Dynamic network link prediction method based on node importance and edge feature learning

Abstract

The invention discloses a dynamic network link prediction method based on node importance and edge feature learning, and aims to improve prediction precision and time-dependent modeling capability of missing links in a complex dynamic network. According to the method, the influence of node centrality and attribute characteristics on network evolution is comprehensively considered by constructing time-aware node importance measurement; meanwhile, multi-dimensional feature modeling is carried out on the edges, the features comprise topological structures, node similarity and time evolution features, different features are fused through a self-adaptive weighting mechanism, and the expression capacity of the node relation is improved. On the basis, deep dynamic embedding of node representation is realized by combining a graph neural network and a time sequence modeling technology, so that an evolution rule of a node structure along with time change is captured. The method is suitable for practical scenes with remarkable dynamic evolution characteristics, such as social networks, citation networks and recommendation systems, and has good expandability and interpretability. Experimental results show that the method is superior to an existing link prediction method on various dynamic network data sets, and has remarkable advantages in the aspects of prediction accuracy, time sensitivity and generalization ability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of complex network analysis and artificial intelligence, and particularly relates to a link prediction method based on node importance and edge feature learning. The application is suitable for link prediction and structure analysis of dynamic evolving networks such as social networks, biological information networks, communication networks and recommendation systems. BACKGROUND

[0002] In the research of complex networks, link prediction is a key task, which aims to predict the future possible connections in the network or identify the edges that are not observed but actually exist. This task has wide applications in friend recommendation in social networks, protein interaction prediction in biological networks, topology optimization in communication networks, and user-item matching in recommendation systems. With the continuous expansion of the scale of real networks and the increasing significance of dynamic evolution characteristics, traditional link prediction methods face new challenges.

[0003] Complex networks usually have characteristics such as large scale, sparse structure and dynamic evolution, which make the traditional link prediction methods based on topological similarity have obvious limitations. Most of these methods rely on local neighborhood information of nodes, such as common neighbors, Jaccard coefficient and other indicators, which are difficult to effectively capture the global structure features and dynamic evolution rules in the network. Especially in the dynamic network scenario, the network structure changes over time, and traditional static prediction methods cannot adapt to this dynamic characteristic, leading to a decline in prediction performance.

[0004] In recent years, with the development of deep learning technology, graph neural network (GNN) has become an important tool for link prediction research. GNN can learn the low-dimensional vector representation of nodes by iteratively aggregating neighbor node information, and then be used for edge existence prediction. However, there are still two main problems in existing GNN-based link prediction methods: first, the importance difference of nodes in the network is generally ignored, which affects the formation of connections. In fact, nodes in the network often have different connection attractiveness due to their location, influence, and other factors; second, most methods use an indirect way of first learning node embedding and then synthesizing edge features from node embedding, which not only introduces computational redundancy, but also may cause information loss. The importance difference of nodes in the network is a key factor affecting the formation of connections. For example, in social networks, users with high influence are more likely to establish new connections; in protein-protein interaction networks, key protein nodes are more likely to form new interactions. However, existing methods often treat nodes as equally important and fail to effectively quantify the impact of node importance on connection probability. On the other hand, existing edge feature learning methods usually need to obtain node embedding first, and then generate edge features through concatenation, dot product or neural network. This indirect generation method not only has low computational efficiency, but also is difficult to quickly adapt to changes in network structure in dynamic network environment.

[0005] Therefore, how to establish an efficient edge feature direct generation mechanism in a dynamic network environment while fully considering the impact of node importance on connection formation has become a key to improving link prediction performance. The present invention is proposed in this background, which builds a direct generation mechanism from node features to edge features and combines a node importance quantification model, aiming to achieve more efficient and accurate dynamic network link prediction. This method not only can significantly improve the computational efficiency, but also can better capture the network dynamic evolution law, providing new technical support for dynamic network analysis. SUMMARY

[0006] The present invention aims to overcome the two main problems existing in the existing link prediction methods: first, most methods fail to fully consider the importance difference of nodes in the network, which affects the formation of connections, leading to deviations in the prediction results from the actual network evolution law; second, traditional edge feature generation methods based on node embedding rely on multi-step indirect conversion, which has high computational redundancy and is difficult to adapt to the efficiency requirements of dynamic networks. Therefore, the present invention proposes a dynamic network link prediction method based on node importance and edge feature learning, which builds a direct generation mechanism from node features to edge features and introduces a node importance quantification model, effectively improving the efficiency and accuracy of link prediction.

