Network topology visualization method

Abstract

The invention discloses a network topology visualization method. The method comprises the following steps: configuring and preparing original data parameters of a network topology structure; inputting and storing original data parameters; cleaning and preprocessing the data of the original data parameters; a Louvain algorithm is used to identify communities in the network, and partitioning is carried out; performing layout of the network topology of each subarea by using an improved force steering algorithm, and adjusting layout parameters; adjusting the relative positions of the subarea network topologies, adjusting the positions of the subarea network topologies in the whole network topology, and merging the results obtained by the subarea network topology division algorithm; and drawing an obtained result, and outputting network topological graph information. The network topology visualization method provided by the invention considers various network condition scenes, not only improves the processing efficiency and the visual quality of layout, but also has wide application potential and remarkable practical value, and can effectively support the requirements of modern network design and management.

Description

Technical Field

[0001] The present invention relates to the fields of network security and network management, and in particular to a method for visualizing network topology. Background Art

[0002] With the explosive growth of Internet data, graph data processing has become an indispensable role in social life. Most current network simulation technologies use digital twin technology to simulate the real network structure, thereby creating a simulated network similar to the real environment. This highly simulated network environment not only provides researchers with a risk-free testing platform, but also makes network design and security analysis more efficient and accurate. In addition, the visualization of complex network topology is a key tool for understanding large network systems. It greatly simplifies the diagnosis and optimization process of network problems by converting complex network structures into intuitive graphical representations.

[0003] The visual system is the main way for humans to obtain information, which also emphasizes the core role of visualization in data presentation. By converting abstract network data into intuitive graphics, it not only helps users effectively understand network characteristics, patterns and behaviors, but also supports data operations and analysis, so as to make accurate predictions and judgments. Therefore, network topology visualization is not only an important development direction for network security and management, but also a key technology to improve network operation efficiency and response speed. With the continuous expansion and complexity of the network, effective visualization tools have become necessary to monitor network health, optimize performance and prevent security threats.

[0004] Current network topology visualization tools are mainly designed for network topologies at a specific level, and they often lack the ability to adapt to topologies of different levels and types. This defect has prevented many layout algorithms from fully utilizing the inherent characteristics of the network structure, thus limiting layout efficiency and visual effects. Especially in modern scenarios where network scale and density are rapidly increasing, existing visualization layout algorithms face significant challenges, such as high computational time complexity and poor layout effects, which seriously affect the practicality and feasibility of the algorithms. In addition, as the network continues to expand, these tools are often unable to handle large-scale data flows, resulting in slow processing speeds and the inability to update network status in real time, which increases the difficulty of network operation and maintenance. Summary of the invention

[0005] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is the high computational complexity and unsatisfactory layout effect faced when processing large-scale and complex network topology structures. Existing methods are usually unable to meet the dual requirements of processing speed and visual effect at the same time, and the development complexity is high. Especially in the design of complex large-scale network structure systems, the lack of efficiency and effect is particularly obvious, and the usage scenarios are limited. Therefore, the present invention provides a method for visualizing network topology. Taking into account a variety of network situation scenarios, this method not only improves the processing efficiency and the visual quality of the layout, but also has a wide range of application potential and significant practical value, and can effectively support the needs of modern network design and management.

[0006] To achieve the above object, the present invention provides a method for visualizing network topology, comprising the following steps:

[0007] Configure and prepare raw data parameters of network topology;

[0008] Input and store the original data parameters of the network topology structure to ensure that the format and structure of the input data are correct;

[0009] After receiving the input raw data parameters, the data of the raw data parameters are cleaned and preprocessed;

[0010] For the cleaned and preprocessed data, the Louvain algorithm is used to identify communities in the network and partition them;

[0011] The improved force-directed algorithm is used to layout the network topology of each sub-area after the partitioning results, and the layout parameters are adjusted;

[0012] Adjust the relative positions of each sub-area network topology, adjust the positions of nodes in the overall network topology according to the logical relationship between nodes, and merge the results obtained by the network topology partitioning algorithms of each sub-area;

[0013] The obtained results are plotted and the network topology information is output to realize the visualization of complex network topology structure.

[0014] Furthermore, the original data parameters are the connection relationship and interaction data of each node in the network, including source node information, target node information and weight information.

