paradigm. The core reason is that a node's potential influence in a social network is strongly correlated with its neighborhood topology—the more neighbors a node has, the greater its influence should be. This characteristic is inherently consistent with the principle of GNNs, which capture higher-order dependencies of nodes through multi-layer neighborhood aggregation mechanisms. Furthermore, this invention can improve generalization ability by training parameters on small-scale graphs and then applying them to different graphs.

[0052] The two collaborative graph neural networks are StateGNN and InfGNN. StateGNN focuses on modeling the state information of nodes, while InfGNN focuses on modeling the influence features of nodes. Through the close collaboration of these two networks, more accurate and richer node embedding representations are generated.

[0053] However, since traditional GNNs are mainly applied to static graphs and cannot capture the dynamic features of graphs, this invention constructs a time-based neighborhood information aggregation mechanism. This mechanism not only considers the direct connections between nodes but also incorporates the time dimension, enabling the model to intelligently filter and aggregate neighborhood node information based on time information.

[0054] (1) Time-based aggregation mechanism

[0055] In DCIC, the propagation of influence depends not only on the connections between nodes but also strictly on the existence time of those connections. Therefore, it is inappropriate to directly and indiscriminately aggregate information from all neighboring nodes when aggregating neighborhood information. To better reflect the propagation process of DCIC, the time factor must be taken into account, and only the information from neighboring nodes that meets the time requirements should be aggregated.

[0056] by Figure 1 Taking node 2 as an example, if the time factor is ignored, node 2 can receive information from nodes 3 and 6 in the first information aggregation phase. In the second round of aggregation, it can further acquire information from nodes 5 and 7. However, in the DCIC model, strict timing constraints must be followed: the connection time between node 2 and node 6 is 1, while the connection time between node 6 and node 5 is 0. This means that, according to the time sequence, node 2 cannot form an effective propagation channel with node 5. Therefore, in the actual information aggregation process, node 2 should not include the information from node 5 in its aggregation scope.

[0057] To accurately determine the effective propagation path for each node, directly traversing the entire graph to obtain precise results is often extremely time-consuming, which is impractical. Therefore, this invention employs a simplified method. In the first round of information aggregation, all nodes aggregate information from all their direct neighbors. In subsequent aggregation rounds, the judgment process is optimized: if the maximum timestamp in the edges connected to a node's neighbor is not less than the timestamp at which the node is connected to that neighbor, then the neighbor's information is considered to be aggregateable.

[0058] While this simplification method may exaggerate the actual influence range of nodes to some extent, it significantly improves the efficiency of information aggregation. This trade-off allows for a relatively reasonable approximate estimate of the information propagation range while maintaining high computational speed.

[0059] Based on this concept, this invention proposes time-based neighborhood information aggregation mechanisms for both outgoing and incoming directions. The specific aggregation steps of this mechanism are as follows:

[0060] 1) Initialize the time when nodes can transmit information and the time when they can be aggregated. First, two key parameters need to be set for each node u: and , representing the time when a node can transmit information in the inbound direction and the time when it can be aggregated in the outbound direction, respectively, and initialized. , This ensures that the first round of aggregation can reach all neighbors, without needing to consider the time factor in the first round.

[0061] 2) Select neighboring nodes to be aggregated. For the inbound direction (i.e., the direction of information flow towards the current node), the aggregation time of the inbound neighboring node must be less than or equal to a certain point in the time interval of the edge's existence; only then can information be transmitted from node u to node v. For each inbound edge... , It is the edge The set of existing discrete time points needs to be transformed into ,in, For outgoing directions (i.e., the direction from the current node to other nodes), the aggregation time of outgoing neighbor nodes must be greater than or equal to a certain point in the edge's time interval for the influence of u to be transmitted to v. For each outgoing edge... It needs to be converted ,in, .

[0062] 3) Merging Parallel Edges. After selecting neighboring nodes that can be aggregated, parallel edges may be encountered, meaning there are multiple edges connecting the same pair of nodes with different time attributes. To simplify the process and avoid redundancy, parallel edges need to be merged. For inbound edges, they are merged into a single edge, whose time attribute is the earliest time point among all parallel edges, i.e. ,in, It only contains the earliest time point. Similarly, for the outgoing direction, therefore, for parallel edges in the outgoing direction, the merging rule is similar to that for the incoming direction, i.e. ,in, Using the earliest edge existence time as the time of merging subsequent edges is a strategy aimed at aggregating information to a greater extent.

[0063] 4) Neighborhood Aggregation and Node Embedding Representation Update. After obtaining the merged edge set, a neighborhood aggregation operation is performed, and the node embedding representation is updated accordingly. The specific steps of this process will be described in detail in StateGNN and InfGNN.