[0007] The technical solutions of the present invention are as follows:

[0008] 1. Node importance measure

[0009] In dynamic networks, the importance of nodes is not fixed but dynamically adjusted with the evolution of time and structural changes. To accurately depict the structural status and propagation influence of nodes at different time steps, the present invention proposes a time-step-based node importance measure method. This method introduces a time decay function and an evolution difference mechanism based on the fusion of traditional centrality indicators to dynamically reflect the global control ability and local connection activity of nodes in the network, thereby providing stable and interpretable dynamic feature support for subsequent edge feature learning and link prediction.

[0010] 1) Dynamic network modeling

[0011] Let the state of the dynamic network at time step t be represented as:

[0012] G t =(V t ,E t ),t=1,2,...,T (1)

[0013] Where V t is the node set at time step t, E t is the edge set at that moment. The node set and its connection relationship change over time, and there may be addition, deletion of nodes and increase or decrease of edges, thus forming a dynamic topology evolution sequence {G1,G2,...,G T}. On this basis, the comprehensive importance score of node v i at time step t is defined as:

[0014]

[0015] Where, represent the degree centrality, closeness centrality and betweenness centrality of the node at time step t, respectively; Δ t (v i ) represents the dynamic difference item of node centrality over time, which is used to depict the evolution trend of the structural status of the node; α, β, γ, δ are adjustable weight parameters to balance the influence of each indicator.

[0016] 2) Time-weighted degree centrality

[0017] The degree centrality of a node reflects the number and strength of its direct connections. In dynamic networks, to reflect the timeliness and activity level of node connections, a time decay function is introduced to define the time-weighted degree centrality as:

[0018]

[0019] Where |V t | is the total number of nodes in the network at time t, and Aij (t) indicates the node v i connected with node v j whether there is a connection at time t (1 if yes, 0 otherwise); t ij indicates the time step when the two nodes last established a connection; λ > 0 is the time decay coefficient. This formula shows that newer connections contribute more to the importance of the node, while older connections decay over time, thus more consistent with the characteristics of the time effectiveness of dynamic networks.

[0020] 3) Dynamic closeness centrality

[0021] Closeness centrality is used to measure the accessibility between a node and other nodes, reflecting the efficiency of information propagation from the node to other nodes in the network. In dynamic networks, the distance between nodes changes over time, so the dynamic closeness centrality at time step t is defined as:

[0022]

[0023] where |V t | denotes the total number of nodes in the network at time step t, dist t (v i ,v j ) denotes the shortest path length between node v i and v j at time step t, to prevent a small constant from dividing by zero. If a node is located in the center of the network or in a high connectivity area, its average distance is shorter, and its closeness centrality is higher, indicating that it plays a more significant role in propagation and diffusion.

[0024] 4) Dynamic betweenness centrality

[0025] Betweenness centrality is used to describe the "intermediary" ability of a node in the shortest path transmission, i.e., the degree to which the node controls information flow, and the dynamic betweenness centrality is defined as:

[0026]

[0027] where σ st denotes the number of shortest paths between node v s and v t , and σ st (v i ) is the number of paths passing through node v i . The higher the betweenness centrality, the stronger the role of the node as a bridge or relay in the network, and removing the node may lead to a decrease in network connectivity. In a dynamic scenario, by calculating the change in betweenness centrality through a sliding time window, structural mutations or key node shifts can be identified.

[0028] 5) Time evolution difference item

[0029] To capture the rate of change of node importance over time, a time evolution difference term is introduced:

[0030]

[0031] where I t (v i ) represents the importance indicator of node v i at time step t. The term I t-1 (v i ) represents the importance indicator of node v i at the previous time step t-1. This term reflects the trend of the increase or decrease of the importance of the node in the adjacent time step. When Δ t (v i ) > 0, the importance of the node increases, possibly due to the addition of new connections or the enhancement of the topological position; when Δ t (v i ) < 0, it means that the node is gradually marginalized.