[0015] Furthermore, after receiving the input raw data parameters, the raw data parameters are cleaned and preprocessed, specifically including:

[0016] Check whether there is any missing node or edge information, data format error or illegal characters. If the connection relationship between nodes does not meet expectations, correct or delete it; complete or interpolate missing data points, and use data inference methods to ensure the integrity of network data;

[0017] After cleaning, the original data is uniformly converted into a standard format, and the numerical data is standardized. The standardized data structure includes the source node Source, the destination node Target, and the weight Weight.

[0018] Furthermore, the Louvain algorithm is used to identify the communities in the network and partition the cleaned and preprocessed data, so as to quickly identify different communities in the network through the gradual optimization of blockiness.

[0019] Furthermore, the Louvain algorithm is used to identify communities in the network and partition them, including the following steps:

[0020] 1) Initial partitioning and modularity optimization: First, each node is considered as a community. Then, through local optimization of modularity, the nodes in the network are assigned one by one to the community that can maximize the modularity. This process will continue until no node can be further moved to improve the modularity.

[0021] 2) Community aggregation: Next, the obtained communities are aggregated and each community is regarded as a separate node to construct a new network. On this new network, the edge weight between communities is the sum of the edge weights between different communities in the original network.

[0022] 3) Repeat the steps above on the aggregated network, i.e., allocate nodes by optimizing the modularity, and then aggregate the community again until the modularity is no longer significantly improved.

[0023] Furthermore, the nodes in the network are first assigned one by one to the communities that can maximize the modularity through local optimization of the modularity. Specifically, at the initialization, each node forms a community by itself.

[0024] Then, for each node, try to move it into the community of all its neighboring nodes and select the community that increases the modularity the most;

[0025] This step is repeated until the modularity cannot be further increased by moving nodes;

[0026] The modularity formula is as follows:

[0027]

[0028] Among them A ij Indicates the actual connection between node i and node j. If there is an edge connection, the value is 1; otherwise, the value is 0. i and k jare the degrees of nodes i and j, i.e., the number of connections with other nodes, m is the total number of edges in the network, δ(c i ,c j ) is an indicator function. When nodes i and j belong to the same community, the function value is 1, otherwise it is 0. i k j / 2m is the expected number of connections between node i and node j in a random network.

[0029] Furthermore, the communities are then aggregated and treated as single nodes, and the above steps are repeated on the aggregated network until the modularity no longer increases. Specifically, when local movement can no longer improve the modularity, the Louvain algorithm treats the currently found community as a new supernode, and the connections between communities become new edges. The weight of the edge is the sum of the original edges between communities. After that, the Louvain algorithm repeats the process of the local optimization phase on this new simplified network.

[0030] Furthermore, when calculating the gravitational force between nodes within the community, the community coefficient α is introduced to enhance this gravitational force. This coefficient is dynamically adjusted according to the average connection density of nodes within the community and the size of the community. For the node pair i and j within the community, the gravitational formula is adjusted to:

[0031]

[0032] Where d is the actual distance between nodes, k is a constant, and d opt is the ideal distance. When α is greater than 1, the attraction between nodes in the same community is enhanced.

[0033] Furthermore, an improved force-directed algorithm is used to layout the network topology of each sub-area after the partitioning results, and the layout parameters are adjusted. Specifically, an improved force-directed layout algorithm is used to perform independent layout on each independent sub-area, and the position of the nodes is adjusted according to the interaction force between the nodes to optimize the visual display effect of the network.

[0034] Furthermore, in the improved force-directed algorithm, temperature is used to control the step size of node movement. The higher temperature in the initial stage allows nodes to perform larger random movements to explore more layout solutions. When the temperature decreases, the step size of node movement decreases and the layout is refined. The formula is as follows:

[0035] T(t)=T0·α t

[0036] Where T(t) is the temperature at the tth iteration; T0 is the initial temperature; is the temperature decay factor, usually 0<α<1; and t is the number of iterations.

[0037] Technical Effects

[0038] The present invention provides a method for visualizing network topology, which uses the Louvain partitioning algorithm to subdivide a complex network structure into multiple sub-areas, and provides a structured framework for layout optimization by identifying densely connected clusters or communities in the network, thereby simplifying the subsequent processing process. Subsequently, an improved force-directed layout algorithm is applied in each independent sub-area, which simulates the repulsion and attraction between nodes according to the principles of physical mechanics to ensure that the node layout inside the sub-area is tight and orderly. By performing local optimization on each sub-area, the method significantly reduces the number of global iterations, improves the calculation speed and layout accuracy. Finally, the layout results of all sub-areas are merged to form a unified and coherent network view. This integration method not only ensures the overall visual aesthetics, but also maintains the functionality and practicality of the layout. Compared with traditional methods, the present invention not only improves the layout efficiency, but also meets the visualization requirements of network topology in various application scenarios such as Internet of Vehicles, satellite networks, and industrial networks, and provides an effective tool for real-time network monitoring, security analysis, and system optimization.

