Method for estimating node importance of a multilayer network

Abstract

The application relates to a node importance estimation method of a multi-layer network, comprising the following steps: collecting communication network topology information, operation state parameters of each node and link transmission parameters in real time; an intra-layer module performs hierarchical learning, and higher-order group-level dependency relationships beyond pair edges are captured by using hypergraph modeling, so that importance evidence of a specific layer is generated; a cross-layer module introduces a bridge node to establish a clear path between layers, so as to promote feature exchange when there is a significant difference in the structure and density of each layer; a nested contrast learning module enhances the cross-layer similarity of the same node in different layers by aligning the representations of the same node in different layers, while maintaining the distinguishability between different nodes; the importance coefficient of each node in the network is calculated; and a routing optimization strategy is performed according to the importance coefficient of each node.

Description

Technical Field

[0001] This invention belongs to the field of communication network technology, and particularly relates to a method for estimating the importance of nodes in multi-layer networks. Background Technology

[0002] Node importance estimation (NIE) is a crucial task in network science, aiming to quantify the influence, salience, or popularity of nodes based on a target definition of importance in a specific application. This concept typically extends beyond simple structural salience: in many real-world systems, importance is inherently semantic and context-dependent, shaped by node attributes (e.g., content, profile, functionality) and relational structures (e.g., interactions, dependencies). Therefore, accurate node importance estimation is a cornerstone of numerous downstream applications, including node routing optimization scenarios in communication networks.

[0003] Early attempts often treated "importance" as a proxy for network centrality and estimated it using topology-driven metrics such as PageRank and degree centrality. The rise of deep learning shifted node importance estimation (NIE) towards data-driven modeling, where importance is learned from supervisory or surrogate signals rather than prescribed by fixed centrality formulas. In particular, graph neural networks (GNNs) provide a canonical approach that combines node attributes with neighborhood structure, encoding them into latent representations that better reflect semantic importance. GENI pioneered the use of attention-based aggregation to learn importance representations with structural information. Subsequent research has further enhanced this paradigm by incorporating richer semantic cues and modeling uncertainties, resulting in more robust and application-appropriate importance estimates.

[0004] Despite this progress, most existing graph neural network (GNN)-based heterogeneous information extraction (NIE) methods implicitly operate in a flattened relation space, where diverse interactions are either ignored or compressed into a single propagation graph. A common strategy for handling this heterogeneity is the meta-path paradigm, which represents semantic relations as a predefined sequence of node / edge types. However, this sequence-based view tends to be inconsistent with real-world networks in two key ways. First, this paradigm typically treats each meta-path as an independent semantic channel, making it difficult to capture the relevance between relations. Meta-path-based methods often model these paths independently and aggregate their effects separately, making it challenging to capture the relevance between corresponding contexts. Second, meta-paths are often hand-designed and domain-specific, which limits their generalization ability and may miss task-relevant semantics when importance signals do not conform to predefined templates. Summary of the Invention

[0005] The limitations described above prompt this application to move beyond the meta-path paradigm and towards a multi-layer network perspective with heterogeneous relationships. In multi-layer networks, relational semantics are represented as independent layers and jointly learned by leveraging intra-layer structure and cross-layer dependencies. This representation naturally reduces reliance on hand-constructed relational sequences. However, existing research on multi-layer networks has largely focused on network representation learning for link prediction and node classification, while node importance estimation (NIE) in multi-layer environments has received relatively limited attention. Importantly, directly applying multi-layer representation learning techniques to node importance estimation is not straightforward, as importance estimation involves more than just learning embeddings that perform well on reconstruction or classification objectives. On the one hand, layers may exhibit significantly different topological features (e.g., connection patterns, densities, and edge weights) and semantics, making it difficult to design a unified mechanism to consistently and comparably infer node importance within each layer. On the other hand, the cross-layer influence on importance can be dynamic and non-linear, involving complex synergistic effects; therefore, capturing how importance evidence propagates and aligns between layers requires explicit modeling of inter-layer interactions. Finally, a robust approach must integrate the importance evidence from each layer into a unified metric, while preserving the unique semantics of each layer and avoiding the ambiguity introduced by flattening heterogeneous relationships.

