Social network link prediction and community detection visual analysis platform based on machine learning

Abstract

The invention discloses a social network link prediction and community detection visual analysis platform based on machine learning. The social network link prediction and community detection visual analysis platform comprises a user-defined module which is used for designing a social network prediction direction, a corresponding prediction algorithm and a user-defined data set by a user according to requirements; the data set and algorithm importing module is used for importing a social network prediction direction designed by a user according to requirements, a corresponding prediction algorithm and a self-defined data set into a system; the selection module is used for selecting a data set and a prediction algorithm, the data set comprises a user-defined data set and a data set stored in the system, and the prediction algorithm comprises a user-defined prediction algorithm and a prediction algorithm stored in the system; the data analysis module is used for preprocessing the selected data set, analyzing the connection relation of the network and taking the connection relation as original data for link prediction and community detection to perform link prediction and community detection; and the visualization module is used for visually displaying the original data, the link prediction and the community detection result.

Description

Technical Field

[0001] The present invention relates to the technical field of social network analysis, and more specifically to a social network link prediction and community detection visualization analysis platform based on machine learning. Background Art

[0002] With the rapid development and popularization of the Internet, social networks have become an indispensable part of people's daily lives. In these networks, people form social relationships by establishing connections (or links), thus forming a complex social network structure. Social network analysis is not limited to direct connections between individuals, but also involves broader issues such as community structure and information dissemination patterns.

[0003] In social networks, predicting new social relationship links (i.e., link prediction) and detecting community structures (i.e., community detection) are important research directions. Link prediction helps understand the potential relationships between nodes in the network, while community detection reveals the potential group structure and social clustering of nodes in the network. However, due to the complexity and scale of social networks, traditional analysis methods often have difficulty in effectively processing large-scale data and extracting hidden patterns.

[0004] The rapid development of machine learning technology has provided new opportunities for solving complex problems in social network analysis. Through machine learning algorithms, large-scale network data can be used to discover patterns and rules hidden behind the network. For example, the link prediction model based on graph neural network can predict the probability of forming new social relationships by learning the implicit features between nodes; while clustering algorithms can help discover the community structure in the network and provide a deep understanding of the network structure and information dissemination dynamics.

[0005] Although existing machine learning algorithms can provide powerful analytical capabilities, their results are often abstract and complex. In order to make the analysis results more interpretable and applicable, it is crucial to develop a visual analysis platform that integrates link prediction and community detection functions. Such a platform can not only help researchers and analysts quickly explore and understand the structure and dynamics of social networks, but also provide support for decision makers, such as in social network marketing and influence analysis.

[0006] At the same time, although the existing network link prediction systems all have reliable and efficient prediction algorithms, when we want to predict other directions, we need to find other corresponding platforms. In order to facilitate the diversified needs of users, it is obviously necessary to develop a platform with algorithm and data set submission functions to meet the diversified needs of users as much as possible. Such a platform can save users' time and improve users' satisfaction with the algorithm. Summary of the invention

[0007] In view of this, the present invention provides a social network link prediction and community detection visualization analysis platform based on machine learning, which can help researchers and analysts quickly explore and understand the structure and dynamics of social networks through visualization, and meet the diversified needs of users.

[0008] In order to achieve the above object, the present invention adopts the following technical solution:

[0009] A machine learning-based social network link prediction and community detection visualization analysis platform, including:

[0010] Custom module: used for users to design social network prediction directions and corresponding prediction algorithms as well as customized data sets according to their needs;

[0011] Dataset and algorithm import module: used to import the social network prediction direction and corresponding prediction algorithm designed by users according to their needs and customized data sets into the system;

[0012] Selection module: used to select data sets and prediction algorithms. Data sets include user-defined data sets and data sets stored in the system. Prediction algorithms include user-defined prediction algorithms and prediction algorithms stored in the system.