[0032] 6) Comprehensive representation and normalization of node importance

[0033] To unify the indicators of different dimensions, normalization processing is adopted:

[0034]

[0035] The normalized node importance has a value range of [0, 1] and can be directly used as the input for subsequent edge feature learning, which is used to adjust the probability distribution of potential link generation. For example, in the generation of candidate edge (v i , v j ), the difference in node importance can be used to define the connection attraction function:

[0036]

[0037] This formula indicates that if the importance of both nodes is high, the possibility of forming a new edge increases accordingly, thereby realizing link prediction based on the global influence of nodes.

[0038] The node importance measurement method of the present application introduces a time decay function and an evolution difference term based on traditional centrality indicators, which can dynamically depict the structural position and time sequence change trend of nodes. This method not only improves the ability to identify key nodes in link prediction, but also reflects the timeliness and sustainability of the influence of nodes in the network evolution process, providing accurate node layer dynamic feature support for subsequent edge feature learning and graph neural network modeling.

[0039] 2) Edge feature learning mechanism

[0040] In dynamic network link prediction, the expression of edge features directly determines the ability of the model to capture potential connection relationships. Traditional methods usually generate edge features indirectly through node embedding splicing or vector operations, which has problems such as high computational redundancy, obvious information loss, and difficulty in adapting to dynamic changes. Therefore, the present application proposes an edge feature learning mechanism based on direct mapping of node features, which realizes efficient modeling and adaptive updating of edge structure features in dynamic networks by constructing an end-to-end mapping relationship from node features to edge features and introducing node importance weighting and time decay mechanisms.

[0041] 1) Dynamic edge feature definition

[0042] At time step t, the dynamic network can be represented as:

[0043] G t =(V t ,E t ,X t ) (9)

[0044] Where V t is the node set, E t is the edge set, represents the node feature matrix. For any two nodes v i ,v j ∈V t , the edge feature is defined as:

[0045]

[0046] Where f θ (·) represents the edge feature generation function, and the parameter θ is learned by the neural network; and are the normalized importance values of nodes i and j at time step t, respectively. This formula realizes the fusion expression of node features and node importance at the edge layer, so that the dynamic influence difference of nodes is directly reflected in the feature generation stage.

[0047] 2) Node feature mapping mechanism

[0048] To reduce the redundancy of the edge feature generation process, the present application adopts a node feature direct mapping mechanism to construct an end-to-end mapping function from nodes to edges:

[0049]

[0050] In the formula, || represents the vector splicing operation, W e and b e are trainable parameters, and σ(·) is a nonlinear activation function LeakyReLU. By introducing the node feature difference term The model can depict the feature similarity difference between nodes; and the node importance term is used to adjust the potential strength of the connection, so that important nodes contribute more to edge features.

[0051] Compared with the traditional two-step process of "node embedding → edge feature", this mechanism has significant efficiency advantages. On the one hand, it reduces the redundant embedding synthesis step and reduces the computational complexity; on the other hand, it avoids the information loss introduced by multiple feature transformations, so that the model can better preserve the original semantic relationship between nodes.

[0052] 3) Time decay and evolution weight mechanism

[0053] In dynamic networks, the existence and strength of edges change over time. To depict the importance difference of edges at different times, a time decay weight function is introduced:

[0054]

[0055] wherein, represents the time step of the last interaction or connection between nodes v i and v j , and λ > 0 is the time decay coefficient. This weight is used to adjust the time effectiveness of the edge feature. The newer interaction has a higher weight, and the contribution of the earlier connection gradually decays, thereby reflecting the characteristics of "time-effective connections" in the network. On this basis, the time-weighted edge feature is defined as:

[0056]

[0057] This formula ensures that the edge feature can adaptively reflect the dynamic evolution process of the network, so that the model pays more attention to the recent structural change trend when predicting future links.

[0058] 4) Node importance weighted fusion

[0059] The formation of edges not only depends on the structural similarity of nodes, but also is affected by the importance of nodes in the network. Therefore, a node importance fusion term is introduced, and the connection attraction function is defined as:

[0060]

[0061] wherein, β > 0 is a balance coefficient for controlling the influence degree of node importance on edge formation probability. When both nodes have high importance, the connection attraction is stronger, and the prediction probability also increases. The final edge feature is represented as:

[0062]

[0063] The fusion mode substantially realizes multi-dimensional coupling of structural features, time features and node importance features, so that the edge features not only contain semantic similarity between nodes, but also reflect the status difference of nodes and time dynamics.