[0006] To address these challenges, this application proposes a Hierarchical Graph Hypernetwork (HiGH), a framework specifically designed for Node Importance Evaluation (NIE) in multi-layer networks. This application employs a two-level design: first, intra-layer importance is learned by capturing higher-order dependencies within each layer; then, cross-layer information exchange is achieved through lightweight connectors linking different layers. Above this structural backbone, nested contrastive targets are used to align important evidence across layers, while separating layer-specific patterns from cross-layer consistency signals, thereby obtaining a unified importance metric.

[0007] To achieve the above objectives, the node importance estimation method for multi-layer networks disclosed in this application includes the following steps: Real-time acquisition of multi-layer communication network topology information, operating status parameters of each node, and link transmission parameters; The modules within a layer perform hierarchical learning and utilize hypergraph modeling to capture higher-order, group-level dependencies beyond paired edges, thereby generating layer-specific evidence of importance. The cross-layer module introduces bridge nodes to establish explicit paths between layers, thereby facilitating feature exchange when there are significant differences in the structure and density of each layer. The nested contrastive learning module enhances the cross-layer similarity of the same node by aligning its representations across different layers, while maintaining the distinguishability between different nodes. Calculate the importance score for each node in the network; Based on the importance score of each node, network nodes are classified. Based on the node classification results and link bandwidth utilization, routing control signaling is generated and sent to routers and switches in the network to adjust data forwarding paths and avoid links whose link bandwidth utilization exceeds a preset threshold.

[0008] Furthermore, the network topology information includes a set of nodes and a set of links; the operating status parameters include node processor utilization, memory usage, and data cache size; and the link transmission parameters include link bandwidth utilization, transmission latency, and packet loss rate; based on the network topology information, node operating status parameters, and link transmission parameters.

[0009] Furthermore, the multi-layer network is composed of graphs. Through mapping function and To characterize, among which and Representing the node type set and edge type set respectively. It is a set of nodes; a set of edges. Classified as A type-specific subset; each node and edge ,satisfy: .

[0010] Furthermore, the nested contrastive learning module performs the following steps: introducing a nested contrastive learning objective, and ensuring the consistency of the learned representations by aligning the representations of the same nodes across layers. Specifically, for a three-layer network... In contrast, cross-layer consistency is achieved through a scalable contrastive learning paradigm that handles arbitrary layers. Middle node The representation ,in Represents a set of layers; features within a layer are represented by a layer-specific adjacency matrix. Transformation learning, where the topological structure of each layer guides the propagation of features: ; in This represents the initial feature set of the network. Represents a node Embedded, It is the number of nodes; the transformation learning includes learnable parameters, wherein Represents the weight matrix. This represents the bias term, enabling adaptive feature projection. To maintain the consistency of the same node across different layers and the heterogeneity among different nodes, a contrastive learning objective was constructed, namely: for a two-layer network Layers and Any node in the layer Its positive sample pairs are generated by the node in Layers and Layer representation The negative sample pairs consist of the representations of a node and its neighboring nodes across different layers. Through this negative sampling, the model learns to recognize the unique contextual roles of nodes across different layers; the InfoNCE objective function is used to compute the layers. and Inter-layer contrastive learning loss ,layer and Inter-layer contrastive learning loss and layers and Inter-layer contrastive learning loss ; The total contrastive loss is obtained by summing the three contrastive learning losses: ; Nested methods enforce cross-layer consistency for the same node, thereby prompting the model to learn a unified representation that is consistent across different relation types.

[0011] Furthermore, the module within the layer performs the following steps: For each layer The diagram is shown as follows , It is a set of edges The A subset; degree centrality The K-kernel algorithm is used to capture local and global features; Then, the node The K-core score is defined as If node belong Nucleus diagram but not belonging to Nucleus diagram; Learnable parameters The importance of adaptively integrating these standardized features; ; For each graph Construct a hypergraph , It is a picture The set of superedges, where superedges are created by selecting a few nodes with the highest ranking, and each superedge... Defined as the set of nodes within the KNN nearest neighbors of the central node; Subsequently, a Hypergraph Neural Network (HGNN) is used to encode the hypergraph structure. In the HGNN, information aggregation is performed through a two-stage process, where node features are first aggregated into hyperedges and then diffused back to the nodes. Specifically... Indicates the first The first in the layer The embedding of a hyperedge is achieved by integrating the initial features of all its constituent nodes. To calculate the combinatorial representation: ; in, This represents the learnable weights assigned to each hyperedge, while The representation is contained in the hyperedge. The set of nodes in; The updated hyperedge representation is propagated back to its constituent nodes through aggregation operations to optimize node embedding: ; in, Represents a node The set of connected hyperedges, This represents the learnable weight parameters for hyperedge aggregation; in a three-layer network architecture, nodes Through progressive hypergraph feature transformation across hierarchical structures, we obtain layer, Layers and Layer representation , and ; Finally, the three representations are integrated through a fusion mechanism to generate the final hypergraph representation for each node: ; in, It is the Sigmoid function. , , They are layer, Layers and Layer representation, They are layer, Layers and Layer nodes The representation of hyperparameters Control the relative contribution of each superlayer during the aggregation process.