[0064] 5) Update and Specifically, It should be updated to the minimum existence time of all edges pointing to node u. , ;if or Then let and It is -1.

[0065] 6) Repeat steps 2)-5) until the specified number of times is reached.

[0066] To better understand this process, Figure 4 For example, Figure 4 The upper part represents the aggregation process of the two rounds in the inbound direction, the lower part represents the aggregation process in the outbound direction, and the left side represents the node u of each round. and The value is explained in the outward direction. In the first round, it is selected that no neighboring nodes need to be selected. Then, parallel edges are merged according to the rules mentioned above, and finally, the value is updated. : (Because node 1 has no incoming neighbors). Similarly, we can obtain In the second round, neighboring nodes are selected first; for example, for an edge... ,have That is, retaining edges The entire time set for the edge ,have This means that the edge needs to be deleted. Repeat the same operation for the remaining edges, and finally merge the parallel edges.

[0067] (2) StateGNN

[0068] StateGNN is designed to capture and update the state information of nodes. First, based on the initial state of node u... and Perform initial state fusion, resulting in the initial state vector. The calculation is as follows:

[0069] (11)

[0070] in, and It is a learnable parameter matrix. This indicates that node u has been selected by entity A, otherwise This indicates that node u was not selected by entity A; This indicates that node u belongs to entity B. This indicates that node u does not belong to entity B. LeakyReLU is a non-linear activation function with a negative slope of 0.01.

[0071] StateGNN consists of R layers (R=3) of graphical convolutions. Composition, specific structure as follows Figure 5 As shown. The i-th layer The state vector of node u The update will be performed according to the following formula:

[0072] (12)

[0073] (13)

[0074] in, It is the state vector of node u in the (i-1)th layer. It is the edge The probability of propagation on the surface, It is a two-layer perceptron used to capture nonlinear relationships. It is based on the set of incoming neighbors of node u obtained through a time-based aggregation mechanism. Furthermore, to enhance the model's stability, a graph normalization layer, GraphNorm, is introduced.

[20] The state vector is normalized. and It is a learnable parameter matrix. It is a bias term.

[0075] (3) InfGNN

[0076] The purpose of InfGNN is to model the influence scale of nodes. It combines the current state of a node with the influence features of its neighboring nodes, and the initial influence feature vector of node u. It is a d-dimensional vector of all zeros, where d is set to 64. InfGNN consists of R layers (R=3) of graphical convolutions. composition, Structure such as Figure 6 As shown.

[0077] The i-th layer The formula for updating the node influence feature vector is as follows:

[0078] (14)

[0079] (15)

[0080] in, It is the edge The probability of propagation on the surface, It is a two-layer perceptron used to capture nonlinear relationships. It is based on the set of out neighbors of node u obtained through a time-based aggregation mechanism. It is a learnable parameter matrix. This is a bias term. Specifically, when aggregating neighbor information, already selected nodes are removed to better guide the model in learning node state information.

[0081] (4) Multi-head self-attention

[0082] After aggregation through the R layer, multi-head attention is used to further extract and fuse features from the results of each layer. Specifically, scaled dot product attention is replaced with additive attention to better suit the influence task. The specific process is as follows:

[0083] First, construct the input sequence: And use it as the query Q, key K and value V.

[0084] Linear transformation: For each head (there are H heads in total), perform different linear transformations on the query Q, key K, and value V to obtain the query for each head. ,key Sum :

[0085] (16)

[0086] (17)

[0087] (18)

[0088] in, , , It is a learnable parameter matrix.

[0089] Calculate the additive attention for each head: For each head h, calculate the additive attention. First, calculate the query... s and keys , ( yes The j-th row, yes (line l)

[0090] (19)

[0091] It is a learnable parameter vector, and then the attention weights are calculated. : (20)

[0092] Finally, the weights and values ​​are summed in a weighted manner to obtain the output for each head:

[0093] (twenty one)

[0094] yes The rth line.

[0095] Concatenation and Linear Transformation: Concatenate the outputs of all heads and perform a linear transformation to obtain the final output.

[0096] (twenty two)

[0097] in, This is the final linear transformation matrix. Finally, the results of the multi-head attention are summed, and after linear transformation and regularization, the final node embedding is obtained:

[0098] (twenty three)

[0099] in, It is a normalization layer. It is a learnable parameter matrix. yes The rth line.

[0100] 2.1.2 Q-value calculation:

[0101] Based on the node embeddings obtained above, the Q-value of each node is calculated for use in the seed selection decision process. The formula for calculating the Q-value is as follows:

[0102] (twenty four)

[0103] in, , It is a learnable parameter matrix. It is a two-layer sensor. It is the set of all parameters of the model.

