A network fairness enhancement method and system based on fiedler vector
By identifying potential structural cuts in the network and establishing connections between key nodes, the network topology is optimized using Fiedler vectors, thus solving the network topology bottleneck problem and improving network connectivity and service fairness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIDIAN UNIV
- Filing Date
- 2026-04-17
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies are insufficient to effectively improve topology bottlenecks at the network structure level, resulting in excessively long paths for some nodes, low efficiency in cross-regional communication, and uneven service experience. There is a lack of direct engineering methods and theoretical basis.
By constructing the normalized Laplacian matrix of the network, obtaining the Fiedler vector, identifying potential structural cuts, and establishing connections between key nodes, the network topology is optimized to improve connectivity and service fairness.
It significantly improves the overall connectivity and robustness of the network, reduces QoE imbalance, reduces resource waste, and improves network operating efficiency and stability.
Smart Images
Figure CN122395055A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of communication network optimization, complex network structure design, and graph computation technology, specifically involving a network fairness enhancement method and system based on Fiedler vectors. It utilizes spectral graph theory to quantitatively analyze the overall network structure and identifies topological bottleneck node pairs based on Fiedler vectors, thereby guiding the addition of edges to improve network connectivity and service experience fairness. This structural optimization method, system, and electronic equipment are described. Background Technology
[0002] With the continuous expansion of network scale and the rapid growth of service types, multi-service sharing of network resources has become the mainstream operating mode. In complex networks, due to uneven node distribution, unreasonable connection relationships, or structural defects formed by historical evolution, the network often has potential topological bottlenecks. These bottlenecks can lead to excessively long paths between some node pairs and reduced efficiency in cross-regional communication, thereby increasing the differences in Quality of Experience (QoE) and affecting overall fairness and system stability.
[0003] Existing technologies typically improve network performance in the following ways: 1. Link expansion: Increase transmission capacity by increasing bandwidth or upgrading hardware equipment, but the cost is high; 2. Routing optimization: Relies on dynamic path selection to distribute traffic, but cannot fundamentally change the topology; 3. Resource scheduling: Balances service load through algorithms, but its effectiveness is limited in structurally constrained networks; 4. Empirical topology enhancement: such as randomly adding edges or prioritizing connections to nodes with high centrality, but lacks theoretical basis and is prone to resource waste.
[0004] Research shows that the overall performance ceiling of a network is largely constrained by its topology. When a network has significant "cuts" or weakly connected regions, even with continuous increases in resource investment, it is difficult to significantly improve global performance. Therefore, how to perform targeted optimization of networks at the structural level has become a crucial problem that urgently needs to be solved in the field of network engineering.
[0005] Spectral graph theory provides an important tool for characterizing network structure. The second smallest eigenvalue of the normalized Laplacian matrix (i.e., algebraic connectivity) reflects the overall connectivity of the network, and its corresponding eigenvector—the Fiedler vector—can be used to reveal potential structural partitions within the network. However, existing research largely remains at the theoretical analysis stage, lacking engineering methods that can be directly implemented, such as: 1. How to use Fiedler vectors to accurately locate the positions where new connections should be added; 2. How to achieve the greatest connectivity improvement with the least cost; 3. How to establish a direct link between structural optimization and QoE network fairness improvement.
[0006] Therefore, it is of great significance to propose a network structure optimization method with clear computational steps, engineering deployment capability, and predictable optimization results. Summary of the Invention
[0007] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a network fairness enhancement method and system based on Fiedler vectors. By analyzing spectral features, key node pairs affecting the overall network connectivity are identified, and connections are established between these nodes, thereby effectively improving algebraic connectivity, alleviating topological bottlenecks, reducing QoE imbalance, and enhancing network robustness and operational efficiency.
[0008] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a network fairness enhancement method based on Fiedler vectors, comprising the following steps: Construct the topology diagram of the target network to be optimized; Construct the normalized Laplacian matrix of the topology graph, obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, and use it as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. Analyze the Fiedler vectors to identify potential structural cuts in the target network; Establish new physical links or logical connections between the potential structural cuts to enhance network fairness.