[0064] 5) Edge feature update and timing smoothing

[0065] To cope with the continuous changes of the dynamic network, the timing smoothing mechanism is further introduced to update the edge features of adjacent time steps by exponential smoothing:

[0066]

[0067] wherein η∈[0,1] is a smoothing coefficient for adjusting the fusion ratio of the current feature and the historical feature. The mechanism can maintain the stability of the feature when the network changes dramatically, reduce the fluctuation of the prediction result, and improve the robustness of the model in the dynamic scene.

[0068] 6) Edge feature space normalization and learnability

[0069] To avoid the bias caused by different dimensional features to the model learning, the normalization operation is adopted:

[0070]

[0071] The normalized feature vector has a unified scale and can be directly input into the graph neural network for further edge prediction or similarity calculation. The edge feature learning mechanism can be combined with any type of dynamic graph neural network to realize efficient end-to-end link prediction.

[0072] 3, Graph neural network modeling

[0073] After obtaining the node importance measure and edge feature representation, to realize efficient prediction of potential links in the dynamic network, the application constructs a time-aware dynamic graph neural network modeling method. The method is based on time steps, jointly models the time features of nodes and edges, and realizes dynamic update of node state and accurate estimation of potential link probability by introducing time gating mechanism and edge weight guided aggregation.

[0074] First, the dynamic network at time step t is represented as:

[0075] G t =(V t ,E t ,X t ,H t ) (18)

[0076] wherein V t is a node set, E t is an edge set, and Xt node feature matrix, H t edge feature matrix, containing node similarity and temporal weight information. The dynamic graph sequence can be represented as G = {G1, G2,..., G T}, the goal is to predict the existence probability of potential edges at time step T+1 according to the historical network state. Secondly, in order to depict the dynamic change characteristics of nodes at different time steps, the present application improves the traditional graph convolution (GCN) model and introduces a time-aware update mechanism. The state update formula of the node at time step t is:

[0077]

[0078] where, is the hidden vector representation of node v i , and is its neighbor set; is the dynamic attention weight based on edge feature ; and is the time gating coefficient, ΔI t (v i ) represents the change amount of node importance, which is used to enhance the response ability of the model to structural evolution. After feature aggregation, in order to further fuse the time evolution information of the node, the present application adopts a time decay weight mechanism to perform weighted average on the state of the node at the last τ time steps, and the formula is as follows:

[0079]

[0080] where e -βk is an exponential decay factor, and β>0 controls the decay rate. This design ensures that the model can smoothly track the trend of the change of the node over time, avoiding the instability of single time step prediction. Finally, based on the updated node representation and edge feature, the prediction function of the edge existence probability is defined as:

[0081]

[0082] where φ(·) is a multi-layer perception MLP, and σ(·) is a Sigmoid function, representing the probability of the existence of the edge between the node pair (u, v) at time step t+1. This function integrates the structural difference between nodes, edge semantic features and time information, and realizes the direct prediction of future potential connections.

[0083] In summary, the application makes three key improvements on the basis of the traditional GNN framework: (1) Introducing a time gating mechanism driven by node importance changes to achieve dynamic feature adjustment; (2) Fusing edge feature attention weights in the aggregation process to improve the accuracy of information transmission; (3) Maintaining the smooth perception of historical states through a time decay fusion strategy. This model can simultaneously capture node evolution, edge semantics and time dependence in a dynamic network environment, effectively improving the accuracy and generalization ability of link prediction.

[0084] Table 1 is the flow of the dynamic network link prediction algorithm proposed by the application.

[0085] Table 1: Flow of the dynamic network link prediction algorithm proposed by the application

[0086] BRIEF DESCRIPTION OF DRAWINGS

[0087] In order to make the purpose, technical scheme and beneficial effects of the application clearer, the application provides the following drawings for illustration:

[0088] Figure 1 The overall flowchart of the dynamic network link prediction method proposed by the application;

[0089] Figure 2 The link prediction AUC performance comparison chart of the application and other comparative methods on different data sets;

[0090] Figure 3 The link prediction AP performance comparison chart of the application and other comparative methods on different data sets. DETAILED DESCRIPTION

[0091] In order to make the application technical scheme, advantages and purposes of the application clearer, the application will be described in detail below in combination with specific embodiments.

[0092] 1. Data set

[0093] In order to comprehensively evaluate the performance advantages of the dynamic network link prediction method proposed by the application, five representative real network data sets are selected, covering social, academic, e-commerce and trust networks in different fields. All data sets contain multiple time steps of dynamic structure to verify the generalization ability and stability of the model in the node evolution and edge dynamic change scenario.