[0104] To train the parameters in the model, the DDQN architecture is used for model training to obtain the optimal Q-function. DDQN is an improved version of DQN, which effectively reduces the DQN cost.

[19] Overestimation of Q-value. The loss function of DDQN uses the mean squared error (MSE) as the optimization objective, and the specific calculation formula is as follows:

[0105] (25)

[0106] in, , These are all the parameters in the target network model. It is the discount factor that determines the importance of future rewards.

[0107] Algorithm 1 details the training process. For each sequence, a training graph is first randomly selected from the dynamic training graph set, and the seed set is initialized. Then, based on... The strategy selects K seed nodes, that is, randomly selects a new node with probability ε to add to the target seed set. The node with the largest Q value is selected with a probability of 1-ε and added. Then the quadruple is placed into the experience buffer pool. Finally, it is retrieved from the experience buffer pool. A set of samples was randomly selected from the middle. Perform parameters Update, and use every m sequences Update target network parameters .

[0108] Algorithm 1: Training of DDQN Input: A set of training dynamic networks D, compete seeds ,Budget K, Episode L, Experience replay buffer JOutput: parameters . ;for episode e <- 1 to LdoRandomly select a training network from D ; ; ; Save training model every 10 episodes; <- +max(0, ( - ) ( -e +1) / );for do ;endfor t <- 1 to K doUniformly sample anumber c from [0, 1);if then Randomly select a node ;else for i = 1 to R do for doUpdate by (12)(13) Update by (14)(15) end for end for for doCalculate by (23); end forfor do Calculate by (24);end forend if Select ; Add to ; ;end forSample a random batch from ;Update by Adam optimizer with ;Update from Θ every mepisodes;end forreturn Θ.

[0109] 2.3 Seed Selection Strategy

[0110] In Li et al. [2] The study indicates that iterative seed node selection is nearly identical to the Top-k strategy. However, experimental results show that in smaller networks, the Top-k strategy exhibits a significant difference compared to the iterative strategy, while in large-scale networks, their performance is similar, but the iterative strategy is more time-consuming. Therefore, a compromise strategy is proposed for small-scale networks. This strategy does not directly select the Top-k nodes, but instead selects a certain number of nodes with the highest Q-values ​​in each iteration until the seed set size requirement is met. This strategy aims to balance efficiency and propagation range. For large-scale networks, the Top-k selection strategy continues to be used.

[0111] Algorithm 2: Seeds selection procedure Input: Dynamic network , Competitive seed set , Budget K,Parameters Θ, Strategy Output: Target seed set Initializetarget seed set ; ; for p dofor do ;endfor i = 1 to R dofor doUpdate by (12)(13);Update by (14)(15);end forend forfor doCalculate by (23);end forfor doCalculate by (24);end for - Select Top-p nodes by ; ; ; end forend if return .

[0112] Algorithm 2 describes the seed selection strategy. For a given dynamic network... Competitive seed set Budget K, trained parameters Θ, and policy First, initialize the target seed set. Initial state And the embedding vector for each node. Then, based on the trained parameters, the node embedding vector is obtained, and the Q-value is calculated based on this vector. Then, based on the given... Select a node to add to the target seed set. Finally, the target seed set is obtained. .

[0113] The competitive influence maximization method (algorithm) of dynamic social networks driven by deep reinforcement learning and graph neural networks proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0114] Based on the method proposed in this invention, a competitive influence maximization system for dynamic social networks driven by deep reinforcement learning and graph neural networks is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks during runtime.

[0115] The developed system (software) computer program is stored on a computer-readable storage medium, and the computer program is configured to implement the steps of the above-described method for maximizing the competitive influence of a dynamic social network driven by deep reinforcement learning and graph neural networks when invoked by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0116] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0117] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0118] The beneficial effects of the present invention will be described below with reference to specific embodiments.

[0119] Example 1

[0120] 1. Performance Comparison

[0121] Nine publicly available datasets were selected for the experiments. Hypertex t

[21] These are dynamic networks of face-to-face interaction collected during the ACM Hypertext 2009 conference; High-School

[21] It is a network of connections among high school students in Marseille, France. (email-Eu-core)

[22] It is the targeted email network involved in the 2016 Democratic National Committee email leak; Mammalia

[22] It is an interaction network of voles; an interaction is counted whenever two voles are trapped in at least one shared trap. (CollegeMsg)

[22] It consists of private messages sent on an online social network at the University of California, Irvine; Tech-As-Topology

[22] It is a network connecting autonomous systems on the Internet; Slashdot-Threads

[23] It is the reply network of the technology website Slashdot; Epinions

[23] It is a user trust network for the online social networking site Epinions; Digg-Friends

[23] This is a directed friendship network collected by Digg in 2009. A detailed description of the dataset is shown in Table 1.