[0009] In the step of constructing the topology graph of the target network to be optimized, the topology graph of the target network to be optimized is represented as an undirected graph G=(V,E), where node V represents a switch, router, server or terminal device; and edge E represents a physical link or logical connection between nodes.
[0010] The normalized Laplacian matrix of the constructed topology graph is then used to obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, which serves as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. The specific method is as follows: Construct the adjacency matrix of the topological graph; Construct the degree matrix based on the constructed adjacency matrix; Construct a normalized Laplacian matrix based on the adjacency matrix and degree matrix; The constructed normalized Laplacian matrix is subjected to eigenvalue decomposition, and the eigenvector corresponding to the second smallest eigenvalue is obtained as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network.
[0011] In the step of performing eigenvalue decomposition on the constructed normalized Laplacian matrix and obtaining the eigenvector corresponding to the second smallest eigenvalue as the Fiedler vector, The smallest eigenvalue of the normalized Laplacian matrix is 0, corresponding to a vector of all 1s; The second smallest eigenvalue is called the algebraic connectivity of the graph, which is used to measure the strength of the connectivity of the target network. The eigenvector corresponding to the second smallest eigenvalue is the Fiedler vector, which reveals the potential structural partitioning trend of the target network. The Fiedler vector is an n-dimensional column vector, where n is the total number of nodes in the target network. The i-th component value of this vector is assigned to the node. Fiedler component values .
[0012] The method for analyzing Fiedler vectors to identify potential structural cuts in the target network is as follows: Normalize each Fiedler component value of the Fiedler vector and calculate the normalized Fiedler component value of each node; The target network node is divided into multiple candidate sub-regions based on the normalized Fiedler component values; For non-adjacent node pairs across sub-regions, the normalized Fiedler distance of the node pair is calculated based on the normalized Fiedler component value of each node. The potential structural cuts of the target network are identified based on the normalized Fiedler distance.
[0013] The normalization process for each Fiedler component value of the Fiedler vector is performed, and the formula for calculating the normalized Fiedler component value of each node is as follows:
[0014] in, Represents a node The normalized Fiedler component values are used to measure the relative position of the node in the potential structural cut; Represents the nodes in the Fiedler vector. The corresponding component values; Represents a node The degree.
[0015] The method for dividing the target network node into multiple candidate sub-regions based on the normalized Fiedler component values is as follows: The target network node is divided into two candidate sub-regions, positive and negative, based on the sign of the normalized Fiedler component values. The clustering algorithm is used to process all normalized Fiedler component values, and several sub-regions with significant numerical differences are identified as candidate sub-regions.
[0016] For non-adjacent node pairs spanning sub-regions, the formula for calculating the normalized Fiedler distance of the node pair based on the normalized Fiedler component value of each node is as follows:
[0017] in, Represents a node With nodes Distance metric in Fiedler vector space; This represents the normalized Fiedler component values of the two nodes; The method for identifying latent structural cuts in a target network based on the normalized Fiedler distance is as follows: The non-adjacent node pairs across sub-regions are sorted based on the normalized Fiedler distance. Node pairs with a normalized Fiedler distance greater than a preset threshold are identified as priority candidate connection pairs, and the nodes of the node pairs are located on both sides of the potential structural cut.
[0018] The method further includes, after the step of establishing new physical links or logical connections between the potential structural cuts to enhance network fairness, the following: After establishing new physical links or logical connections between potential structural cuts, the algebraic connectivity of the target network is recalculated, and the network performance changes are evaluated based on the recalculated algebraic connectivity.
[0019] Secondly, the present invention provides a network fairness enhancement system based on Fiedler vectors, comprising: The graph construction module is used to construct the topology graph of the target network to be optimized. The spectral analysis module is used to construct the normalized Laplacian matrix of the topology graph, obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, and use it as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. The bottleneck identification module is used to analyze Fiedler vectors and identify potential structural cuts in the target network. The execution module is used to establish new physical links or logical connections between the potential structural cuts, thereby enhancing network fairness.