[0012] Furthermore, the cross-layer module performs the following steps: To facilitate cross-layer information transmission, a bridge node is introduced. First, the initial features are... Integrate with the learned representations from each layer to generate updated feature representations of the matrix: ; in, It is a hyperparameter that determines the proportion of features in each layer; A multi-layer network contains a set of bridge nodes. Features of bridge nodes To enhance cross-layer propagation, It is the number of bridge nodes. It is the first One bridge node; Regarding bridge nodes and intra-layer connections, the candidate edge set is defined as follows: Then randomly select a subset of the edges: ; in It is a hyperparameter that controls the total number of edges; the first The correlation matrix of bridge nodes in the layer is obtained through get: ; It is the th in the correlation matrix Line number Column elements; No. The graphs of the layers are aggregated to generate the final adjacency matrix. , ; in It is a matrix consisting entirely of 1s. It is the adjacency matrix of the r-th layer; Features in layer r Bridge node features Connect to build hierarchical embeddings and enhanced embedding , It is the feature dimension; , ; To emphasize embeddings from different layers, hierarchical features are integrated. , It is the dimension of the hierarchical features, and separable convolution is used for dimensionality reduction to balance effectiveness and computational efficiency: ; in It is a weight matrix.

[0013] Each layer is concatenated column by column to form an integrated feature representation: ; in, These are learnable parameters used to control the weights for layer-by-layer feature aggregation. It combines the features of each layer after integration. These are the hierarchical features of each layer; the adjacency matrices of specific layers are integrated to form a unified graph representation; Through trainable weighted coefficients Adaptively aggregate layer-specific structural patterns to generate an integrated adjacency matrix The contribution of each layer is dynamically learned from the data: ; Multilayer graph convolutional networks are used for comprehensive meta-path information fusion; the basic single-layer GCN module operates as follows: ; These are features learned after the first convolutional layer, and the weight matrix can be trained. It is used as a learnable linear transformation to project node features into the latent representation space; in order to account for the different contributions of meta-paths of different lengths in the node importance metric, This is the learnable weight matrix of the convolutional layer. The formula for multi-layer convolution is:

[0014] Final network representation By fusing metapath features of different lengths from all convolutional layers, we obtain: ; This represents the total number of convolutional layers.

[0015] Furthermore, the node importance score is calculated as follows: Through weighted hyperparameters Feature splicing combines non-bridge nodes with the hypergraph representation. Integration: ; It was before The characteristics of each node; After obtaining the node representation, the importance score S of the node is obtained through a linear transformation combined with the nonlinear activation function LeakyRelu(): ; in, Represents the learnable weight matrix. This represents the bias vector.

[0016] The beneficial technical effects of this application are as follows: This is the first time that the problem of node importance estimation has been formally defined and solved within a multi-layer network framework.

[0017] A hypergraph-based intra-layer encoder is introduced to capture higher-order interactions, along with an adaptive importance selector that reduces computational complexity while constructing information-rich hyperedges.

[0018] A nested contrastive learning scheme with inter-layer bridge nodes is designed to maintain the similarity between the representations of the same node in different layers, while maintaining the distinguishability between different nodes. Attached Figure Description

[0019] Figure 1 This is the overall flowchart of this application. Detailed Implementation

[0020] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0021] This application first introduces relevant knowledge in this technical field: 1. Importance Estimation (NIF): Early research on node importance assessment mainly focused on network centrality measures, including degree centrality, betweenness centrality, proximity centrality, and eigenvector centrality. These centrality metrics systematically evaluate and rank nodes based on their structural position within the network. Modern node importance inference (NIE) has expanded from isomorphic graphs to analyze heterogeneous graphs and knowledge graphs using graph neural networks (GNNs). 2. Multi-layer Network Embedding: Real-world graphs inherently possess multiple characteristics, encompassing various relationships and interactions between node pairs. To facilitate the representation and analysis of these nodes and edges, various multi-layer network embedding methods have been proposed. Existing multi-layer network representation learning methods are primarily designed for general tasks and lack optimization in quantifying node importance.