[0122] Table 1

[0123]

[0124] The D2G-DCIM proposed in this invention will be compared with the following algorithms in terms of performance:

[0125] Degree: Degree is a heuristic method based on node degree, which selects the seed node by the out-degree of the node.

[0126] Degree Discount [5] It also uses a heuristic selection based on degree, but further considers the issue of overlapping influence between nodes. When a node is selected as the seed node, the degrees of its neighboring nodes are discounted accordingly to reduce overlapping effects.

[0127] Dynamic Degree [4] This method is similar to the Degree algorithm, but it is based on dynamic graphs and can more accurately reflect the dynamic information of the graph.

[0128] Dynamic Degree Discount [4] Dynamic Degree Discount is a dynamic version of the Degree Discount algorithm, calculated based on the Dynamic Degree of nodes.

[0129] Dynamic CI [4] Dynamic CI extends the traditional CI algorithm for static graphs to dynamic graphs, enabling it to adapt to dynamic changes in the graph.

[0130] Lazy Greedy

[10] Lazy Greedy can significantly reduce the number of computations without changing the output of the greedy algorithm, achieving speedups of up to 700 times, and can reach [a certain speedup] in DCIM problems. An approximate solution.

[0131] Entropy Based [6] It is a centrality measurement method based on entropy, which comprehensively considers time information and neighborhood information to calculate the entropy value of a node, and evaluates its importance by calculating the entropy value of the node.

[0132] S2V-DQN [1] An algorithm using DRL (Device Logic Reduction) to solve the graph combinatorial optimization problem, employing Chen... [3] The code was modified by others to suit IM tasks.

[0133] ToupleGDD [3] A novel model for applying DRL to solve traditional IM problems, with good generalization ability.

[0134] During the model training phase, firstly, 10 random dynamic graphs are generated as training datasets, each containing 50 to 100 nodes. Specifically, for each dynamic graph, this invention employs the Erdős-Renyi (ER) random graph model (with edge connection probabilities set to 0.002), generating 100 to 200 snapshots. These snapshots are then used to construct a dynamic graph. Considering the time-sensitivity of dynamic networks, recently active interactions are given higher weight in information propagation; therefore, the edge probability is calculated based on the following formula. The probability of :

[0135] (26)

[0136] in, This refers to the number of snapshots, i.e., the maximum duration of a snapshot. The formula above calculates the difference between the duration of each edge's existence and the maximum duration of a snapshot. A quadratic function is then used to make the weight of the edge decrease as the difference increases, and a min function ensures the minimum value is not zero. The numerator part represents the edges... The number of interactions is weighted and summed based on time, while the denominator is the weighted sum of the number of interactions between node v and all its incoming neighbor nodes. For all test network graphs, self-loops are first removed, then the times on the edges are renumbered starting from 0, and the probabilities on the edges are set using the formula described above.

[0137] During training, the exploration probability ε linearly decays from 1 to 0.05 and remains thereafter until training ends. Using the Monte Carlo method, 10,000 simulations are performed to obtain the mean of the propagation range, which is used to estimate the propagation of the seed set's influence during training. Other relevant parameter settings are shown in Table 2.

[0138] Table 2

[0139]

[0140] All comparison algorithms, except for S2V-DQN and ToupleGDD, were implemented using Python code, strictly following the descriptions in their respective papers. Specifically, for the Lazy Greedy algorithm, 1000 Monte Carlo simulations were used to estimate the extent of influence diffusion. For other algorithms, the optimal parameter settings were followed according to their respective papers.

[0141] All experiments were performed on a single computer running a 64-bit Ubuntu 20.04 operating system, equipped with a Xeon(R) Platinum 8352V CPU, 90GB of RAM, and a 4090 GPU with 24GB of video memory. This ensured the consistency and comparability of the experimental results.

[0142] 2. Seed selection strategy

[0143] Four seed selection strategies were compared: iterative strategy; hybrid selection strategy, which involves iteratively selecting 5 nodes, then selecting 5 nodes at once, and finally performing four more iterations, selecting 10 nodes each time (denoted as 1_5&5_1&10_4); batch iterative strategy, which involves iterating five times, selecting 10 nodes each time (denoted as 10_5); and top-k strategy. Furthermore, the time required for each strategy to select a seed set of size 50 was calculated. To accurately evaluate the propagation computation efficiency of each strategy, all experiments were independently repeated ten times, and the average time was calculated to eliminate random errors from single experiments.