[0020] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a network fairness enhancement method and system based on Fiedler vectors. Through a directional edge-addition strategy based on Fiedler vectors, it optimizes the overall network structure, achieving enhanced connectivity and improved service fairness under limited resource input. This is reflected in the following aspects: Significantly enhanced global structural optimization capabilities: Traditional network optimization methods often rely on local metrics (such as node degree, link utilization, or betweenness centrality) for decision-making, which can easily lead to "local optima." This invention utilizes spectral features to characterize the overall network topology, identifies potential cut regions from a global perspective, and establishes connections between key nodes, making the optimization direction more precise and thus avoiding resource waste caused by blind expansion.
[0021] Capable of accurately identifying and eliminating topological bottlenecks: Fiedler vectors can reveal relatively weakly connected regions in a network. When vector components show significant separation, it usually indicates a potential structural cut in the network. This invention, by calculating the normalized Fiedler distance between nodes and prioritizing connections between cross-cut node pairs, effectively reduces the risk of the network being "split" into multiple weakly connected sub-regions, thus structurally improving network integrity.
[0022] The improvement in network algebraic connectivity is predictable: after adding new connections, the algebraic connectivity of the network typically shows an upward trend, and this indicator directly reflects the overall connectivity of the network. Compared with random edge addition or empirical topology enhancement, the optimization results of this invention have clear theoretical support, enabling network planners to estimate optimization benefits before implementation and reducing the uncertainty of engineering decisions.
[0023] Improving QoE (Quality of Experience) fairness at its structural roots: Network topology determines the distribution of shortest paths between node pairs, and path differences are often a significant cause of uneven user experience. This invention reduces latency differences and congestion probability by increasing cross-regional connections, making the path length distribution more concentrated. Compared to strategies that rely solely on service scheduling, this method can reduce QoE fluctuations at the structural level, achieving more stable service quality.
[0024] Achieve higher performance gains with limited new links: Because this invention employs a "high-value edge priority" strategy, network performance can typically be significantly improved by adding only a small number of connections. This feature makes it particularly suitable for scenarios where link construction costs are high or deployment is limited, such as wide area communication networks, satellite networks, and cross-regional data center interconnections.
[0025] Enhancing network robustness and fault tolerance: Higher connectivity means more alternative paths exist within the network. When some nodes or links fail, data can still be transmitted through other paths, thereby reducing the impact of single-point failures on the overall system and improving the stability and reliability of network operation. Attached Figure Description
[0026] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a topology diagram of the target network of the present invention; Figure 3 This is a schematic diagram illustrating the effectiveness of the Fiedler vector structure intervention in Embodiment 2 of the present invention. Detailed Implementation
[0027] To further understand the content of this invention, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.
[0028] Example 1 like Figure 1 As shown, a network fairness enhancement method based on Fiedler vectors includes the following steps: S1: Construct the topology diagram of the target network to be optimized; S2: Construct the normalized Laplacian matrix of the topology graph, obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, and use it as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. S3: Analyze the Fiedler vectors to identify potential structural cuts in the target network; S4: Establish new physical links or logical connections between the potential structural cuts to enhance network fairness.
[0029] Specifically, in S1, the topology graph of the target network model to be optimized is constructed. The topology graph of the target network to be optimized is represented as an undirected graph G=(V,E), such as... Figure 2 As shown. Wherein: (1) Node V represents a switch, router, server, or terminal device; (2) Edge E represents the physical link or logical connection between nodes.
[0030] In an alternative implementation, the graph may also be a weighted graph, where weights are used to represent link capacity, latency, or reliability.
[0031] Specifically, in S2, the normalized Laplacian matrix of the topological structure graph is constructed, and the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix is obtained as the Fiedler vector.
[0032] S21: Construct the adjacency matrix W of the topological graph; The adjacency matrix W is used to describe the connection relationships between nodes V. If node V... With nodes If there is a link between them, then (In a weighted network, this could be link weights, such as bandwidth or reliability); if no connection exists, then This matrix is a symmetric matrix.
[0033] S22: Construct the degree matrix D based on the constructed adjacency matrix; The degree matrix D is a diagonal matrix, and its i-th diagonal element Equal to node The degree of a node is the number of edges directly connected to it (in a weighted graph, it is the sum of the connection weights). Off-diagonal elements are all 0.
[0034] S23: Construct the normalized Laplacian matrix based on the adjacency matrix and degree matrix. The specific formula is as follows:
[0035] in, For the normalized Laplace matrix, It is an identity matrix.