[0039] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a method for visualizing network topology according to a preferred embodiment of the present invention;

[0041] Figure 2 It is a structural schematic diagram of a method for visualizing network topology according to a preferred embodiment of the present invention;

[0042] Figure 3 It is a data structure diagram of an input data source of a method for visualizing network topology in a preferred embodiment of the present invention;

[0043] Figure 4 It is a result schematic diagram of a method for visualizing network topology according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] In the following description, specific details such as specific internal procedures and techniques are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present invention. However, it should be clear to those skilled in the art that the present invention may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present invention.

[0046] like Figure 1 As shown, an embodiment of the present invention provides a network topology visualization method, which is a network topology visualization method based on combining sub-area partitioning and an improved force-directed algorithm, and specifically includes the following steps:

[0047] Step 101, configure and prepare original data parameters of the network topology structure. The data parameter information is the connection relationship and interaction data of each node in the network, specifically including source node information, destination node information and weight information.

[0048] Step 102, input and store the original network topology data parameters to ensure the format and structure of the input data. The format of the input data is divided into three parts, namely: source node Source, target node Target and weight value Weight.

[0049] Step 103: Before data analysis, the original network structure data is cleaned and preprocessed as necessary, including:

[0050] Check whether there is any missing node or edge information, data format error or illegal characters. If the connection relationship between nodes does not meet expectations (such as self-loops or repeated edges), they should also be corrected or deleted; missing data points should be supplemented or interpolated, and data inference methods should be used to ensure the integrity of network data.

[0051] The original data is uniformly converted into a standard format, and the numerical data is standardized to ensure the consistency of the numerical range. The standardized data structure includes the source node Source, the destination node Target, and the weight Weight.

[0052] Step 104: Use the Louvain algorithm to identify and partition the cleaned and preprocessed data into communities in the network. Use the Louvain algorithm to identify community size and structural characteristics, use the maximum modularity to identify and partition tightly connected node groups in the network, and adjust the attraction and repulsion to ensure high cohesion within the group and low interconnection between groups.

[0053] Through the gradual optimization of modularity, different communities in the network can be quickly identified. This step is divided into two stages: first, the local optimization of modularity, assigning nodes in the network one by one to communities that can maximize modularity; then, the communities are aggregated, treated as single nodes, and the above steps are repeated on the aggregated network until the modularity no longer increases. The modularity formula is as follows:

[0054]

[0055] Among them A ij Indicates the actual connection between node i and node j (if there is an edge connection, the value is 1; otherwise the value is 0), k i and k j are the degrees of nodes i and j (i.e., the number of connections with other nodes), m is the total number of edges in the network, and δ(c i ,c j ) is an indicator function. When nodes i and j belong to the same community, the function value is 1, otherwise it is 0. i k j / 2m is the expected number of connections between node i and node j in a random network.

[0056] The network is partitioned using the Louvain algorithm, a hierarchical optimization method used to quickly discover community structures and optimize community partitioning by maximizing modularity. For each node i, the algorithm calculates the potential gain in modularity Q after moving it to the community where each adjacent node is located. Modularity gain is a key factor in determining whether to move node i to a new community, and its calculation formula is as follows:

[0057]

[0058] Among them, ∑ in is the sum of the weights of all internal edges in the community under consideration; k i,in is the sum of the weights of the edges between node i and other nodes in the community; ∑ tot is the total degree of all nodes in the community (including all edges connecting to and outside the community); k i is the degree of node i, that is, the sum of the weights of all edges connected to node i; m is the sum of the weights of all edges in the graph.

[0059] All nodes classified into the same community will be merged into a new super node, and the edges in the network will be merged accordingly. The edge weight of the new graph is the sum of the weights of the corresponding edges between communities in the original graph. The iteration is then repeated until the merge operation no longer leads to a significant increase in modularity.

[0060] Step 105, the improved force-directed algorithm is used to layout the network topology of each sub-area after the partitioning result, and the layout parameters are adjusted. Specifically, the improved force-directed layout algorithm is used to independently layout each independent sub-area, and the position of the node is adjusted according to the interaction force between the nodes to optimize the visual display effect of the network. In the layout process, the concept of temperature is used to control the step size of the node movement.