[0144] from Figure 7 and 8 It is clearly observable that there are certain differences in performance between the Iteration and Top-k strategies on the relatively smaller Hypertext and High-School graphs. However, on the other three larger graphs, the differences are relatively minor. Notably, the two compromise strategies, 1_5 & 5_1 & 10_4 and 10_5, show little difference in propagation range compared to the Top-k strategy, but demonstrate significant improvements in time efficiency. In particular, the 10_5 strategy does not differ much in runtime from the Top-k strategy. For example, in the Hypertext dataset, the Iteration strategy shows an average difference of 4.5% in propagation range compared to the Top-k strategy, but only a 0.2% difference compared to the 10_5 strategy, yet reduces time by 78.7%.

[0145] Conclusion: When processing small datasets, the 10⁻⁵ strategy is an ideal choice because it ensures both a wide propagation range and high computational speed. In contrast, the Iteration strategy does not offer a significant advantage when processing medium to large datasets and is time-consuming. The Top-k strategy, on the other hand, performs excellently when processing medium to large datasets due to its speed and efficiency. Therefore, this invention flexibly selects either the 10⁻⁵ or Top-k strategy based on the size of the dataset to achieve the best propagation effect and computational efficiency.

[0146] 3. Scope of dissemination

[0147] The D2G-DCIM algorithm was compared in detail with other algorithms in terms of propagation range. Specifically, this was done for target seed sets of sizes 10, 20, 30, 40, and 50. The propagation range of the target seed sets obtained by each algorithm was evaluated under 10,000 Monte Carlo simulations. Specifically, a seed selection strategy of 10⁻⁴ was used on Hypertext, High-School, and Mammalia, while a Top-k strategy was used on the remaining datasets.

[0148] Given that the Lazy Greedy algorithm is too time-consuming when processing slightly larger networks, it was decided not to apply it to networks such as Tech-As-Topology, Slashdot-threads, Epinions, and Digg-friends. Similarly, as the number of snapshots increases, the execution time of the Dynamic Degree, Dynamic Degree Discount, and Dynamic CI algorithms also increases significantly; therefore, these algorithms were not adopted on Epinions.

[0149] Four sets of competing seed sets were constructed for experiments: First, based on the out-degree of the nodes, the top 10 and top 20 nodes with the largest out-degree were selected to form two sets of competing seed sets respectively. These two seed sets have high potential influence in the network. Secondly, to increase the diversity and comprehensiveness of the experiment, 10 nodes and 20 nodes were randomly selected to form two other competing seed sets (…). To simulate broader and more random selection scenarios, these four sets of competing seed sets were constructed to comprehensively evaluate the performance of the D2G-DCIM algorithm under different conditions, including its effectiveness when competing with highly influential nodes, and its stability and adaptability in the face of random selection.

[0150] like Figure 9 As shown, in a competitive scenario involving a set of seeds with high potential influence, regardless of... still The propagation range of D2G-DCIM significantly surpasses that of other benchmark algorithms except for Lazy Greedy, and is close to that of Lazy Greedy, though slightly inferior. On multiple datasets including Hypertext, High-School, Mammalia, CollegeMsg, and Email-Eu-Core, the propagation range of D2G-DCIM reaches 98.5%, 95.7%, 97.7%, 99.1%, and 97.7% of that of Lazy Greedy, respectively.

[0151] In the case of random competition for seed set, such as Figure 10 As shown, D2G-DCIM can achieve a propagation range similar to Lazy Greedy. In particular, on the High-school dataset, the propagation range of the D2G-DCIM algorithm even surpasses that of the Lazy Greedy algorithm on certain target seed sets. This phenomenon may be attributed to the fact that the Lazy Greedy algorithm only used 1000 rounds of Monte Carlo simulation when simulating its propagation range, which weakens the performance of the Lazy Greedy algorithm to some extent, thus allowing D2G-DCIM to exhibit a superior propagation range in certain scenarios.

[0152] In contrast, while other algorithms may perform well on certain datasets, their performance fluctuates significantly on others, lacking broad applicability and stability. Notably, ToupleGDD's performance on some datasets is quite close to that of D2G-DCIM. In-depth analysis of these datasets reveals that they all exhibit relatively weak temporal conditions. However, when faced with datasets containing more complex temporal information, ToupleGDD's propagation range is significantly smaller than that of D2G-DCIM. This also demonstrates that these algorithms are not well-suited to complex, dynamic temporal competitive environments.

[0153] In summary, the D2G-DCIM of this invention has excellent performance and wide applicability.