[0036] The normalized Laplace matrix can comprehensively reflect the node connectivity and degree distribution characteristics. Compared with the unnormalized form, it has better numerical stability and comparability for networks of different sizes or with large differences in degree distribution, and is therefore more suitable for network structure analysis in engineering practice.
[0037] S24: Perform eigenvalue decomposition on the constructed normalized Laplacian matrix, and obtain the eigenvector corresponding to the second smallest eigenvalue as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. Where: the smallest eigenvalue of the normalized Laplacian matrix is 0, corresponding to a vector of all 1s; The second smallest eigenvalue is called the algebraic connectivity of the graph, which is used to measure the strength of the connectivity of the target network. The eigenvector corresponding to the second smallest eigenvalue is the Fiedler vector, used to reveal the potential structural partitioning trends of the target network. The Fiedler vector is an n-dimensional column vector, where n is the total number of nodes in the target network. The i-th component value of this vector is assigned to the node. Fiedler component values .
[0038] S3: Analyze the Fiedler vectors to identify potential structural cuts in the target network. Specifically: S31: Normalize each Fiedler component value of the Fiedler vector, and calculate the normalized Fiedler component value of each node, as shown in the following formula:
[0039] in, Represents a node The normalized Fiedler component values are used to measure the relative position of the node in the potential structural cut; Represents the nodes in the Fiedler vector. The corresponding component values; Represents a node The degree, which is the number of edges directly connected to the node, is the sum of the connection weights in a weighted network.
[0040] The above normalization process can prevent high-connectivity nodes from having excessive weight in vector analysis, making different nodes comparable in structural analysis.
[0041] S32: Based on the normalized Fiedler component values, the target network node is divided into multiple candidate sub-regions. Specifically: The target network node is divided into two candidate sub-regions, positive and negative, based on the sign of the normalized Fiedler component values. The clustering algorithm is used to process all normalized Fiedler component values, and several sub-regions with significant numerical differences are identified as candidate sub-regions.
[0042] When a target network has a significant bottleneck, the bottleneck refers to a few edges connecting two relatively dense parts of the network. The component values of the Fiedler vector often exhibit a significant separation. Specifically, the normalized Fiedler component values for some nodes are predominantly positive, while those for other nodes are predominantly negative, or they form two distinct clusters (sub-regions) in terms of numerical magnitude. This phenomenon reflects the existence of potential "weakly connected regions" in the network, meaning that the number of connections between two groups of nodes is small or the link quality is low.
[0043] From the perspective of spectral graph theory, the Fiedler vector essentially describes the optimal direction for binary partitioning the target network while minimizing the number of cross-region edges. When the connection between two sub-regions is weak, the vector will generate a large numerical gradient on both sides of the cut. Therefore, if the component difference of a node pair on the Fiedler vector is large, it usually means that the node pair is located on both sides of a potential structural cut, and adding a connection between them is more likely to significantly improve the overall connectivity of the network.
[0044] In engineering terms, this "component separation" can be understood as a structural boundary that has naturally formed within the network. Establishing a new communication path across this boundary can effectively shorten the cross-regional transmission distance, reduce the risk of congestion, and enhance the network's resilience.
[0045] S33: For non-adjacent node pairs across sub-regions, i.e., there are no directly connected node pairs in the target network. Based on the normalized Fiedler component values of each node, the normalized Fiedler distance of the node pair is calculated.
[0046]
[0047] in, Represents a node With nodes Distance metric in Fiedler vector space; This represents the normalized Fiedler component values of two nodes.
[0048] S34: Identify the potential structural cuts of the target network based on the normalized Fiedler distance.
[0049] Sort all non-directly connected node pairs that meet the criteria in descending order of their Fiedler normalized distance. Node pairs with larger values have higher connection priority; node pairs with a normalized Fiedler distance greater than a preset threshold are identified as priority candidate connection pairs, where the nodes of the node pair are located on opposite sides of a potential structural cut, indicating that the nodes... With nodes Located on either side of a potential structural cut, adding connections between them is more likely to significantly improve overall network connectivity and alleviate topological bottlenecks.
