Dual verification-based graph clusterability fast detection method and system

Abstract

This invention belongs to the field of information detection and provides a fast graph clustering detection method and system based on dual verification. This invention captures topological features through lazy random walk sampling and constructs a structurally similar graph to verify clustering properties. For each candidate cluster, multiple edges are uniformly and randomly sampled from the edge set corresponding to that cluster in the original graph. The label with the highest frequency among the sampled edges is counted, and its empirical proportion is calculated. Based on the comparison between the empirical proportion and a set threshold, it is determined whether the original graph satisfies label consistency. The entire process is completed within sublinear query complexity. This invention incorporates label consistency constraints into the clustering test, making the judgment criteria simultaneously cover topological cohesion and semantic homogeneity, thus improving the speed and accuracy of graph clustering detection.

Description

Technical Field

[0001] This invention belongs to the field of information detection, specifically relating to a rapid method and system for detecting graph clusterability based on dual verification. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Graph clustering, as a core task in complex network analysis, has wide applications in areas such as social network information recommendation, construction of knowledge graphs for specific scenarios, and establishment and management of bioinformatics networks.

[0004] The existing technology has the following main drawbacks: The problem of missing semantic information: Existing clusterability testing methods (such as those based on random walks or spectral analysis) only focus on the topological structure of the graph, completely ignoring the rich semantic labels attached to nodes or edges. In practical applications, a structurally highly cohesive group of nodes cannot form a meaningful semantic community if its internal edge labels are mixed and diverse (such as the intertwining of "friends," "colleagues," and "strangers" relationships in a social network). Graphs judged as "clusterable" by existing methods often experience a significant decrease in clustering quality after the introduction of label constraints.

[0005] The high computational cost is a significant issue: the conventional approach to determining graph clustering ease is to directly execute a full graph clustering algorithm and then evaluate the results using metrics such as modularity and silhouette coefficient. This method has a time complexity of at least linear O(n) or even superlinear, resulting in enormous computational overhead and limited scalability when dealing with large-scale graph datasets with millions or more nodes. Especially during data preprocessing, it's impossible to pre-select graph data worthy of in-depth computation, leading to wasted resources.

[0006] Lack of a fast pre-detection mechanism: Current technology lacks a theoretically guaranteed algorithm that can complete the decision in sublinear time. Users are forced to make a dilemma between "ignoring semantic information for fast detection but with unreliable results" and "preserving semantic information but incurring the cost of full-graph computation," which cannot meet the management needs of large-scale labeled graph data.

[0007] Dynamic network monitoring is challenging: For dynamic graphs that evolve over time, the quality of community structure may change in real time. Existing methods, due to computational efficiency limitations, struggle to achieve high-frequency clusterability monitoring and cannot promptly capture the degradation of semantic consistency and structural cohesion. Summary of the Invention

[0008] To address the aforementioned problems, this invention proposes a fast graph clustering detection method and system based on dual verification. This invention enables deep semantic and structural fusion, possesses theoretical reliability, and can complete the fast graph clustering detection in sublinear time.

[0009] According to some embodiments, the present invention adopts the following technical solution: A fast graph clusterability detection method based on dual verification includes the following steps: Acquire the image data to be detected, and uniformly and randomly sample multiple vertices from the vertex set of the image data to be detected to form a sampling set; For each sampled vertex in the sample set, perform several lazy random walks of a certain length. Each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. Record the destination of each walk and statistically obtain the empirical probability distribution of the destination of the walk with a set number of steps starting from the sampled vertex. Using the sample set as the vertex set, construct a new graph. For any pair of sampled vertices in the vertex set, calculate the distance between the empirical probability distributions of their wander endpoints. If the distance is less than a preset threshold, connect the corresponding edges in the new graph. Analyze the connected components in the new graph. If the number of connected components exceeds the predetermined upper limit of the number of clusters, the graph is determined not to satisfy the structural clustering property. Otherwise, each connected component in the new graph is regarded as a candidate cluster. For each candidate cluster, multiple edges are uniformly and randomly sampled from the edge set corresponding to the candidate cluster in the original graph. The label with the highest frequency among the sampled edges is counted, and its empirical proportion is calculated. If the empirical proportion of a candidate cluster is less than a set threshold, the original graph is determined to satisfy label consistency and has clusterability. Otherwise, the graph is determined not to satisfy structural clustering.