[0022] The following section will provide a formal description of the problem of node importance estimation in multilayer networks.

[0023] Multilayer networks: Multilayer networks are represented by graphs Through mapping function and To characterize, among which and Representing the node type set and edge type set respectively. It is a set of nodes. Because R contains various edge types, G contains multiple layers of different node types. Edge set Divided into |R| type-specific subsets Its corresponding adjacency matrix Each node and edge They happen to belong to the same type, satisfying |O| + |R|>2. It's worth noting that multiple types of edges exist within the same node pair ( )between.

[0024] Node Importance: Node Importance A value is a set of scalar values ​​reflecting the importance of entities in a graph, where N is the number of nodes. This value is non-negative. For example, in a communication network, nodes are classified according to their importance coefficients to perform route optimization and avoid links whose bandwidth utilization exceeds the preset load. Nodes with high importance coefficients undertake critical forwarding, cross-layer bridging, and traffic aggregation functions in multi-layer communication networks; once overloaded or failing, they can cause widespread network jitter. Therefore, identifying critical nodes in a communication network is a crucial step in ensuring the normal operation of the communication network.

[0025] like Figure 1 As shown, this application proposes a method for node importance estimation in multi-layer networks. This method learns node representations by jointly modeling intra-layer semantics and cross-layer propagation. Specifically, it includes the following steps: (1) The modules within the layer perform hierarchical learning and use hypergraph modeling to capture higher-order, group-level dependencies beyond paired edges, thereby generating layer-specific importance evidence. (2) The cross-layer module introduces bridge nodes to establish clear paths between layers, so as to facilitate feature exchange when there are significant differences in the structure and density of each layer; (3) The nested contrastive learning module enhances the cross-layer similarity of the same node by aligning the representations of the same node in different layers, while maintaining the distinguishability between different nodes.

[0026] In one embodiment, inter-layer alignment based on nested contrastive learning includes: First, given the structural and semantic heterogeneity between network layers, directly learning node representations may lead to significant differences in the representations of the same node across different layers. Therefore, this application introduces a nested contrastive learning objective, which ensures the consistency of learned representations by aligning the representations of the same nodes across layers. (Using a three-layer network...) Taking this as an example, the framework achieves cross-layer consistency through a scalable contrastive learning paradigm that handles arbitrary layers. Middle node The representation ,in This represents a set of layers. Intra-layer features are first represented by a layer-specific adjacency matrix. Transformation learning, in which the topological structure of each layer guides the propagation of features; ; in This represents the initial feature set of the network. Represents a node Embedded, It is the number of nodes; the transformation learning includes learnable parameters, wherein Represents the weight matrix. This represents the bias term, enabling adaptive feature projection. The initial features of each layer are represented as follows: , , .

[0027] In one embodiment, to maintain the consistency of the same node across different layers and the heterogeneity among different nodes, this application constructs a contrastive learning objective. Specifically, for a two-layer network ( Layers and any node in ) Its positive sample pairs are generated by the node in Layers and Layer representation The negative sample pairs consist of the representations of a node and its neighboring nodes across different layers. Through this negative sampling, the model learns to recognize the unique contextual roles of nodes across different layers. and Inter-layer contrastive learning loss Modeling using the InfoNCE objective function: ; in It's a temperature hyperparameter. Expectation operator. Calculate all node indices The average value. The similarity function sim() is implemented using cosine similarity, which calculates the normalized dot product between two vectors.

[0028] Following the same method, layers and Between layers, by layer and The contrastive learning loss between layers is calculated as follows: ; ; Total comparative loss It is obtained by adding the losses of the three components: ; Nested approaches enforce cross-layer consistency for the same node, thereby enabling the model to learn a unified representation that is robust across different relation types. By learning the diverse contexts of nodes across layers, this process ensures that the final representation is not a reflection of any single relation, but rather a comprehensive and robust integration of multiple relations.

[0029] In traditional multi-node or heterogeneous networks, edges can only represent pairwise relationships between nodes. However, real-world scenarios often involve group interactions among multiple nodes. For example, in communication networks, critical nodes play a more significant role than others. Modeling such networks using hyperedges connecting multiple nodes allows for the representation of higher-order interactions within the group, capturing complex dependency patterns that are difficult to model using only pairwise edges. Therefore, disturbances to nodes on critical dependency paths can lead to more severe systemic failures, and their structural importance can be assessed more accurately within a hypergraph framework. By aggregating hyperedges at different network layers, different types of group relationships can also be modeled. This helps obtain more refined and interpretable importance scores across various relationship contexts.