[0094] The specific description of each data set is as follows:

[0095] 1. UCI: Social network data set, nodes represent members in an academic community, and edges represent communication and interaction between members, suitable for analyzing the dynamic evolution characteristics of small-scale social networks.

[0096] 2. Facebook: A large-scale social network dataset, where nodes represent users and edges represent friendship, used to test the robustness of models in complex social structures.

[0097] 3. Alibaba: An e-commerce behavior network, where nodes represent users or goods and edges represent purchase, browse, and other behavior interactions, used to verify the prediction accuracy of models in commercial interaction networks.

[0098] 4. DBLP: An academic collaboration network, where nodes represent authors and edges represent paper collaboration relationships, reflecting the dynamic characteristics of scientific research collaboration relationships.

[0099] 5. Epinions: A trust network, where nodes represent users and edges represent trust or evaluation relationships, reflecting the dynamic evolution characteristics of social trust systems.

[0100] Table 2 provides a brief statistical summary of the above datasets, including the number of nodes, edges, average degree, clustering coefficient, and time step.

[0101] Table 2: Dataset Introduction

[0102]

[0103] 2. Evaluation Index

[0104] This study uses two indicators, Area Under the ROC Curve (AUC) and Average Precision (AP), to evaluate model performance.

[0105] AUC: The probability that the model ranks the true missing links before random negative samples, measuring the ability of the model to distinguish between positive and negative samples, defined as follows:

[0106]

[0107] Where n is the number of independent comparisons, n' is the number of missing links with higher scores, and n" is the number of comparisons with the same score. A higher AUC indicates a stronger ability of the model to accurately distinguish between existing and non-existing link pairs, and AUC = 1 represents perfect classification.

[0108] AP: The average prediction accuracy of the model at different recall rates, measuring the overall quality of positive samples in the ranking results, defined as follows:

[0109]

[0110] Where P n is the accuracy, R n is the recall rate of the nth threshold. AP focuses on the prediction ability of positive samples (true edges), and a higher value indicates a more accurate model.

[0111] 3. Comparison Methods

[0112] Four typical dynamic network link prediction methods are selected for comparison, covering a variety of modeling paradigms based on random walk, autoencoder, and time series graph neural network. The specific introduction is as follows:

[0113] 1. Dynnode2vec: This method is an extension of node2vec in the dynamic network scenario, based on random walk and word embedding. By preserving the history embedding in the time series and updating the new nodes incrementally, it captures the characteristics of the evolution of node structure over time, and can better depict the continuity of node representation.

[0114] 2. DynGEM: A dynamic network embedding method based on the autoencoder framework, which reuses the weights of the previous moment in the new time step through an incremental training strategy, achieving smooth evolution and time continuity of node representation. This model has high stability and convergence efficiency when dealing with gradually changing network structures.

[0115] 3. T-GCN: A time series graph neural network model combining graph convolution network (GCN) and gated recurrent unit (GRU), which can capture both spatial structure features and temporal dependencies between nodes. T-GCN performs well in scenarios with strong time series characteristics such as traffic networks and social communication.

[0116] 4. DynGAE: A dynamic variant model based on graph autoencoder (GAE), which extracts node features using graph convolution layers at each time step and captures the evolution of node embedding through time series modeling, thereby improving the sensitivity and prediction accuracy of network dynamics.

[0117] 4. Parameter settings

[0118] To ensure the fairness and repeatability of the experiment, the parameters of the proposed method and the comparative model are set and the performance is evaluated under the unified framework. In terms of data set division, the real edges of the network are randomly divided into training, validation and test sets. The same number of negative samples as the positive samples are randomly generated in the training stage to balance the binary classification data. For the five dynamic network data sets, 5% of the edges in the original graph are removed as validation set positive samples, and 10% of the edges are removed as test set positive samples, and the same number of negative samples are generated for both to test the generalization performance of the model at different time steps. The model structure adopts a four-layer neural network, each layer containing 256 hidden units, the optimizer is Adam, the learning rate is 0.01, and the maximum training round is 200. The loss function adopts binary cross entropy to adapt to the binary classification task of link prediction. All experiments are run in the same hardware and software environment, and GPU acceleration is enabled to improve training efficiency. To ensure comparability, the four comparative methods (Dynnode2vec, DynGEM, T-GCN, DynGAE) are all reproduced according to the recommended parameters of the original paper or public implementation. The performance evaluation adopts AUC and AP indicators to measure the prediction accuracy and ranking ability, each group of experiments is independently run for 10 times, and the average value is taken to reduce random fluctuations. All experiments are based on PyTorch Geometric to realize the graph neural network model, and Scikit-learn and NetworkX tools are used to complete similarity calculation and graph structure processing.