[0010] As an alternative implementation method, the process of acquiring the graph data to be detected includes: the graph data to be detected is a labeled undirected graph. ,in For vertex set, Let L be the edge set, L represent the edge label function, and Σ be the label set; Parameters for obtaining the data of the image to be detected include the upper limit k of the number of clusters and the lower bound of the internal conductivity. Upper bound of external conductivity Main tag ratio lower bound and distance parameters .

[0011] As an alternative implementation, the process of uniformly and randomly sampling multiple vertices from the vertex set of the graph data to be detected includes: from the vertex set... A uniform random sample of s vertices is formed to create a sample set S, where the number of samples is... n is the total number of vertices. is the distance parameter, and k is the upper limit of the number of clusters.

[0012] As an alternative implementation, for each sampled vertex in the sampling set, performing a number of lazy random walks of a certain length includes: for each sampled vertex... ,implement m The second length is l A lazy random walk is used, where each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. The destination of each walk is recorded, and the results are statistically analyzed. u Departure l Empirical probability distribution of the end point of the walk .

[0013] As a further step, the length of the lazy random walk l Set to with Proportional Here, n is the lower bound of the internal conductivity, and n is the size of the graph.

[0014] As an alternative implementation, constructing a new graph and calculating the distance between the empirical probability distributions of the wander endpoints of any pair of sampled vertices in the vertex set includes: using the sample set S as the vertex set, constructing a new graph H, called a structurally similar graph, and calculating the distance between the empirical probability distributions of the wander endpoints of any pair of sampled vertices. Calculate its wander endpoint distribution and The squared Euclidean distance between them; if this distance is less than a preset threshold... Then connect the edges in the new graph H. threshold Based on the scale of the graph data and distance parameters set up.

[0015] As an alternative implementation, the distance is either JS divergence or Wasserstein distance.

[0016] As an alternative implementation, if the empirical proportion of a candidate cluster is less than a set threshold, the process of determining that the original image satisfies label consistency and possesses clusterability includes: if there is a candidate cluster... Then determine the graph To ensure label consistency, For distance parameters, Lower bound of main label ratio, judgment graph It possesses clustering properties; If the decision graph does not satisfy structural clustering, it needs to be modified at least... Only edges or their labels can satisfy the definition of clusterability. To the maximum extent, For the scale of the graph, This is the distance parameter.

[0017] As an alternative implementation method, during the process of uniformly and randomly sampling multiple edges, the number of edges sampled... Set to with Proportional, of which To ensure a controllable error probability, the accuracy of the dominant label proportion estimation is guaranteed by using the Hofding inequality. For distance parameters, The lower bound of the primary label ratio is k, and the upper bound of the number of clusters is k.

[0018] As an alternative implementation method, vertex sampling adopts weighted sampling, prioritizing nodes with weight coefficients higher than a set value as the starting point for the walk.

[0019] A fast graph clusterability detection system based on dual verification includes: The sampling set construction module is configured to acquire the graph data to be detected, and to uniformly and randomly sample multiple vertices from the vertex set of the graph data to be detected to form a sampling set; The lazy random walk module is configured to perform a number of lazy random walks of a certain length for each sampled vertex in the sample set. Each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. The endpoint of each walk is recorded, and the empirical probability distribution of the endpoint of the walk with a set number of steps from the sampled vertex is obtained. The new graph construction module is configured to use the sample set as the vertex set to construct a new graph. For any pair of sampled vertices in the vertex set, the distance between the empirical probability distributions of their wander endpoints is calculated. If the distance is less than a preset threshold, the corresponding edge is connected in the new graph. The connected component judgment module is configured to analyze the connected components in the new graph. If the number of connected components is greater than the predetermined upper limit of the number of clusters, the graph is determined not to satisfy the structural clustering property. Otherwise, each connected component in the new graph is regarded as a candidate cluster. The clusterability determination module is configured to, for each candidate cluster, uniformly and randomly sample multiple edges from the edge set corresponding to that candidate cluster in the original graph, count the labels that appear most frequently among the sampled edges, and calculate their empirical proportions. If the empirical proportion of a candidate cluster is less than a set threshold, the original graph is determined to satisfy label consistency and has clusterability; otherwise, the graph is determined not to satisfy structural clustering.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention deeply integrates semantics and structure: it incorporates label consistency constraints into clusterability testing, so that the judgment criteria simultaneously cover topological cohesion and semantic homogeneity, which is more in line with the understanding of "meaningful communities" in applications such as social network information recommendation and the construction of knowledge graphs for specific scenarios, and avoids the generation of pseudo-communities with mixed labels.