[0030] However, the original method of constructing hyperedges by connecting each node to its KNN nearest neighbors in each layer of a multi-layer network suffers from high computational complexity. The number of hyperedges grows exponentially; for a set containing N nodes, the size of the hyperedges can reach [amount missing]. To address this issue and meet the requirements of NIE tasks, this application designs an adaptive important node selector that integrates the local and global importance of nodes.

[0031] Specifically, for each layer The diagram is shown as follows , It is a set of edges The A subset. To consider node importance while maintaining low computational complexity, the classic degree centrality and K-kernel algorithm (The core decomposition of networks: theory, algorithms and applications. In The VLDBJournal, Vol. 29. 61-92) are chosen to capture local and global features, respectively. To capture local structural information, this application first calculates the degree centrality score: ; in, Represents a node The degree, N represents the graph The number of nodes in the K-core graph. Then, the K-core graph. yes The subgraph, in which And it satisfies of The largest subgraph. Nodes The K-core score (denoted as core( Defined as If node belong Nucleus diagram but not belonging to Nucleus diagram.

[0032] Ultimately, by incorporating learnable parameters The importance of adaptively integrating these standardized features: ; HiGH for each graph Construct a hypergraph , It is a picture The set of superedges, where the top-ranked edges are selected... Use nodes to create hyperedges, and assign each hyperedge to a node. Defined as the set of nodes within the KNN nearest neighbors of the central node. Mathematically: ; Represents a node and picture The shortest path between them.

[0033] Subsequently, Hypergraph Neural Networks (HGNNs) were used to encode hypergraph structures. In HGNNs, information aggregation occurs through a two-stage process, where node features are first aggregated into hyperedges and then diffused back to the nodes. Specifically, Indicates the first The first in the layer The embedding of a hyperedge is achieved by integrating the initial features of all its constituent nodes. To calculate the combinatorial representation: ; in, This represents the learnable weights assigned to each hyperedge, while The representation is contained in the hyperedge. The set of nodes in the [theme / system].

[0034] Subsequent steps include propagating the updated hyperedge representation back to its constituent nodes via an aggregation operation to optimize node embedding; ; in, Represents a node The set of connected hyperedges, This represents the learnable weight parameters for hyperedge aggregation; in a three-layer network architecture, nodes Through progressive hypergraph feature transformation across hierarchical structures, we obtain layer, Layers and Layer representation , and Finally, these multi-level representations are integrated through a fusion mechanism to generate the final hypergraph representation for each node; ; in It is the Sigmoid function. , , They are layer, Layers and Layer representation, They are layer, Layers and Layer nodes The representation of hyperparameters Control the relative contribution of each superlayer during the aggregation process.

[0035] Nested contrastive learning can align the representations of the same nodes across different levels. However, it primarily operates at the loss level and lacks a pathway for feature propagation between different relational graphs. To facilitate cross-layer information transfer, in one embodiment, this application introduces bridge nodes.

[0036] The process first involves initial features This is then integrated with the learned representations from each layer. The integration subsequently generates an updated feature representation of the matrix. ; in, It is a hyperparameter used to determine the feature ratio of each layer.

[0037] A multi-layer network contains a set of bridge nodes. Features of bridge nodes To enhance cross-layer propagation, It is the number of bridge nodes. It is the first One bridge node; Regarding bridge nodes and intra-layer connections, the candidate edge set is defined as follows: Then randomly select a subset of the edges: ; in It is a hyperparameter that controls the total number of edges; the first The correlation matrix of bridge nodes in the layer is obtained through get: ; It is the th in the correlation matrix Line number Column elements; No. The graphs of the layers are aggregated to generate the final adjacency matrix. , ; in It is a matrix consisting entirely of 1s. It is the adjacency matrix of the r-th layer; Features in layer r Bridge node features Connect to build hierarchical embeddings and enhanced embedding , It is the feature dimension; , ; To emphasize embeddings from different layers, hierarchical features are integrated. , It is the dimension of the hierarchical features, and separable convolution is used for dimensionality reduction to balance effectiveness and computational efficiency: ; in It is a weight matrix.