[0050] S4: Establish new physical links or logical connections between the potential structural cuts to enhance network fairness.
[0051] Preferably, before finally determining the connection to be established, the node pairs in the candidate connection list are further filtered in conjunction with one or more network engineering constraints, including: link construction cost, node port capacity, network security policy, and geographical deployment restrictions.
[0052] S5: After establishing new physical links or logical connections between potential structural cuts, recalculate the algebraic connectivity of the target network and evaluate the network performance changes based on the recalculated algebraic connectivity.
[0053] An increase in algebraic connectivity is used to indicate a structural improvement in a network in at least one of the following aspects: reduced network cut size, shortened cross-regional paths, increased information propagation speed, and enhanced network resilience.
[0054] Furthermore, if the network fails to meet the preset algebraic connectivity metric or fairness target, the steps of adding new connections, recalculating algebraic connectivity, and evaluating network performance changes are repeated until the preset target is achieved. This process can be performed offline during the network planning phase or triggered periodically during the operation phase.
[0055] Example 2 To further illustrate the effectiveness of the method of this invention, simulation experimental results can be used for supplementary explanation. For example... Figure 2 As shown, the horizontal axis represents the number of newly added edges, and the left vertical axis represents the algebraic connectivity of the network. The right vertical axis represents the QoE imbalance index I.
[0056] As the connection across structural cuts continues to increase based on the normalized Fiedler distance, it can be observed that: (1) The network algebraic connectivity shows a continuous upward trend, indicating that the overall connectivity has been enhanced; (2) The QoE imbalance index decreased synchronously, indicating that the experience differences between different nodes or services gradually narrowed; (3) Significant performance gains can be achieved in stages with a small number of new edges, demonstrating that targeted edge addition has higher optimization efficiency than random edge addition.
[0057] The simulation results above verify that the structural optimization strategy proposed in this invention can effectively alleviate topological bottlenecks under limited resource input conditions and achieve synergistic optimization of connectivity improvement and fairness enhancement.
[0058] Meanwhile, the method of this invention has significant advantages in improving the fairness of QoE networks. This is because network topology directly affects the distribution of the shortest paths between node pairs, and path length is closely related to service latency, packet loss probability, and stability. By increasing connections across structural cuts, the distribution of path lengths can be made more concentrated, thereby reducing the differences in user experience between different users and improving overall fairness.
[0059] In summary, this invention can indirectly improve service layer performance through structural optimization, avoiding the diminishing marginal returns problem caused by relying solely on business scheduling.
[0060] Example 3 A network fairness enhancement system based on Fiedler vectors includes: The graph construction module is used to construct the topology graph of the target network to be optimized. The spectral analysis module is used to construct the normalized Laplacian matrix of the topology graph, obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, and use it as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. The bottleneck identification module is used to analyze Fiedler vectors and identify potential structural cuts in the target network. The execution module is used to establish new physical links or logical connections between the potential structural cuts, thereby enhancing network fairness.
[0061] The evaluation module is used to recalculate the algebraic connectivity of the target network after establishing new physical links or logical connections between potential structural cuts, and to evaluate the changes in network performance based on the recalculated algebraic connectivity.
[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
Claims
1. A network fairness enhancement method based on Fiedler vectors, characterized in that, Includes the following steps: Construct the topology diagram of the target network to be optimized; Construct the normalized Laplacian matrix of the topology graph, obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, and use it as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. Analyze the Fiedler vectors to identify potential structural cuts in the target network; Establish new physical links or logical connections between the potential structural cuts to enhance network fairness.
2. The network fairness enhancement method based on Fiedler vectors according to claim 1, characterized in that, In the step of constructing the topology graph of the target network to be optimized, the topology graph of the target network to be optimized is represented as an undirected graph G=(V,E), where node V represents a switch, router, server or terminal device; and edge E represents a physical link or logical connection between nodes.
3. The network fairness enhancement method based on Fiedler vectors according to claim 2, characterized in that, The normalized Laplacian matrix of the constructed topology graph is then used to obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, which serves as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. The specific method is as follows: Construct the adjacency matrix of the topological graph; Construct the degree matrix based on the constructed adjacency matrix; Construct a normalized Laplacian matrix based on the adjacency matrix and degree matrix; The constructed normalized Laplacian matrix is subjected to eigenvalue decomposition, and the eigenvector corresponding to the second smallest eigenvalue is obtained as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network.