[0013] Data analysis module: used to preprocess the selected data set, analyze the connection relationship of the network and use it as the raw data for link prediction and community detection, and perform link prediction and community detection based on the selected data set and the selected prediction algorithm;

[0014] Analysis result saving module: used to save the results of link prediction and community detection;

[0015] Visualization module: used to visualize the results of raw data, link prediction and community detection.

[0016] Preferably, the prediction algorithm includes a link prediction algorithm and a community detection algorithm. The link prediction algorithm includes a resource allocation index, a Jaccard coefficient, a Jacquard index and a common neighbor index. The community detection algorithm includes an asynchronous fluid community algorithm, an asynchronous label propagation algorithm, a label propagation algorithm and an AICD algorithm (a community detection algorithm based on an autoencoder).

[0017] Preferably, the preprocessing includes: processing of outliers and missing values, processing of data redundancy and numerical conflicts, normalization and regularization of data, sampling of data, and unification of data range and format;

[0018] The number of nodes, number of edges, network density, maximum degree, minimum degree, average degree, clustering coefficient and degree similarity of the preprocessed data are calculated as the raw data for link prediction and community detection.

[0019] Preferably, the community detection algorithm is obtained after passing the training, wherein the specific training process of the AICD algorithm is:

[0020] 1) Define the objective function:

[0021]

[0022] Among them, M is the Laplace matrix, α, q are hyperparameters, S is the similarity matrix, J D is the reconstruction error term, J E is the sparsity regularization, J r eg is the smoothness adjustment item;

[0023] 2) Construct an adjacency matrix based on the connection relationship of the network, and convert the adjacency matrix into a similarity matrix through Dice similarity:

[0024]

[0025] Where N represents the number of neighbors of a node. represents the number of common neighbors of node i and node j, Represents a single node v i ,v j The number of neighbors of

[0026] 3) Calculate the optimal solution of the objective function through the similarity matrix.

[0027] Preferably, the optimal solution of the objective function is calculated by the similarity matrix, specifically including:

[0028] By continuously iterating and updating X i and Y q The optimal value of , the specific update formula is:

[0029]

[0030] After the iteration is completed, X i and Y q as the optimal value of the objective function.

[0031] Preferably, X i and Y q The multiplication update rule for is:

[0032]

[0033] Among them, ⊙ represents element-wise multiplication, and the division symbol represents element-wise division.

[0034] Preferably, a Python third-party library is used to visualize the connection relationship of the network through a box plot, a stacked line graph, or a three-line table.

[0035] Preferably, it also includes an audit and verification module for verifying the social network prediction direction and the corresponding prediction algorithm designed by the user according to the needs. The social network prediction direction is imported into the system only when it matches the corresponding prediction algorithm.

[0036] Preferably, the connection relationship of the network includes the number of nodes, the number of edges, network density, maximum degree, minimum degree, average degree, clustering coefficient, degree similarity and connection characteristics, and the connection characteristics are reflected by centrality, degree centrality and closeness centrality.

[0037] Preferably, the centrality calculation formula is:

[0038]

[0039] Where V is the node set, is the number of shortest (S, t) paths, and is the number of paths that pass through some node v other than S;

[0040] The degree centrality calculation formula is:

[0041]

[0042] Among them, K i represents the number of existing edges connected to node i, and N-1 represents the number of edges connecting node i to other nodes;

[0043] The formula for calculating closeness centrality is:

[0044]

[0045] Among them, d i It represents the average distance from node i to the rest of the points. The reciprocal of the average distance is the closeness to the centrality.

[0046] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a social network link prediction and community detection visualization analysis platform based on machine learning, which has the following advantages:

[0047] (1) Based on the original machine learning algorithm analysis, the present invention provides a visualization module, which can make the calculated data more clear at a glance, reduce the difficulty of data analysis for users, and reduce the burden.

[0048] (2) The present invention provides a data preservation function, which facilitates subsequent research work.

[0049] (3) Compared with other link prediction systems, the present invention is more flexible. It is not just a single social network link prediction, but a diversified link prediction system that can add or delete functions based on user needs. It only needs to provide the platform with corresponding data sets and algorithms to implement predictions in multiple aspects.