[0061] Combined with step 104 and step 105, the algorithm flow chart is as follows Figure 2 As shown, the steps are as follows:

[0062] Firstly, the Louvain algorithm is used to initialize the partition of the complex network structure, with the aim of decomposing the large network into several smaller sub-networks, where each community consists of nodes with a high density of connections between them.

[0063] Then the gravity coefficient α is dynamically adjusted according to the connection density and size of the community. α is dynamically adjusted based on the average density of nodes within the community. If the connection density within the community is high, α needs to be reduced to avoid overcrowding; if the nodes in the community are too dispersed, α needs to be increased to improve cohesion. The gravity formula is as follows:

[0064]

[0065] Where d is the actual distance between nodes, k is a constant, and d opt is the ideal distance, while α (greater than 1) enhances the attraction between nodes in the same community.

[0066] At the same time, avoid overlap between communities and adjust β to optimize according to the size of the network and the spatial distribution of the community. The adjustment of β is based on the spatial distribution of the community and the size of the network. If the distance between communities is too close, β needs to be increased; if the distance between communities is too far, β needs to be reduced. The appropriate β can effectively prevent overlap between different communities and ensure that the distance between communities is not too large. The repulsion formula is as follows:

[0067]

[0068] where d is the actual distance between nodes, k is a constant, and β (greater than 1) is targeted at node pairs between communities to ensure that appropriate community spacing is maintained between different communities.

[0069] The initial setting rules for the two coefficients are as follows:

[0070] 1) α: This coefficient should reflect the closeness between nodes in the community. This coefficient is proportional to the internal connection density of the community. Initially, you can start with a medium value of 1.5 and then dynamically adjust it according to the above situation.

[0071] 2) β: This coefficient is used to adjust the node repulsion between communities and avoid node overlap between communities. It can start with an intermediate value of 1.2 and then be dynamically adjusted according to the above situation.

[0072] The method of the present invention is described below by taking an aviation network as an example, wherein the aviation network is divided into five regional communities through the Louvain partitioning algorithm, and the number of nodes and the number of connections in each community are different.

[0073] The initial settings are α=1.5 and β=1.2, where α promotes close connections between airports within the community and increases the density of routes within the region, and β ensures that communities maintain appropriate independence and avoids excessive integration of routes in different regions.

[0074] The average connection density (the average number of flights between airports within each community) and the average shortest distance between communities (the average flight distance between airports in communities) were then calculated for each community.

[0075] If it is found that the average connection density of community 1 is 20% higher than the network average, it means that flights between airports within community 1 are very frequent. In order to prevent over-concentration, α of community 1 is reduced to 1.5*(1-0.2)=1.2.

[0076] If it is found that the average shortest distance between community 2 and community 3 is 7 units, and the expected threshold is twice 10 units, that is, 20 units, it is necessary to increase the repulsion to expand the distance between the two communities, and adjust β between community 2 and community 3 to 1.2*(10 / 7)=1.7.

[0077] At the same time, when performing node layout, a temperature control mechanism is introduced to optimize the layout of each independent community: the moving step of the node in each iteration is controlled by the temperature T(t) to improve the flexibility and efficiency of the layout. The specific operations are as follows:

[0078] 1) Setting a higher initial temperature T0 allows nodes to move in a larger range in the early stage, which helps to quickly jump out of possible local optimal solutions.

[0079] 2) Through the formula T(t) = T0·α t Controls the temperature to decrease step by step, where α is a decay factor ranging from 0 to 1, such as 0.95, which means that the temperature will decrease by 5% after each iteration.

[0080] 3) As the temperature gradually decreases, the node movement step size decreases accordingly, allowing the algorithm to refine the node positions and gradually tend to a more stable and balanced layout.

[0081] Steps 106-107, adjust the relative positions between the sub-areas. First, initialize the initial position of the nodes in each sub-area randomly generated to ensure uniform distribution on the two-dimensional plane to avoid overlap. Then, iteratively update the results of each sub-area obtained in steps 104 and 105. The new position calculation formula of each node is p new =p old +α·F

[0082] Where F is the net force on the node, α is the learning rate, and the node position is updated through repeated iterations until the system converges to the set threshold, usually 0.01. It can be considered that convergence has been achieved and the iteration can be stopped.

[0083] In this process, the object G is constructed through the NetWorkX library using the optimized sub-area information. First, a graph object is created to store node and edge information. Specifically, for each optimized sub-area, its node is added to the graph, and the node location information of the sub-area is used to locate the node, and the node ID and related attributes are saved. Next, the connecting edges between the sub-areas are added to form a complete network structure.