4. The network fairness enhancement method based on Fiedler vectors according to claim 3, characterized in that, In the step of performing eigenvalue decomposition on the constructed normalized Laplacian matrix and obtaining the eigenvector corresponding to the second smallest eigenvalue as the Fiedler vector, The smallest eigenvalue of the normalized Laplacian matrix is 0, corresponding to a vector of all 1s; The second smallest eigenvalue is called the algebraic connectivity of the graph, which is used to measure the strength of the connectivity of the target network. The eigenvector corresponding to the second smallest eigenvalue is the Fiedler vector, which reveals the potential structural partitioning trend of the target network. The Fiedler vector is an n-dimensional column vector, where n is the total number of nodes in the target network. The i-th component value of this vector is assigned to the node. Fiedler component values .
5. A network fairness enhancement method based on Fiedler vectors according to claim 4, characterized in that, The method for analyzing Fiedler vectors to identify potential structural cuts in the target network is as follows: Normalize each Fiedler component value of the Fiedler vector and calculate the normalized Fiedler component value of each node; The target network node is divided into multiple candidate sub-regions based on the normalized Fiedler component values; For non-adjacent node pairs across sub-regions, the normalized Fiedler distance of the node pair is calculated based on the normalized Fiedler component value of each node. The potential structural cuts of the target network are identified based on the normalized Fiedler distance.
6. The network fairness enhancement method based on Fiedler vectors according to claim 5, characterized in that, The normalization process for each Fiedler component value of the Fiedler vector is performed, and the formula for calculating the normalized Fiedler component value of each node is as follows: in, Represents a node The normalized Fiedler component values are used to measure the relative position of the node in the potential structural cut; Represents the nodes in the Fiedler vector. The corresponding component values; Represents a node The degree.
7. A network fairness enhancement method based on Fiedler vectors according to claim 6, characterized in that, The method for dividing the target network node into multiple candidate sub-regions based on the normalized Fiedler component values is as follows: The target network node is divided into two candidate sub-regions, positive and negative, based on the sign of the normalized Fiedler component values. The clustering algorithm is used to process all normalized Fiedler component values, and several sub-regions with significant numerical differences are identified as candidate sub-regions.
8. A network fairness enhancement method based on Fiedler vectors according to claim 7, characterized in that, For non-adjacent node pairs spanning sub-regions, the formula for calculating the normalized Fiedler distance of the node pair based on the normalized Fiedler component value of each node is as follows: in, Represents a node With nodes Distance metric in Fiedler vector space; This represents the normalized Fiedler component values of the two nodes; The method for identifying latent structural cuts in a target network based on the normalized Fiedler distance is as follows: The non-adjacent node pairs across sub-regions are sorted based on the normalized Fiedler distance. Node pairs with a normalized Fiedler distance greater than a preset threshold are identified as priority candidate connection pairs, and the nodes of the node pairs are located on both sides of the potential structural cut.
9. A network fairness enhancement method based on Fiedler vectors according to claim 8, characterized in that, The method further includes, after the step of establishing new physical links or logical connections between the potential structural cuts to enhance network fairness, the following: After establishing new physical links or logical connections between potential structural cuts, the algebraic connectivity of the target network is recalculated, and the network performance changes are evaluated based on the recalculated algebraic connectivity.
10. A network fairness enhancement system based on Fiedler vectors, comprising a network fairness enhancement method based on Fiedler vectors as described in any one of claims 1 to 9, characterized in that, include: The graph construction module is used to construct the topology graph of the target network to be optimized. The spectral analysis module is used to construct the normalized Laplacian matrix of the topology graph, obtain the eigenvector corresponding to the second smallest eigenvalue in the constructed normalized Laplacian matrix, and use it as the Fiedler vector. Each component of the Fiedler vector corresponds to a node in the target network. The bottleneck identification module is used to analyze Fiedler vectors and identify potential structural cuts in the target network. The execution module is used to establish new physical links or logical connections between the potential structural cuts, thereby enhancing network fairness.