[0119] 5. Results and analysis

[0120] To verify the effectiveness and superiority of the method described in the application, five representative dynamic network data sets UCI, Facebook, Alibaba, DBLP and Epinions are selected for experiment, and the performance of the existing typical dynamic network link prediction methods Dynnode2vec, DynGEM, T-GCN and DynGAE is compared. The evaluation indexes of the experiment are AUC and AP, which are used to comprehensively measure the prediction accuracy and ranking ability of the model. The AUC results of each method under different data sets are shown in Table 3, and the AP results are shown in Table 4. In the table, Propose is the application, and the black and bold parts are the best performance.

[0121] Table 3: AUC of link prediction of each method under different data sets

[0122]

[0123] Table 4: AP of link prediction of each method under different data sets

[0124]

[0125]

[0126] As can be seen from Tables 3 and 4, the method of the application achieves the optimal performance on all data sets, with an average increase of about 2% to 3% in AUC and about 3% in AP. In the UCI and Facebook two dynamic networks with strong time dependence and social attributes, the performance improvement is particularly significant, indicating that the application has better dynamic modeling capability in capturing the frequency change of node interaction and the evolution law of structure. Compared with existing methods, the application can dynamically reflect the temporal changes of node centrality, attribute features and edges through the time-aware node importance measurement and edge feature adaptive fusion mechanism, thereby achieving accurate characterization of the potential link formation mechanism. In the Alibaba, DBLP and Epinions heterogeneous or sparse networks, the application also maintains stable performance advantages, showing strong generalization and robustness. This shows that the method is not only suitable for relatively stable citation or knowledge networks, but also can effectively deal with complex dynamic scenarios where nodes and edges continue to evolve over time.

[0127] Overall, traditional methods such as Dynnode2vec and DynGEM mainly focus on static embedding learning and are difficult to capture time evolution features; T-GCN and DynGAE consider time sequence information, but are insufficient in modeling dynamic changes in node importance and edge features. In contrast, the application builds a time-aware node importance measurement and multi-dimensional edge feature fusion model, and combines an adaptive weighting mechanism to achieve dynamic optimization of multiple features, thereby significantly improving the accuracy of dynamic network link prediction and the temporal modeling capability.

[0128] The above is only a specific implementation in the application, but the protection scope of the application is not limited thereto, and any person skilled in the art can understand and think of transformations or replacements within the technical scope disclosed by the application, which should be covered within the scope of the application.

Claims

1. A dynamic network link prediction method based on node importance and edge feature learning, characterized in that, Includes the following steps: (1) Construct a dynamic network time series model to obtain a multi-time-step topology evolution sequence {G1,G2,...,G...} T }, where G t =(V t E t V t Let E be the set of nodes at time step t. t Given the set of edges at time step t, time step size T, and time decay coefficient λ, initialize the node embedding vector and edge feature matrix; (2) For each time step t∈{1,2,...,T}, perform dynamic network modeling and node importance measurement: define node v i The overall importance score at time step t is I t (v i The formula is: in, These represent the degree centrality, proximity centrality, and betweenness centrality of a node at time step t, respectively; Δ t (v i ) represents the dynamic difference term of node centrality over time, used to characterize the evolution trend of node structural status; α, β, γ, and δ are adjustable weight parameters used to balance the influence of various indicators. (3) Based on node features and node importance, generate dynamic edge features and apply time decay weights: a) For any two nodes v i ,v j ∈V t Its edge features are defined as: Among them, f θ (·) represents the edge feature generation function, and the parameter θ is learned by the neural network; and are the normalized importance values ​​of node i and node j at time step t, respectively. b) To characterize the difference in importance of edges at different times, a time-decay weighting function is introduced: in, Represents node v i With v j The time step of the most recent interaction or connection establishment, λ > 0 is the time decay coefficient. This weight is used to adjust the temporal effectiveness of edge features. Newer interactions have higher weights, and the contributions of earlier connections gradually decay, thus reflecting the "time-sensitive connection" feature in the network. (4) Construct a time-aware dynamic graph neural network (T-GNN), update node representations and predict links. a) Define node v i The state update formula at time step t is: in, For node v i The implicit vector representation of . Gather for its neighbors; For edge feature-based Dynamic attention weights; Let ΔI be the time gating coefficient. t (v i ) represents the change in node importance, used to enhance the model's responsiveness to structural evolution. b) A time decay weighting mechanism is used to calculate a weighted average of the states of a node over the most recent τ time steps, as shown in the following formula: c) Based on the updated node representations and edge features, the prediction function for the probability of edge existence is defined as follows: Here, φ(·) represents a multilayer perceptron (MLP), and σ(·) represents the sigmoid function. This function integrates structural differences between nodes, edge semantic features, and temporal information to achieve direct prediction of potential future connections. (5) Output the probability of future links between node pairs (i,j).