[0084] Then, set the visualization properties of the node, including the size and color of the node. The size of the node can be adjusted according to its degree to reflect the importance of the node, while the color can be set according to the type or characteristics of the sub-area to improve readability.

[0085] After the graph is built, the network topology is drawn using the Matplotlib library. At the same time, the network node and edge information is output in csv format, including the ID of each node, as well as the source, target, and weight information of the edge, for subsequent data analysis and processing.

[0086] The following is an example of a random network topology visualization method based on combining sub-area partitioning and improved force-directed algorithm proposed in an embodiment of the present invention. The input data source is as follows. Figure 3 As shown, the data structure is:

[0087] Source Target Weight

[0088] They are source node, target node and weight, where weight may have different meanings in different network scenarios. For example, in a traffic network or network flow, weight usually represents the flow through a certain edge; in other infrastructure networks such as power grids, edge weights can represent the maximum carrying capacity of pipelines, wires, etc.; in social networks, edge weights can represent the degree of trust and importance between individuals.

[0089] The results obtained by the method of the present invention are as follows Figure 4As shown. This example consists of 25 nodes and 66 edges. The corresponding number is displayed on the right side of each node. The number of nodes, the number of edges, the partitioning time of the Louvain algorithm, and the layout time of the entire algorithm are also marked in the lower right corner of the figure. Node colors represent different communities: By coloring the nodes in different colors, you can intuitively see which nodes belong to the same community. Each community is distinguished by a different color, which also reflects the relative independence between communities. Nodes with the same color tend to have more connections in the network, while nodes with different colors have fewer connections.

[0090] In addition, the edge weight information affects the following two aspects:

[0091] 1) Distance between nodes: The larger the weight, the smaller the calculated gravitational force, which means that the attraction between two nodes is weakened, resulting in an increase in the distance between the nodes; the weight directly affects the final distance between the nodes. The edge with a larger weight makes the corresponding two nodes farther apart in the graph, while the edge with a smaller weight makes the nodes closer.

[0092] 2) Community structure: Weights do not directly determine the division of communities, but they will affect the structure and visualization of communities. When performing community detection, the Louvain algorithm considers edge connectivity and modularity. Weights will affect the calculation of modularity. Edges with larger weights will cause connected nodes to be assigned to the same community because their connections are stronger.

[0093] After testing in this embodiment, the efficiency of network partitioning and layout has been significantly improved. In multiple tests with different input data sets, the average layout time has been reduced by about 34%. Such a significant improvement makes the algorithm perform well in large-scale network applications that require fast network analysis and visualization, and due to the influence of partitioning, the algorithm has an average clustering coefficient of about 15% higher than that of ordinary force-directed algorithms. Such an improvement can also make the nodes more concentrated in the same community, reflecting a tighter internal structure in the network.

[0094] The embodiment of the present invention provides a network topology visualization method based on combining sub-area partitioning and an improved force-directed algorithm. The complex network structure is subdivided into multiple sub-areas by the Louvain partitioning algorithm. By identifying densely connected clusters or communities in the network, a structured framework is provided for layout optimization, which simplifies the subsequent processing process. Subsequently, an improved force-directed layout algorithm is applied in each independent sub-area. This algorithm simulates the repulsion and attraction between nodes according to the principles of physical mechanics to ensure that the node layout inside the sub-area is tight and orderly. By locally optimizing each sub-area, the method significantly reduces the number of global iterations, improves the calculation speed and layout accuracy. Finally, the layout results of all sub-areas are merged to form a unified and coherent network view. This integration method not only ensures the overall visual aesthetics, but also maintains the functionality and practicality of the layout. Compared with traditional methods, the present invention not only improves the layout efficiency, but also meets the visualization requirements of network topology in various application scenarios such as Internet of Vehicles, satellite networks and industrial networks, and provides an effective tool for real-time network monitoring, security analysis and system optimization.

[0095] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for visualizing network topology, characterized in that: The following steps are involved: Configure and prepare raw data parameters of network topology; Input and store the original data parameters of the network topology structure to ensure that the format and structure of the input data are correct; After receiving the input raw data parameters, the data of the raw data parameters are cleaned and preprocessed; For the cleaned and preprocessed data, the Louvain algorithm is used to identify communities in the network and partition them; The improved force-directed algorithm is used to layout the network topology of each sub-area after the partitioning results, and the layout parameters are adjusted; Adjust the relative positions of each sub-area network topology, adjust the positions of nodes in the overall network topology according to the logical relationship between nodes, and merge the results obtained by the network topology partitioning algorithms of each sub-area; The obtained results are plotted and the network topology information is output to realize the visualization of complex network topology structure.