[0050] (4) The visualization system has an independently created algorithm ALCD. The ALCD algorithm has achieved good results through experiments and comparison with other popular community detection algorithms (such as LabelPropagation, BigClam, DYNMOGA, etc.). That is, it can accurately discover the community structure and help discover user groups under different event themes in social networks.

[0051] (5) There are many prediction methods in link prediction, such as Jacquard index, common neighbor index, resource allocation coefficient, etc. Different methods have their own advantages and can increase flexibility in practical applications so as to observe the analysis results from different angles.

[0052] (7) During the operation of the algorithm, the maximum degree, minimum degree, average degree, number of nodes, number of edges, network density, clustering coefficient after removing self-loops and other data collected will be presented to facilitate users to understand the original data.

[0053] (8) The visualization system can be further improved and optimized, such as adding more charts and visualization controls, supporting more algorithms and data sets, and improving the performance and stability of the system to meet the continuous needs and challenges of users.

[0054] (9) The visualization system uses interfaces for connection. When we need to add new prediction directions and algorithms, we only need to add an interface to the new data set and algorithm and it can be used normally. This makes future updates and optimizations extremely convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0056] Figure 1 A schematic diagram of the structure of the social network link prediction and community detection visualization analysis platform based on machine learning provided by the present invention.

[0057] Figure 2 This is a flow chart of the AICD algorithm provided by the present invention.

[0058] Figure 3 A schematic diagram of the structure of a social network link prediction and community detection visualization analysis platform based on machine learning in another embodiment of the present invention.

[0059] Figure 4 The NMI results of different models provided by the present invention in non-overlapping community detection.

[0060] Figure 5 The ARI results of different models provided by the present invention in non-overlapping community detection.

[0061] Figure 6 The NMI indicator evaluation results of different models provided by the present invention on the overlapping community LFR network.

[0062] Figure 7 ARI indicator evaluation results of different models provided by the present invention on overlapping community LFR networks. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] The embodiment of the present invention discloses a social network link prediction and community detection visualization analysis platform based on machine learning, such as Figure 1 As shown, including:

[0065] Custom module: used for users to design social network prediction directions and corresponding prediction algorithms as well as customized data sets according to their needs;

[0066] Dataset and algorithm import module: used to import the social network prediction direction (such as infectious disease transmission path, etc.) and corresponding prediction algorithms and customized data sets designed by users according to their needs into the system; it should be noted here that if the prediction algorithm and data set are stored internally, they do not need to be imported again.

[0067] Selection module: used to select data sets and prediction algorithms. Data sets include user-defined data sets and data sets stored in the system. Prediction algorithms include user-defined prediction algorithms and prediction algorithms stored in the system.

[0068] Data analysis module: used to preprocess the selected data set, analyze the connection relationship of the network and use it as the raw data for link prediction and community detection, and perform link prediction and community detection based on the selected data set and the selected prediction algorithm;

[0069] Analysis result saving module: used to save the results of link prediction and community detection;

[0070] Visualization module: used to visualize the results of raw data, link prediction and community detection.

[0071] The present invention defines a custom module according to customer needs, so that users can use the system according to their own needs and meet the diverse needs of users.

[0072] The link prediction and community detection steps of the present invention are specifically as follows:

[0073] Step 1: Load the selected model (prediction algorithm) into memory and input a dataset.

[0074] Step 2: Preprocess the data set input in step 1.

[0075] Step 3: Input the test data from step 2 into the model loaded in step 1 and perform the prediction operation.

[0076] Step 4: After the model prediction in step 3 is completed, the prediction results will be output. At the same time, the platform will visualize and display the results.

[0077] In this embodiment, the data analysis module uses Python's numpy and pandas libraries to preprocess the data set, including: processing of outliers and missing values, processing of data redundancy and numerical conflicts, normalization and regularization of data, and data sampling;

[0078] The number of nodes, number of edges, network density, maximum degree, minimum degree, average degree, clustering coefficient and degree similarity of the preprocessed data are calculated as data to help link prediction and community detection.