[0021] This invention can achieve sublinear high-efficiency detection: only requires Subgraph queries have a much shorter runtime than full-graph clustering algorithms. For graphs with millions of nodes, they can complete the determination in seconds without loading the full graph data. Memory usage is sublinearly related to the number of vertices n, and they are highly scalable.

[0022] The theoretical guarantee of this invention is reliable: based on the fast mixing theorem for random walks within good clusters, and statistical tools such as Hofding's inequality and joint bounds, it is rigorously proven mathematically that the algorithm makes a correct decision with at least a 2 / 3 probability (which can be amplified to an arbitrary constant probability through repeated runs), and its reliability is supported by solid theory.

[0023] This invention enables the quantification of rejection strength: it not only outputs a binary decision but also quantifies the "distance" between the tested graph and the ideal clusterable state. This clarifies the minimum number of edges / labels that need to be modified, providing precise guidance for graph data cleaning.

[0024] This invention has high adaptability, supports plug-in graph data source access, and the parameters can be flexibly adjusted. It can be used as a standalone tool or deeply integrated into a graph database management system as an intelligent pre-filter to improve the overall pipeline efficiency.

[0025] This invention has dynamic monitoring capabilities: the extremely low cost of a single detection makes it possible to periodically clusterable monitor dynamic graphs, and can capture quality degradation events of community structure in the evolution process in real time.

[0026] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0027] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0028] Figure 1 This is a flowchart illustrating the overall process of one embodiment. Figure 2 This is a schematic diagram illustrating the construction of a structural similarity diagram for one embodiment. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0030] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0031] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0032] Where there is no conflict, the embodiments and features described in this application may be combined with each other.

[0033] Example 1 A fast graph clustering detection method based on dual verification of labels and structure is proposed. The core idea is to capture topological features through lazy random walk sampling, construct a structural similarity graph to verify clustering properties, and then sample edge labels for candidate clusters to verify semantic consistency. The entire process is completed within sublinear query complexity, such as... Figure 1 As shown, the method steps are as follows: S1. Define label-aware clustering: for a given labeled undirected graph ,in For vertex set, Let L be the edge set, E→Σ be the edge label function, and Σ be the label set. Given parameters: upper bound k for the number of clusters, and lower bound for the internal conductivity. Upper bound of external conductivity Main tag ratio lower bound Distance parameters . (Image) yes - Clusterable if and only if there exists a partition containing at most k clusters. This makes it possible for each cluster Simultaneously satisfying: (a) Structural cohesion: clusters Transitivity within the subgraph ; (b) Structural separability: clusters External conductivity relative to the entire graph ; (c) Tag consistency: There exists a primary tag. This makes in cluster Of all the edges, the one labeled is The proportion of the edges is not less than .

[0034] S2. Parameter Input and Vertex Sampling: Receive the image to be detected Query interface and parameters From the vertex set A uniform random sample of s vertices is formed to create a sample set S, where the number of samples is... , where n is the total number of vertices.

[0035] S3. Lazy Random Walk and Endpoint Distribution Estimation: For each sampled vertex ,implement m The second length is l A lazy random walk is used. Each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. The destination of each walk is recorded, and the results are statistically analyzed. u Departure l Empirical probability distribution of the end point of the walk .

[0036] S4. Construct a structural similarity graph H, such as Figure 2 As shown: Using the sample set S as the vertex set, a new graph H is constructed, called a structurally similar graph. For any pair of sampled vertices... Calculate its wander endpoint distribution and The square of the Euclidean distance between them ( (Distance). If the distance is less than a preset threshold. Then connect the edges in H. Threshold Based on the size of the graph and parameters set up.

[0037] S5. Structural Connectivity Verification: Analyze the connected components in the structurally similar graph H. If the number of connected components in H is greater than k, then graph G does not satisfy structural clustering, and proceed to S8; otherwise, treat each connected component in H as a candidate cluster. Now, let's move on to the next step.