2. A method for visualizing network topology according to claim 1, characterized in that: The original data parameters are the connection relationship and interaction data of each node in the network, including source node information, target node information and weight information.

3. A method for visualizing network topology according to claim 2, characterized in that: After receiving the input raw data parameters, the raw data parameters are cleaned and preprocessed, including: Check whether there is any missing node or edge information, data format error or illegal characters. If the connection relationship between nodes does not meet expectations, correct or delete it; complete or interpolate missing data points, and use data inference methods to ensure the integrity of network data; After cleaning, the original data is uniformly converted into a standard format, and the numerical data is standardized. The standardized data structure includes the source node Source, the destination node Target, and the weight Weight.

4. A method for visualizing network topology according to claim 1, characterized in that: For the cleaned and preprocessed data, the Louvain algorithm is used to identify the communities in the network and partition them, so as to quickly identify different communities in the network through the gradual optimization of blockiness.

5. A method for visualizing network topology according to claim 4, characterized in that: The Louvain algorithm is used to identify communities in the network and partition them, including the following steps: 1) Initial partitioning and modularity optimization: First, each node is considered as a community. Then, through local optimization of modularity, nodes in the network are assigned one by one to communities that can maximize modularity. This cycle is repeated until no nodes can be further moved to improve modularity. 2) Community aggregation: Next, the obtained communities are aggregated and each community is regarded as a separate node to construct a new network. On this new network, the edge weight between communities is the sum of the edge weights between different communities in the original network. 3) Repeat the steps above on the aggregated network, i.e., allocate nodes by optimizing the modularity, and then aggregate the community again until the modularity is no longer significantly improved.

6. A method for visualizing network topology according to claim 5, characterized in that: First, through local optimization of modularity, nodes in the network are assigned one by one to communities that can maximize modularity. Specifically, at initialization, each node forms a community. Then, for each node, try to move it into the community of all its neighboring nodes and select the community that increases the modularity the most; This step is repeated until the modularity cannot be further increased by moving nodes; The modularity formula is as follows: Among them A ij Indicates the actual connection between node i and node j. If there is an edge connection, the value is 1; otherwise, the value is 0. i and k j are the degrees of nodes i and j, i.e., the number of connections with other nodes, m is the total number of edges in the network, δ(c i ,c j ) is an indicator function. When nodes i and j belong to the same community, the function value is 1, otherwise it is 0. i k j / 2m is the expected number of connections between node i and node j in a random network.

7. A method for visualizing network topology according to claim 6, characterized in that: The communities are then aggregated and treated as single nodes, and the above steps are repeated on the aggregated network until the modularity no longer increases. Specifically, when local movement can no longer improve the modularity, the Louvain algorithm treats the currently found community as a new supernode, and the connections between communities become new edges. The weight of the edge is the sum of the original edges between communities. After that, the Louvain algorithm repeats the process of the local optimization phase on this new simplified network.

8. A method for visualizing network topology according to claim 6, characterized in that: When calculating the gravitational force between nodes within a community, the community coefficient α is introduced to enhance this gravitational force. This coefficient is dynamically adjusted according to the average connection density of nodes within the community and the size of the community. For node pairs i and j within the community, the gravitational formula is adjusted to: Where d is the actual distance between nodes, k is a constant, and d opt is the ideal distance. When α is greater than 1, the attraction between nodes in the same community is enhanced.

9. A method for visualizing network topology according to claim 1, characterized in that: An improved force-directed algorithm is used to layout the network topology of each sub-area after the partitioning results, and the layout parameters are adjusted. Specifically, an improved force-directed layout algorithm is used to independently layout each independent sub-area, adjust the position of the nodes according to the interaction force between the nodes, and optimize the visual display effect of the network.

10. A method for visualizing network topology according to claim 9, characterized in that: In the improved force-directed algorithm, temperature is used to control the step size of node movement. The higher temperature in the early stage allows nodes to move randomly to explore more layout solutions. When the temperature decreases, the step size of node movement decreases and the layout is refined. The formula is as follows: T(t)=T0·α t Where T(t) is the temperature of the tth iteration; T0 is the initial temperature; is the temperature attenuation factor, usually 0<α<1; t is the number of iterations.

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