[0079] In this embodiment, if Figure 3 As shown, it also includes an audit and verification module, which is used to verify the social network prediction direction and the corresponding prediction algorithm designed by the user according to the needs. Only when the social network prediction direction matches its corresponding prediction algorithm will it be imported into the platform system, thereby ensuring the accuracy of the data.

[0080] In this embodiment, the prediction algorithm includes a link prediction algorithm and a community detection algorithm. The link prediction algorithm includes a resource allocation index, a Jaccard coefficient, a Jacquard index and a common neighbor index. The community detection algorithm includes an asynchronous fluid community algorithm, an asynchronous label propagation algorithm, a label propagation algorithm and an AICD algorithm.

[0081] And the community detection algorithm is obtained after passing the training, such as Figure 2 As shown, the specific training process of the AICD algorithm is:

[0082] 1) Define the objective function and hyperparameters α and q:

[0083]

[0084] Where M is the graph Laplacian matrix, M = DS, where D is a diagonal matrix, each element of which is the sum of the elements of each row in the S matrix, α, q are hyperparameters, S is the similarity matrix, J D To reconstruct the error term, it quantifies the adjacency matrix and its low-rank matrix X1, X2, ···, X q With Y q The difference in products ensures the fidelity of the model to the original data, thus providing an accurate representation of the network structure. E It is a sparsity regularizer that encourages the learned features to remain sparse. This sparsity plays a key role in the model as it allows for easier feature selection and interpretation. Due to its sparser nature, each community is expected to have a unique set of dominant features, making the community structure more interpretable. r eg is a smoothness adjustment term, multiplied by a hyperparameter α, which encourages adjacent features to have similar values, which is crucial for preserving local structures in the data. By requiring adjacent nodes that are more likely to belong to the same community to have similar feature representations, it ensures that the model does not cause the similarity matrix to produce an overly fragmented community structure.

[0085] 2) Construct an adjacency matrix based on the network's connection relationship (number of nodes, number of edges, network density, maximum degree, minimum degree, average degree, clustering coefficient, degree similarity, and connection characteristics), and convert the adjacency matrix into a similarity matrix using Dice similarity:

[0086]

[0087] Where N represents the number of neighbors of a node. represents the number of common neighbors of node i and node j, Represents a single node v i ,v j The number of neighbors of

[0088] Among them, the connection characteristics are reflected by centrality, degree centrality and closeness centrality. The connection characteristics refer to the diversity and complexity of the connection relationship, the closeness between nodes, etc. For example, if you want to predict the spread network of infectious diseases, there are many kinds of connection relationships. For example, the person with the disease is connected to the people he contacts. Their relationship may be friends, family members, or strangers:

[0089] Centrality:

[0090] Where V is the node set, is the number of shortest (S, t) paths, and o(S, t|V) is the number of those paths that pass through some node v other than S.

[0091] Degree Centrality:

[0092] Among them, K i represents the number of existing edges connected to node i, and N-1 represents the number of edges connecting node i to other nodes.

[0093] Closeness Centrality:

[0094] Among them, d i It represents the average distance from node i to the rest of the points. The reciprocal of the average distance is the closeness to the centrality.

[0095] 3) Input the hyperparameters α, q, similarity matrix S, Laplace matrix M, and maximum number of iterations C into the algorithm to calculate the optimal solution of the objective function, including:

[0096] By continuously iterating and updating X i and Y q The optimal value of , the specific update formula is:

[0097]

[0098] After the iteration is completed, X i and Y q as the optimal value of the objective function.

[0099] Among them, X i and Y q The multiplication update rule for is:

[0100]

[0101] Among them, ⊙ represents element-wise multiplication, and the division symbol represents element-wise division.

[0102] This update process is repeated iteratively. There are three conditions for the end of the iteration. The first is that the number of iterations reaches the preset maximum number of iterations. The second is when the output data (X i and Y q ) has reached a certain threshold, and the third is the output value (X i and Y q ) has converged. When one of the three conditions is met, the iterative update ends. i and Y q The matrix is ​​the optimal value that minimizes the objective function.