[0038] S6. Label Consistency Verification: For each candidate cluster From the candidate cluster in the original graph Uniform random sampling in the corresponding edge set Edges. Analyze the labels that appear most frequently among the sampled edges and calculate their empirical proportion. If a candidate cluster exists... Then determine the graph If label consistency is satisfied, proceed to step S7; otherwise, proceed to step S8.

[0039] S7. Acceptance Decision: Output "Accept", decision graph have - Clusterability.

[0040] S8. Rejection Decision: Output "Reject", decision graph yes keep away - Clusterability, i.e., requires at least [modification] Strip or its label ( Only when the maximum value is reached can the definition of clusterability be satisfied.

[0041] In this embodiment, the length of the lazy random walk in step S3 l Set to with This is proportional to ensure that random walks can mix rapidly within real clusters with high internal conductivity, making the endpoint distribution approximate a uniform distribution.

[0042] In this embodiment, the number of sampled edges in step S6 Set to with Proportional, of which To ensure a controllable error probability, the accuracy of the dominant label proportion estimation is guaranteed by the Hofding inequality.

[0043] In some embodiments, when constructing a structural similarity graph, the following can be used: Replace the distance with JS divergence or Wasserstein distance to enhance sensitivity to differences in distribution shape, especially suitable for graphs with large differences in degree distribution within clusters.

[0044] In some embodiments, vertex sampling can employ weighted sampling, prioritizing the selection of nodes with high height as the starting point for the walk, thereby improving the efficiency of covering the real cluster. However, the number of samples needs to be adjusted to compensate for the estimation bias caused by the non-uniform distribution.

[0045] In some embodiments, structural verification and label verification can be performed in parallel rather than sequentially. That is, side label streaming sampling is started while candidate clusters are being built, and the process is terminated immediately when the number of any component exceeds the limit or the label ratio is insufficient, further reducing latency in the average case.

[0046] The method provided in Embodiment 1 above can be applied to information recommendation based on social networks (such as friend recommendation or product recommendation), construction of knowledge graphs for specific scenarios (such as construction of knowledge graphs for power systems, construction of knowledge graphs for medicine, etc.), establishment and management of bioinformatics networks, etc.

[0047] To further illustrate the technical effects of this invention in practical applications, specific implementation scenarios in various fields are provided below. These scenarios, targeting specific types of graph data, elaborate on the specific application steps, parameter configurations, and practical effects of the method, fully demonstrating the adaptability and practical value of this invention in different industries.

[0048] This embodiment provides a method for detecting the spread of false information on social networks based on a dual verification mechanism. It addresses the technical problems of excessive computational resource consumption and high response latency in traditional full-graph clustering algorithms when dealing with hundreds of millions of users, and enables sublinear time-based pre-detection and real-time early warning of false information spreading communities.

[0049] Application Scenario Overview: This embodiment is applied to the quality assessment of user interaction graph data on social media platforms. The graph data is a labeled undirected graph. vertex set Includes platform user nodes (scale) n Usually between 10 6 Up to 10 8 (scale), edge set Side label function represents user-to-user forwarding, commenting, and liking behaviors. L:E→Σ Map the edges to the semantic set Σ={σ1,σ2,σ3}, where σ1 identifies the behavior of spreading false information, σ2 identifies the behavior of spreading true information, and σ3 identifies the behavior of spreading unverified information.

[0050] Method execution flow: 1. Parameter initialization: Receives clusterability determination parameters, preferably configuring an upper limit on the number of clusters. Lower bound of internal conductivity Upper bound of external conductivity Main tag ratio lower bound and distance parameters Those skilled in the art can adjust the above parameters according to the actual granularity of public opinion monitoring; such adjustments are equivalent substitutions in this embodiment.

[0051] 2. Weighted Vertex Sampling: To improve coverage efficiency for high-influence propagation hubs, a weighted sampling strategy is used instead of uniform sampling. For example, for each vertex... Assign weights Sampling according to this weight distribution The vertices constitute the sampling set. S The typical sampling scale is 3000±20% of core user nodes.