[0038] Each layer is concatenated column by column to form an integrated feature representation: ; in, These are learnable parameters used to control the weights for layer-by-layer feature aggregation. It combines the features of each layer after integration. These are the hierarchical features of each layer; the adjacency matrix of a specific layer is integrated to form a unified graph representation.

[0039] Through trainable weighted coefficients Adaptively aggregate layer-specific structural patterns to generate an integrated adjacency matrix The contribution of each layer is dynamically learned from the data:

[0040] In one embodiment, a multi-layer graph convolutional network is used for comprehensive meta-path information fusion. The basic single-layer GCN module operates as follows: ; Trainable weight matrix This is used as a learnable linear transformation to project node features into the latent representation space. To account for the different contributions of meta-paths of varying lengths to the node importance metric, It is the learnable weight matrix in convolutional layer l; ; Final network representation By fusing metapath features of different lengths from all convolutional layers, we obtain: ; This represents the total number of convolutional layers.

[0041] Finally, this application uses weighted hyperparameters. Feature splicing combines non-bridge nodes with the hypergraph representation. Integration: ; It was before The characteristics of each node; After obtaining the node representation, the node importance score S is obtained through a linear transformation, followed by the non-linear activation function LeakyRelu(). ; in, Represents the learnable weight matrix. This represents the bias vector.

[0042] After obtaining the importance scores of each node in the communication network, the network nodes are classified according to their importance scores. Nodes with higher importance scores are classified as core nodes, and their traffic is limited during overload to avoid links whose bandwidth utilization exceeds a preset threshold. Nodes with lower importance scores are classified as ordinary nodes, handling most ordinary traffic. Nodes with even lower importance scores are classified as edge nodes, handling only local traffic services and not relaying traffic. Based on the node classification results, for core nodes, routing control signaling is generated in conjunction with link bandwidth utilization and sent to routers and switches in the network to adjust data forwarding paths, avoiding links whose bandwidth utilization exceeds a preset threshold. When the CPU utilization, memory usage, and other indicators of a core node exceed the threshold, no new routing paths are allocated through that node; existing connections are allowed to disconnect naturally without being directly cut off. The process involves generating routing control signaling and distributing it to routers and switches in the network to adjust data forwarding paths. Specifically, this includes: encapsulating standardized routing control signaling based on generated forwarding path table entries; using a signaling message format recognizable by network devices, such as the Flow-Mod flow table modification message of the OpenFlow protocol; the signaling message carrying the flow table matching field to be updated, action instructions, priority parameters, etc.; where the matching field includes the source and destination addresses of the data packets, and the action instructions include modifying / adding flow table entries and deleting forwarding entries corresponding to overloaded links. The routing control signaling is then distributed to the corresponding routers and switches within the multi-layer communication network via the southbound interface; upon receiving the routing control signaling message, the routers and switches parse the message content and perform flow table update operations: deleting forwarding entries using overloaded links from their local flow tables and writing new forwarding path table entries.

[0043] This application evaluates its method on three publicly available real-world datasets: the Workspace Face-to-Face Interactive Temporal Network Dataset, the WS Small World Network Dataset, and the LFR Random Network Dataset.

[0044] To comprehensively evaluate the model in this application, node importance scoring and node importance ranking are considered. This application employs three baseline methods: (1) classic graph neural network (GNN) based methods: GCN, GraphSage, and RGCN; (2) multi-layer network based methods: MHGCN, BPHGNN, and UAN; (3) single-layer node importance evaluation (NIE) methods: GENI, RGTN, HIVEN, MCRL, and LICAP. This application uses node importance scoring metrics (root mean square error (RMSE) and median absolute error (MedAE)) and node importance ranking metrics (NDCG@100, Spearman correlation coefficient, and Overlap@100) to evaluate performance.

[0045] Table 1 compares the proposed algorithm with several baseline methods using two regression metrics (RMSE and MedAE). Best and second-best results are highlighted in bold and underlined, respectively. A two-tailed t-test was further performed, and the resulting P-value is reported in the last row. Overall, the results show that the proposed method utilizes multiple networks more effectively and generates more accurate importance scores. Among all baseline methods, the NIE-specific method outperforms classic graph neural network (GNN)-based and multiple network-based methods in most cases. In contrast, classic GNN-based and multiple network-based methods lack NIE-oriented feature extraction. These findings suggest that an architecture and training objective specifically designed for importance estimation are more effective in node scoring.