[0103] After obtaining these two matrices, select matrix Y q As the matrix used for analysis, Y q The data rows and columns represent the probability of the row node being in the column community respectively. For example, the value of the i-th row and j-th column is 0.36, which means that the probability of node i being in the j-th community is 0.36.

[0104] A reliable model is obtained by evaluating and optimizing the obtained model. If it is reliable in itself, the model is used after evaluation by the NMI and ARI indicators. To evaluate the quality of community discovery, the Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI) are used, both of which are included in the sklearn toolkit.

[0105] NMI is an indicator to measure the similarity between two sets. Its value ranges from 0 to 1. The closer the value is to 1, the closer the community division result is to the real community structure. Its definition is as follows:

[0106]

[0107] Among them, A represents the clustering result, that is, the result of community division, and B represents the real community label. I(A,B) represents the mutual information between A and B, and H(A) and H(B) represent the entropy of community A and the real label B respectively. The calculation formula of mutual information I(A,B) is as follows:

[0108]

[0109] Where k represents the number of clusters and m represents the number of categories. ij It is the number of samples whose clustering result is category i and whose true label is category j divided by the total number of samples. i and p j They represent the number of samples whose clustering results are category i and whose true labels are category j divided by the total number of samples.

[0110] The entropy H(A) is calculated as follows:

[0111]

[0112] ARI (Automated Readability Index), also known as the Adjusted Rand Index, is another evaluation indicator used to measure clustering results. The value range of ARI is between -1 and 1, and a larger value indicates that the clustering result is closer to the actual situation. Its definition is as follows:

[0113]

[0114] Among them, RI is the Rand Index and Expected is the mathematical expectation.

[0115] In the model evaluation, if the NMI value is close to 0 instead of 1, then it can be determined that the model is unreliable. In order to make the model reliable, the hyperparameters can be adjusted, and then the adjusted model can be trained and evaluated until the NMI value is close to 1. Then it can be said that the results obtained by this model are reliable.

[0116] ARI and NMI are similar on the surface. Its range is -1 to 1. When the value of ARI is close to -1, the data obtained by the model is unreliable. Similar to NMI, it is necessary to manually adjust the hyperparameters and perform training and evaluation again until the value of ARI is close to 1. At this time, it can be said that the data obtained by this model is reliable.

[0117] The following is the comparison of the evaluation indicators of the ALCD algorithm after execution with the currently popular algorithms, as shown in Table 1:

[0118] Table 1 Data comparison

[0119]

[0120] The standardized mutual information NMI and adjusted Rand coefficient ARI scores of each model under the overlapping community dataset are shown in Table 1. It can be seen that the AICD model is equivalent to LabelPropagation (sound event detection algorithm based on neural network), BigClam (label propagation algorithm), DYNMOGA (large network overlapping community detection algorithm), MGV (evolutionary multi-objective optimization method for dynamic network community discovery), and DANMF (modularity-aware graph autoencoder) and achieved good results.

[0121] like Figure 4 and Figure 5 The results of NMI and ARI of different models for non-overlapping community detection are shown. For the NMI index, the AICD model outperforms other algorithms on the Enron, KIT and GN_data datasets, indicating that the AICD method of the present invention is more accurate in mining community structures. However, for the ARI index, the performance of the AICD model on the Enron dataset is slightly lower than that of the DYNMOGA algorithm, with a difference of only 0.07.

[0122] like Figure 6 and Figure 7 As shown in the figure, the evaluation results of NMI and ARI indicators on the overlapping community LFR network are shown respectively. The x-axis of the line graph represents the average connectivity k of the LFR network, ranging from 0.1 to 0.5. The AICD algorithm performs very well in both NMI and ARI indicators. Although almost all algorithms show a significant decline when k=0.5, the AICD model still achieves good results, but slightly lower than MGV. This is because the model incorporates the consideration of the modularity structure of the graph, and better considers the modularity structure of the graph when learning the representation of the graph, which makes the model more accurate in overlapping network detection, especially when there are obvious overlapping communities in the graph.