[0052] 3. Adaptive lazy random walk: For each sampled vertex implement m=100 The second length is The lazy random walk. Preferably, the lazy probability...α The value is dynamically set to 0.3 to adapt to the small-world nature of social networks. The distribution of wander endpoints is recorded. , construct structural features.

[0053] 4. Construction of structural similarity graph: using the sampling set S Construct a structural similarity graph for the vertex set H This embodiment preferably uses the JS divergence measure to measure the distribution difference: ,in When the divergence value is less than the threshold Establishing edges .

[0054] 5. Double verification judgment: If the structural similarity diagram H The number of connected components exceeds k If the original graph does not satisfy structural clustering, then the connected components are considered candidate clusters; otherwise, each connected component is considered a candidate cluster. For each candidate cluster... C i Sample from the corresponding edge set of the original graph Edges (typical value 800), statistical main tag experience ratio When it exists Furthermore, when the main label is σ1, it is determined to be a high-risk false information network, and the system outputs "accept judgment" and triggers an early warning.

[0055] This embodiment completes detection within 30 seconds of the initial outbreak of public opinion, with a query complexity of [missing information]. Memory usage is reduced by more than 95%, and the number of fake interaction edges that need to be cleaned can be quantified. This provides precise guidance for platform governance.

[0056] Example 2 A fast graph clusterability detection system based on dual verification includes: The sampling set construction module is configured to acquire the graph data to be detected, and to uniformly and randomly sample multiple vertices from the vertex set of the graph data to be detected to form a sampling set; The lazy random walk module is configured to perform a number of lazy random walks of a certain length for each sampled vertex in the sample set. Each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. The endpoint of each walk is recorded, and the empirical probability distribution of the endpoint of the walk with a set number of steps from the sampled vertex is obtained. The new graph construction module is configured to use the sample set as the vertex set to construct a new graph. For any pair of sampled vertices in the vertex set, the distance between the empirical probability distributions of their wander endpoints is calculated. If the distance is less than a preset threshold, the corresponding edge is connected in the new graph. The connected component judgment module is configured to analyze the connected components in the new graph. If the number of connected components is greater than the predetermined upper limit of the number of clusters, the graph is determined not to satisfy the structural clustering property. Otherwise, each connected component in the new graph is regarded as a candidate cluster. The clusterability determination module is configured to, for each candidate cluster, uniformly and randomly sample multiple edges from the edge set corresponding to that candidate cluster in the original graph, count the labels that appear most frequently among the sampled edges, and calculate their empirical proportions. If the empirical proportion of a candidate cluster is less than a set threshold, the original graph is determined to satisfy label consistency and has clusterability; otherwise, the graph is determined not to satisfy structural clustering.

[0057] Some embodiments also include a result output and reporting module, which is used to optionally output visualization of structural similarity graph H, candidate cluster size distribution, main label proportion histogram, and a summary of the judgment criteria.

[0058] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of one or more computer-usable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. CD - ROM It takes the form of a computer program product implemented on (such as optical memory, etc.).

[0059] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0060] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0061] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fast method for detecting graph clusterability based on dual verification, characterized in that, Includes the following steps: Acquire the image data to be detected, and uniformly and randomly sample multiple vertices from the vertex set of the image data to be detected to form a sampling set; For each sampled vertex in the sample set, perform several lazy random walks of a certain length. Each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. Record the destination of each walk and statistically obtain the empirical probability distribution of the destination of the walk with a set number of steps starting from the sampled vertex. Using the sample set as the vertex set, construct a new graph. For any pair of sampled vertices in the vertex set, calculate the distance between the empirical probability distributions of their wander endpoints. If the distance is less than a preset threshold, connect the corresponding edges in the new graph. Analyze the connected components in the new graph. If the number of connected components exceeds the predetermined upper limit of the number of clusters, the graph is determined not to satisfy the structural clustering property. Otherwise, each connected component in the new graph is regarded as a candidate cluster. For each candidate cluster, multiple edges are uniformly and randomly sampled from the edge set corresponding to the candidate cluster in the original graph. The label with the highest frequency among the sampled edges is counted, and its empirical proportion is calculated. If the empirical proportion of a candidate cluster is less than a set threshold, the original graph is determined to satisfy label consistency and has clusterability. Otherwise, the graph is determined not to satisfy structural clustering.

2. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, The process of obtaining the data of the image to be detected includes: the data of the image to be detected is a labeled undirected graph. ,in For vertex set, Let L be the edge set, L represent the edge label function, and Σ be the label set; Parameters for obtaining the data of the image to be detected include the upper limit k of the number of clusters and the lower bound of the internal conductivity. Upper bound of external conductivity Main tag ratio lower bound and distance parameters .

3. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, The process of uniformly and randomly sampling multiple vertices from the vertex set of the graph to be detected includes: from the vertex set... A uniform random sample of s vertices is formed to create a sample set S, where the number of samples is... n is the total number of vertices. is the distance parameter, and k is the upper limit of the number of clusters.

4. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, For each sampled vertex in the sample set, the process of performing several lazy random walks of a certain length includes: for each sampled vertex ,implement m The second length is l A lazy random walk is used, where each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. The destination of each walk is recorded, and the results are statistically analyzed. u Departure l Empirical probability distribution of the end point of the walk ; Length of lazy random walk l Set to with Proportional Here, n is the lower bound of the internal conductivity, and n is the size of the graph.

5. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, Constructing a new graph, for any pair of sampled vertices in the vertex set, involves calculating the distance between the empirical probability distributions of their wander endpoints. This process includes: using the sample set S as the vertex set, constructing a new graph H, called a structurally similar graph, where for any pair of sampled vertices... Calculate its wander endpoint distribution and The squared Euclidean distance between them; if this distance is less than a preset threshold... Then connect the edges in the new graph H. threshold Based on the scale of the graph data and distance parameters set up.

6. A fast graph clusterability detection method based on dual verification as described in claim 1 or 5, characterized in that, The distance is either the JS divergence or the Wasserstein distance.

7. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, If the empirical proportion of a candidate cluster is less than a set threshold, the original image is determined to satisfy label consistency. The process of determining that the image is clusterable includes: if a candidate cluster exists... Then determine the graph To ensure label consistency, For distance parameters, Lower bound of main label ratio, judgment graph It possesses clustering properties; If the decision graph does not satisfy structural clustering, it needs to be modified at least... Only edges or their labels can satisfy the definition of clusterability. To the maximum extent, For the scale of the graph, This is the distance parameter.

8. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, During the process of uniformly and randomly sampling multiple edges, the number of edges sampled Set to with Proportional, of which To ensure a controllable error probability, the accuracy of the dominant label proportion estimation is guaranteed by using the Hofding inequality. For distance parameters, The lower bound of the primary label ratio is k, and the upper bound of the number of clusters is k.

9. The fast graph clusterability detection method based on dual verification as described in claim 1, characterized in that, Vertex sampling uses weighted sampling, prioritizing nodes with weight coefficients higher than a set value as the starting point for the walk.

10. A rapid graph clustering detection system based on dual verification, characterized in that, include: The sampling set construction module is configured to acquire the graph data to be detected, and to uniformly and randomly sample multiple vertices from the vertex set of the graph data to be detected to form a sampling set; The lazy random walk module is configured to perform a number of lazy random walks of a certain length for each sampled vertex in the sample set. Each walk has a certain probability of stopping at the current node or randomly jumping to a neighboring node. The endpoint of each walk is recorded, and the empirical probability distribution of the endpoint of the walk with a set number of steps from the sampled vertex is obtained. The new graph construction module is configured to use the sample set as the vertex set to construct a new graph. For any pair of sampled vertices in the vertex set, the distance between the empirical probability distributions of their wander endpoints is calculated. If the distance is less than a preset threshold, the corresponding edge is connected in the new graph. The connected component judgment module is configured to analyze the connected components in the new graph. If the number of connected components is greater than the predetermined upper limit of the number of clusters, the graph is determined not to satisfy the structural clustering property. Otherwise, each connected component in the new graph is regarded as a candidate cluster. The clusterability determination module is configured to, for each candidate cluster, uniformly and randomly sample multiple edges from the edge set corresponding to that candidate cluster in the original graph, count the labels that appear most frequently among the sampled edges, and calculate their empirical proportions. If the empirical proportion of a candidate cluster is less than a set threshold, the original graph is determined to satisfy label consistency and has clusterability; otherwise, the graph is determined not to satisfy structural clustering.

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