[0154] Figure 11 The runtime comparison of D2G-DCIM with other baseline methods on nine datasets is shown. Only a few are reported here. The time is shown in the first case because the time variation is not significant in other cases. Given the order-of-magnitude differences in time consumption between algorithms, a logarithmic y-axis is used to enhance visual contrast. It should be noted that multi-process acceleration was applied to the Entropy Based algorithm on the Slashdot-Threads, Epinions, and Digg-Friends datasets; and multi-process acceleration was also implemented for the Dynamic Degree, Dynamic Degree Discount, and Dynamic CI algorithms on Epinions and Digg-Friends. Based on this figure, the following conclusions can be drawn:

[0155] Overall, D2G-DCIM's runtime is second only to Degree, Degree Discount, and S2V-DQN, and is comparable to ToupleGDD. However, as the network size increases, the runtime of Degree Discount and S2V-DQN gradually surpasses that of D2G-DCIM. In contrast, the runtime of the other algorithms increases significantly with increasing network size, indicating that these algorithms are not suitable for handling medium to large-scale networks. Even on the Digg-Friends dataset with millions of edges, D2G-DCIM's runtime is less than 5 seconds, fully demonstrating its practicality in handling large-scale networks.

[0156] Compared to the Lazy Greedy algorithm, D2G-DCIM achieves orders of magnitude speedup, with average speedups of 1413x, 2749x, 9495x, 22265x, and 13631x in Hypertext, High-School, Email-Eu-Core, Mammalia, and CollegeMsg, respectively, demonstrating the high efficiency of D2G-DCIM.

[0157] In summary, the D2G-DCIM algorithm performs excellently when handling networks of various sizes. Compared with baseline algorithms such as Lazy Greedy, D2G-DCIM achieves significant speedups on multiple datasets, laying a solid foundation for its widespread adoption in practical applications.

[0158] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

[0159] The documents cited in this invention include:

[0160] [1] Khalil, E.; Dai, H.; Zhang, Y.; Dilkina, B.; Song, L. LearningCombinatorial Optimization Algorithms over Graphs. Advances in NeuralInformation Processing Systems 2017, 30, 1–10.

[0161] [2] Li, H.; Xu, M.; Bhowmick, SS; Rayhan, JS; Sun, C.; Cui, J.PIANO: Influence Maximization Meets Deep Reinforcement Learning. IEEETransactions on Computational Social Systems 2023, 10 (3), 1288–1300.

[0162] [3] Chen, T.; Yan, S.; Guo, J.; Wu, W. ToupleGDD: A Fine-DesignedSolution of Influence Maximization by Deep Reinforcement Learning. IEEETransactions on Computational Social Systems 2024, 11 (2), 2210–2221.

[0163] [4] Murata T, Koga H. Extended methods for influence maximization indynamic networks. Computational social networks, 2018, 5: 1-21.

[0164] [5] Chen, W.; Wang, Y.; Yang, S. Efficient Influence Maximization inSocial Networks. In Proceedings of the 15th ACM SIGKDD InternationalConference on Knowledge Discovery and Data Mining; Association for ComputingMachinery: New York, NY, USA, 2009; pp. 199–208.

[0165] [6] Michalski, R.; Jankowski, J.; Pazura, P. Entropy-Based Measurefor Influence Maximization in Temporal Networks. In Computational Science —ICCS 2020; Krzhizhanovskaya, V. V., Závodszky, G., Lees, M. H., Dongarra, J.J., Sloot, P. M. A., Brissos, S., Teixeira, J., Eds.; Springer InternationalPublishing: Cham, 2020; pp. 277–290.

[0166] [7] Tong, G.; Wu, W.; Tang, S.; Du, D.-Z. Adaptive InfluenceMaximization in Dynamic Social Networks. IEEE / ACM Transactions on Networking2016, 25, 112-125.

[0167] [8] Gkolfo, I. S.; Megalooikonomou, V. Maximization Influence inDynamic Social Networks and Graphs. Array 2022, 15, 100226.

[0168] [9] Song, N.; Sheng, W.; Sun, Y.; Lin, T.; Wang, Z.; Xu, Z.; Yang,F.; Zhang, Y.; Li, D. Online Dynamic Influence Maximization Based on DeepReinforcement Learning. Neurocomputing 2025, 618, 129117.

[0169]

[10] Meena, S. K.; Singh, S. S.; Singh, K. DCDIM: DiversifiedInfluence Maximization on Dynamic Social Networks. Computer Communications2025, 232, 108045.

[0170]

[11] Huang, H.; Meng, Z.; Shen, H. Competitive and ComplementaryInfluence Maximization in Social Network: A Follower’s Perspective.Knowledge-Based Systems 2021, 213, 106600.

[0171]

[12] Wang, F.; She, J.; Ohyama, Y.; Jiang, W.; Min, G.; Wang, G.; Wu,M. Maximizing Positive Influence in Competitive Social Networks: A Trust-Based Solution. Information Sciences 2021, 546, 559-572. https: / / doi.org / 10.1016 / j.ins.2020.09.002.