2. The method according to claim 1, characterized in that, In step (2), node v i Time-weighted degree centrality at time step t The defining formula is: Among them, |V t | represents the total number of nodes in the network at time t, A ij (t) represents node v i With node v j Does a connection exist at time t? (1 if it exists, 0 otherwise) ij This represents the time step in which the connection between the two nodes was last established; λ > 0 is the time decay coefficient.

3. The method according to claim 1, characterized in that, In step (2), node v i Dynamic proximity centrality at time step t The defining formula is: Among them, |V t | represents the total number of nodes in the network at time step t, dist t (v i ,v j ) represents node v i With v j The shortest path length at time step t, ò is a small constant to prevent division by zero.

4. The method according to claim 1, characterized in that, In step (2), node v i Dynamic betweenness centrality at time step t The defining formula is: Where, σ st Represents node v s With v t The number of shortest paths between them, σ st (v i ) is the node that passes through v i The number of paths.

5. The method according to claim 1, characterized in that, In step (2), node v i The time evolution difference term Δ at time step t t (v i The definition formula for ) is: Among them, I t (v i ) represents node v i In terms of the importance of time step t, I t-1 (v i ) represents node v i The importance index at the previous time step t-1. This item reflects the increasing or decreasing trend of a node's importance in adjacent time steps. When Δ t (v i When Δ > 0, the importance of a node increases, possibly due to new connections or enhanced topological position; when Δ t (v i If ) < 0, it indicates that the node is gradually becoming marginalized.

6. The method according to claim 1, characterized in that, In step (2), node v i The overall importance score at time step t is I t (v i The normalization formula for ) is: Normalized node importance The value range is [0,1], and it can be directly used as input for subsequent edge feature learning to adjust the probability distribution of potential link generation.

7. The method according to claim 1, characterized in that, The edge feature generation function in step (3) The node feature direct mapping mechanism is adopted, and the formula is as follows: Where || denotes the vector concatenation operation, W e and b e Here are the trainable parameters, and σ(·) is the non-linear activation function LeakyReLU. This is achieved by simultaneously introducing a node feature difference term. The model can characterize the differences in feature similarity between nodes; while the node importance term is used to adjust the potential strength of the connection, so that important nodes contribute more to the edge features.

8. The method according to claim 1, characterized in that, Step (3) also includes node importance weighted fusion and defining the connection attraction function. The formula is as follows: Here, β > 0 is a balance coefficient used to control the degree to which node importance affects the edge formation probability. When both nodes have high importance, their connection attraction is stronger, and the prediction probability also increases.

9. The method according to claim 1, characterized in that, Step (3) also includes temporal smoothing updates of edge features, with the following formula: Where η∈[0,1] is the smoothing coefficient, which is used to adjust the fusion ratio of the current feature and the historical feature.

10. The method according to claim 1, characterized in that, In step (4), the input to the multilayer perceptron (MLP) consists of the structural differences between nodes, edge semantic features, and temporal information, as shown in the following formula: Where φ(·) represents a Multilayer Perceptron (MLP), and σ(·) represents the Sigmoid function. The MLP contains two hidden layers, each using the ReLU activation function, and the output layer has a dimension of 1. Finally, the connection probabilities are obtained through the Sigmoid function. The following is the flowchart of the dynamic network link prediction algorithm proposed in this invention. Table 1: Dynamic Network Link Prediction Algorithm Proposed in This Invention

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