[0046] Table 1 Experimental Results

[0047] Regarding statistical significance, the p-values ​​for all regression indicators were below 0.05, indicating a significant improvement compared to existing techniques. Among the ranking indicators, five had p-values ​​≤ 0.05. This difference may be due to the increasing size of the dataset, with many nodes clustered within similar importance ranges. While the model accurately predicts these ranges, it performs poorly in fine-grained ranking, resulting in statistically insignificant results for some ranking indicators.

[0048] This application proposes a Hierarchical Graph Hypernetwork (HiGH), a method for evaluating node importance based on multi-layer networks. This application models heterogeneous networks as multi-layer structures and learns node representations through intra-layer and cross-layer learning. For intra-layer learning, a hypergraph is used to capture high-order semantic information and complex interactions within each layer. For cross-layer learning, a nested contrastive learning mechanism is employed to enhance consistency between different layers. This process is driven by bridge nodes, which enable information propagation and fusion, ultimately generating node importance scores. Experimental results on three publicly available datasets demonstrate the effectiveness of the proposed method.

[0049] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for estimating the importance of nodes in a multilayer network, characterized in that, Includes the following steps: Real-time acquisition of multi-layer communication network topology information, operating status parameters of each node, and link transmission parameters; The modules within a layer perform hierarchical learning and utilize hypergraph modeling to capture group-level dependencies that go beyond paired edges, thereby generating layer-specific evidence of importance. The cross-layer module introduces bridge nodes to establish explicit paths between layers, so as to facilitate feature exchange when there are significant differences in structure and density between layers; The nested contrastive learning module enhances the cross-layer similarity of the same node by aligning its representations across different layers, while maintaining the distinguishability between different nodes. Calculate the importance score for each node in the network; Based on the importance score of each node, network nodes are classified. Based on the node classification results and link bandwidth utilization, routing control signaling is generated and sent to routers and switches in the network to adjust data forwarding paths and avoid links whose link bandwidth utilization exceeds a preset threshold.

2. The node importance estimation method for a multi-layer network according to claim 1, characterized in that, The network topology information includes a set of nodes and a set of links. The operating status parameters include node processor utilization, memory usage, and data cache size. The link transmission parameters include link bandwidth utilization, transmission latency, and packet loss rate. Based on the network topology information, node operating status parameters, and link transmission parameters.

3. The node importance estimation method for multi-layer networks according to claim 1, characterized in that, The multi-layer network is shown in the figure. Through mapping function and To characterize, among which and Representing the node type set and edge type set respectively. It is a set of nodes; a set of edges. Classified as A type-specific subset; each node and edge ,satisfy: .

4. The node importance estimation method for a multi-layer network according to claim 3, characterized in that, The nested contrastive learning module performs the following steps: It introduces a nested contrastive learning objective, ensuring the consistency of learned representations by aligning the representations of identical nodes across layers. Specifically, for a three-layer network... In contrast, cross-layer consistency is achieved through a scalable contrastive learning paradigm that handles arbitrary layers. Middle node The representation ,in Presentation layer set; Intra-layer features are obtained through a layer-specific adjacency matrix. Transformation learning, where the topological structure of each layer guides the propagation of features: ， in This represents the initial feature set of the network. Represents a node Embedded, It is the number of nodes; the transformation learning includes learnable parameters, wherein Represents the weight matrix. This represents the bias term, enabling adaptive feature projection. To maintain the consistency of the same node across different layers and the heterogeneity among different nodes, a contrastive learning objective was constructed, namely: for a two-layer network Layers and Any node in the layer Its positive sample pairs are generated by the node in Layers and Layer representation The negative sample pairs consist of the representations of a node and its neighboring nodes across different layers. Through this negative sampling, the model learns to recognize the unique contextual roles of nodes across different layers; the InfoNCE objective function is used to compute the layers. and Inter-layer contrastive learning loss ,layer and Inter-layer contrastive learning loss and layers and Inter-layer contrastive learning loss ; Total comparative loss By summing the three contrastive learning losses, we obtain: ， Nested methods enforce cross-layer consistency for the same node, prompting the model to learn a unified representation that is consistent across different relation types.