[0172]

[13] Liang, Z.; He, Q.; Du, H.; Xu, W. Targeted Influence Maximizationin Competitive Social Networks. Information Sciences 2023, 619, 390-405.

[0173]

[14] Yang, S.; Du, Q.; Zhu, G.; Cao, J.; Chen, L.; Qin, W.; Wang, Y.Balanced Influence Maximization in Social Networks Based on DeepReinforcement Learning. Neural Networks 2024, 169, 334-351. https: / / doi.org / 10.1016 / j.neunet.2023.10.030.

[0174]

[15] Liu, J.; You, Z.; Liang, Z.; Du, H. User-Driven CompetitiveInfluence Maximization in Social Networks. Theoretical Computer Science 2024,1018, 114813. https: / / doi.org / 10.1016 / j.tcs.2024.114813.

[0175]

[16] Van Hasselt, H.; Guez, A.; Silver, D. Deep Reinforcement Learningwith Double Q-Learning. In Proceedings of the AAAI Conference on ArtificialIntelligence 2016, 30 (1).

[0176]

[17] Perozzi, B.; Al-Rfou, R.; Skiena, S. DeepWalk: Online Learning ofSocial Representations. In Proceedings of the 20th ACM SIGKDD InternationalConference on Knowledge Discovery and Data Mining; Association for ComputingMachinery: New York, NY, USA, 2014; pp. 701–710.

[0177]

[18] Grover, A.; Leskovec, J. node2vec: Scalable Feature Learning forNetworks. In Proceedings of the 22nd ACM SIGKDD International Conference onKnowledge Discovery and Data Mining; Association for Computing Machinery: SanFrancisco, California, USA, 2016; pp. 855–864.

[0178]

[19] Mnih, V.; Kavukcuoglu, K.; Silver, D.; Rusu, A. A.; Veness, J.;Bellemare, M. G.; Graves, A.; Riedmiller, M.; Fidjeland, A. K.; Ostrovski,G.; et al. Human-Level Control through Deep Reinforcement Learning. Nature2015, 518 (7540), 529–533.

[0179]

[20] Cai, T.; Luo, S.; Xu, K.; He, D.; Liu, T.-Y.; Wang, L. GraphNorm:A Principled Approach to Accelerating Graph Neural Network Training. InProceedings of the International Conference on Machine Learning; PMLR: 2021;pp. 1204–1215.

[0180]

[21] sella, L.; Stehlé, J.; Barrat, A.; Cattuto, C.; Pinton, J.-F.;Van den Broeck, W. What's in a Crowd? Analysis of Face-to-Face BehavioralNetworks. J. Theor. Biol. 2011, 271 (1), 166–180.

[0181]

[22] Rossi, R.A.; Ahmed, N.K. The Network Data Repository withInteractive Graph Analytics and Visualization. In Proceedings of the AAAIConference on Artificial Intelligence; AAAI: 2015.

[0182]

[23] Kunegis, J. KONECT -- The Koblenz Network Collection. InProceedings of the International Conference on World Wide Web Companion; WWW:2013; pp. 1343–1350.

Claims

1. A method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks, characterized in that: Includes the following steps: S100, Collect dynamic social network datasets; S200. Construct the DDQN deep reinforcement learning neural network model Q network. The Q network model is based on two collaborative graph neural networks, StateGNN and InfGNN. StateGNN is used to capture and update the state information of nodes, and InfGNN is used to model the influence features of nodes. Multi-head attention is introduced to further extract and fuse features to obtain more accurate influence features of nodes. A time-based aggregation mechanism is introduced into the network to guide nodes to perform selective operations based on time information when aggregating neighborhood features in both outgoing and incoming directions. S300, Q-network model trained based on DDQN; S400. Input the dynamic social network into the trained Q-network model to calculate the Q value of each node, select seed nodes based on the seed selection strategy, and obtain the target seed set. S500: The target seed set is input into the Dynamic Competitive Independent Cascaded Propagation (DCIC) model for propagation to simulate the complex dynamic changes in real networks and the competitive influence between different entities, thereby maximizing the influence process.

2. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 1, characterized in that: The implementation process of the time-based aggregation mechanism described in S200 is as follows: 1) Initialize the node's transmittable time and aggregation time: Set two key parameters for each node u: and , representing the time when a node can transmit information in the inbound direction and the time when it can be aggregated in the outbound direction, respectively, and initialized. , ; 2) Select the neighbor nodes to be aggregated: For each incoming edge in the inbound direction Transform into ,in, For each outgoing edge in the outgoing direction , transformed ,in, u, v represent nodes in the graph. It is the edge A set of existing discrete time points; 3) Merging parallel edges: For parallel edges in the incoming direction, merge them into one edge, with the time attribute being the earliest time point among all parallel edges; for parallel edges in the outgoing direction, use the earliest existing time of the merged edge as the time of the merged edge, resulting in... , ; 4) Neighborhood aggregation and updating node embedding representation: After obtaining the merged edge set, perform neighborhood aggregation operation and update the node embedding representation accordingly; 5) Update and :Will Updated to the minimum duration of all edges pointing to node u. , ;if or Then let and =-1; Repeat steps 2)-5) until the specified number of times is reached.

3. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 2, characterized in that: The implementation process of StateGNN in S200 is as follows: Based on the initial state of node u and Perform initial state fusion, resulting in the initial state vector. for: in, and It is a learnable parameter matrix. This indicates that node u has been selected by entity A. This indicates that node u was not selected by entity A; This indicates that node u belongs to entity B. This indicates that node u does not belong to entity B; LeakyReLU is a non-linear activation function. StateGNN is composed of R layers of graph convolution. Composition, i-th layer The state vector of node u Update according to the following formula: in, It is the state vector of node u in the (i-1)th layer. It is the edge The probability of propagation on the surface, It is a two-layer perceptron used to capture nonlinear relationships. It is based on the set of in-neighbors of node u obtained through a time-based aggregation mechanism. and It is a learnable parameter matrix. It is a bias term.

4. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 3, characterized in that: The InfGNN described in S200 consists of R-layer graph convolutions. Composition, i-th layer The formula for updating the node influence feature vector is as follows: in, It is the edge The probability of propagation on the surface, It is a two-layer perceptron used to capture nonlinear relationships. It is based on the set of out neighbors of node u obtained through a time-based aggregation mechanism. It is a learnable parameter matrix. It is a bias term.

5. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 4, characterized in that: The implementation process of the multi-head attention function described in S200 is as follows: Construct the input sequence: And use it as the query Q, key K and value V; For each head, perform different linear transformations on the query Q, key K, and value V to obtain the query for each head. ,key Sum : in, , , It is a learnable parameter matrix; For each head h, compute additive attention: in, yes The j-th row, yes The lth line, It is a learnable parameter vector; Calculate attention weights : The weights and values ​​are summed in a weighted manner to obtain the output for each head: in, yes The rth line; The outputs of all the heads are concatenated, and the final output is obtained through a linear transformation: in, It is the final linear transformation matrix; After summing the results of multi-head attention, a linear transformation and regularization are performed to obtain the final node embedding: in, It is layer normalization. It is a learnable parameter matrix. yes The rth line.

6. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 5, characterized in that: The loss function used in step 300 uses the mean squared error (MSE) as the optimization objective, and the specific calculation formula is as follows: in, , These are all the parameters in the target network model. It is the discount factor that determines the importance of future rewards.

7. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 6, characterized in that: The seed selection strategy described in S400 is as follows: For small-scale networks, a certain number of nodes with the highest Q-values ​​are selected in each iteration until the seed set size requirement is met; for large-scale networks, a Top-k selection strategy is adopted.

8. The method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks according to claim 7, characterized in that: The propagation process of the dynamic competitive independent cascading propagation model described in S500 is as follows: The model uses two competing entities, A and B, to vie for the opportunity to activate nodes in the network; each edge in the network... There is an activation probability. Once a node is successfully activated by A or B, it permanently belongs to that entity and can only propagate the influence of that entity; each node has an activation time. The information dissemination process is based on The existence time of the edges is determined together; given the seed sets of two entities A and B. and , The propagation process is as follows: (1) At t=0, all nodes The activation time is set to The remaining nodes The activation time is set to This indicates that it has not yet been activated; (2) At each time step, each newly activated node u has one and only one chance to try to activate its inactive neighbor node v; if u will try to apply probability to v Perform activation; if v is successfully activated, then the activation time of v is set to... If node v receives activation requests from entities A and B simultaneously and is successfully activated, it will randomly choose to accept one of the requests. (3) Continue with step (2) until no new activated nodes appear; The objective of the influence propagation model's competitive influence maximization is to find a seed set containing k target entities. , making In The number of activated nodes is maximized under competitive conditions, which affects the diffusion function. Maximum; mathematically expressed as: in, This represents the influence diffusion function, i.e., the target seed set. In the competition seed The expected number of nodes to be activated under certain conditions.

9. A competitive influence maximization system for dynamic social networks driven by deep reinforcement learning and graph neural networks, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 8, and executes the steps in the above-described method for maximizing competitive influence in dynamic social networks driven by deep reinforcement learning and graph neural networks when it is run.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the method for maximizing competitive influence in a dynamic social network driven by deep reinforcement learning and graph neural networks as described in any one of claims 1 to 8.

Images