[0123] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0124] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A social network link prediction and community detection visualization analysis platform based on machine learning, characterized by: include: Custom module: used for users to design social network prediction directions and corresponding prediction algorithms as well as customized data sets according to their needs; Dataset and algorithm import module: used to import the social network prediction direction and corresponding prediction algorithm designed by users according to their needs and customized data sets into the system; Selection module: used to select data sets and prediction algorithms. Data sets include user-defined data sets and data sets stored in the system. Prediction algorithms include user-defined prediction algorithms and prediction algorithms stored in the system. Data analysis module: used to preprocess the selected data set, analyze the connection relationship of the network and use it as the raw data for link prediction and community detection, and perform link prediction and community detection based on the selected data set and the selected prediction algorithm; Analysis result saving module: used to save the results of link prediction and community detection; Visualization module: used to visualize the results of raw data, link prediction and community detection.

2. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 1 is characterized in that: The prediction algorithms include link prediction algorithm and community detection algorithm. The link prediction algorithm includes resource allocation index, Jaccard coefficient, Jacquard index and common neighbor index. The community detection algorithm includes asynchronous fluid community algorithm, asynchronous label propagation algorithm, label propagation algorithm and AICD algorithm.

3. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 1 is characterized in that: Preprocessing includes: processing of outliers and missing values, processing of data redundancy and numerical conflicts, data normalization and regularization, and data sampling; The number of nodes, number of edges, network density, maximum degree, minimum degree, average degree, clustering coefficient and degree similarity of the preprocessed data are calculated as the raw data for link prediction and community detection.

4. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 2 is characterized in that: The community detection algorithm is obtained after passing the training. The specific training process of the AICD algorithm is as follows: 1) Define the objective function: Among them, M is the Laplace matrix, α, q are hyperparameters, S is the similarity matrix, J D is the reconstruction error term, J E is the sparsity regularization, J r eg is the smoothness adjustment item, Y q is the community relationship matrix; 2) Construct an adjacency matrix based on the connection relationship of the network, and convert the adjacency matrix into a similarity matrix through Dice similarity: Where N represents the number of neighbors of a node. represents the number of common neighbors of node i and node j, Represents a single node v i ,v j The number of neighbors of 3) Calculate the optimal solution of the objective function through the similarity matrix.

5. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 4 is characterized in that: The optimal solution of the objective function is calculated through the similarity matrix, including: By continuously iterating and updating X i and Y q The optimal value of , the specific update formula is: After the iteration is completed, X i and Y q as the optimal value of the objective function.

6. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 5 is characterized in that: X i and Y q The multiplication update rule for is: Among them, ⊙ represents element-wise multiplication, and the division symbol represents element-wise division.

7. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 1 is characterized in that: Use Python third-party libraries to visualize the network's connectivity through box plots, stacked line graphs, or three-line tables.

8. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 1, characterized in that: It also includes an audit and verification module, which is used to verify the social network prediction direction and the corresponding prediction algorithm designed by the user according to the needs. Only when the social network prediction direction matches its corresponding prediction algorithm will it be imported into the system.

9. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 3 is characterized in that: The connection relationship of the network includes the number of nodes, the number of edges, network density, maximum degree, minimum degree, average degree, clustering coefficient, degree similarity and connection characteristics, and the connection characteristics are reflected by centrality, degree centrality and closeness centrality.

10. The social network link prediction and community detection visualization analysis platform based on machine learning according to claim 9, characterized in that: The centrality calculation formula is: Where V is the node set, is the number of shortest (S, t) paths, and is the number of paths that pass through some node v other than S; The degree centrality calculation formula is: Among them, K i represents the number of existing edges connected to node i, and N-1 represents the number of edges connecting node i to other nodes; The formula for calculating closeness centrality is: Among them, d i It represents the average distance from node i to the rest of the points. The reciprocal of the average distance is the closeness to the centrality.

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