5. The node importance estimation method for a multi-layer network according to claim 4, characterized in that, The module within the layer performs the following steps: For each layer The diagram is shown as follows , It is a set of edges The A subset; degree centrality The K-kernel algorithm is used to capture local and global features; Then, if the node belong Nucleus diagram but not belonging to Kernel graph, then nodes The K-core score is defined as ; Learnable parameters The importance of adaptively integrating these standardized features; ， These are the degree centrality coefficient and the K-kernel coefficient; for each graph Construct a hypergraph , It is a picture The set of superedges is created by selecting a few nodes with the highest ranking, and each superedge is... Defined as the set of nodes within the KNN nearest neighbors of the central node; Subsequently, a hypergraph neural network (HGNN) is used to encode the hypergraph structure. In the HGNN, information aggregation is performed through a two-stage process, where node features are first aggregated into hyperedges and then diffused back to the nodes. Specifically... Indicates the first The first in the layer The embedding of a hyperedge is achieved by integrating the initial features of all its constituent nodes. To calculate the combinatorial representation: ， in, This represents the learnable weights assigned to each hyperedge, while The representation is contained in the hyperedge. The set of nodes in; The updated hyperedge representation is propagated back to its constituent nodes through aggregation operations to optimize node embedding: ， in, Represents a node The set of connected hyperedges, This represents the learnable weight parameters for hyperedge aggregation. It is the first A node; in a three-layer network architecture, a node Through progressive hypergraph feature transformation across hierarchical structures, we obtain layer, Layers and Layer representation , and ; Finally, the three representations are integrated through a fusion mechanism to generate the final hypergraph representation for each node: ， in, It is the Sigmoid function. , , They are layer, Layers and Layer representation, They are layer, Layers and Layer nodes The representation of hyperparameters Control the relative contribution of each superlayer during the aggregation process.

6. The node importance estimation method for a multi-layer network according to claim 5, characterized in that, Cross-layer modules perform the following steps: To facilitate cross-layer information transmission, a bridge node is introduced, which will store the initial features. Integrate with the learned representations from each layer to generate updated feature representations of the matrix: ， in, It is a hyperparameter that determines the proportion of features in each layer; A multi-layer network contains a set of bridge nodes. Features of bridge nodes To enhance cross-layer propagation, It is the number of bridge nodes. It is the first One bridge node; Regarding bridge nodes and intra-layer connections, the candidate edge set is defined as follows: Then randomly select a subset of edges. : ， in It is a hyperparameter that controls the total number of edges; the first The correlation matrix of bridge nodes in the layer is obtained through get: ， It is the th in the correlation matrix Line number Column elements; No. The graphs of the layers are aggregated to generate the final adjacency matrix. , ， in It is a matrix consisting entirely of 1s. It is the adjacency matrix of the r-th layer; Features in layer r Bridge node features Connect to build hierarchical embeddings and enhanced embedding , It is the feature dimension; , ， To emphasize embeddings from different layers, hierarchical features are integrated. , It is the dimension of the hierarchical features, and separable convolution is used for dimensionality reduction to balance effectiveness and computational efficiency: ， in It is a weight matrix. ; Each layer is concatenated column by column to form an integrated feature representation: ， in, These are learnable parameters used to control the weights for layer-by-layer feature aggregation. It combines the features of each layer after integration. These are the hierarchical features of each layer; the adjacency matrices of specific layers are integrated to form a unified graph representation; Through trainable weighted coefficients Adaptively aggregate layer-specific structural patterns to generate an integrated adjacency matrix The contribution of each layer is dynamically learned from the data: ， Multilayer graph convolutional networks are used for meta-path information fusion; the basic single-layer GCN module operates as follows: ， These are the features learned after the first convolutional layer, and the trainable weight matrix of the first convolutional layer. It is used as a learnable linear transformation to project node features into the latent representation space; in order to account for the different contributions of meta-paths of different lengths in the node importance metric, It is the first A convolutional layer can learn the weight matrix; the formula for a multi-layer convolution is: ， It is the first The adjacency matrix of the layer, It is the first Layered embedding of layers; Final network representation By fusing metapath features of different lengths from all convolutional layers, we obtain: ， This represents the total number of convolutional layers. It is the first Convolutional layers.

7. The node importance estimation method for a multi-layer network according to claim 6, characterized in that, The node importance score is calculated as follows: Through weighted hyperparameters Feature concatenation combines non-bridge nodes with the hypergraph representation. The nodes are then integrated to obtain the final node representation. : ， It was before The characteristics of each node; After obtaining the node representation, the importance score S of the node is obtained through a linear transformation combined with the nonlinear activation function LeakyRelu(): ， in, Represents the learnable weight matrix. This represents the bias vector.

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