Complex temporal network-based betweenness centrality update calculation method

Abstract

The invention discloses a complex tense network-based betweenness centrality updating calculation method, which comprises the following steps of: initializing a tense graph and a betweenness centrality calculation framework of all nodes, and finishing the construction of a complex tense network betweenness centrality calculation basic structure; inserting, deleting and updating edges in the tense graph, updating a graph structure in the tense network, and completing dynamic updating of the betweenness centrality calculation basic structure of the complex tense network; the betweenness centrality of the complex tense diagram is updated in a mode of combining incremental calculation and global calculation, and the updating efficiency of the betweenness centrality of the tense diagram is optimized; and according to the change of the temporal network, evaluating node importance, and outputting an updated betweenness centrality value. According to the method, the efficiency of temporal network betweenness centrality calculation can be remarkably improved, dynamic changes of network topology and timeliness data can be flexibly coped with, efficient and accurate node importance evaluation is supported, and the requirements of real-time calculation and dynamic updating are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of complex network analysis in network science, and particularly relates to a method for updating and calculating betweenness centrality based on a complex temporal network. Background Art

[0002] As an important measure in network analysis, betweenness centrality is widely used in multiple fields such as social networks, communication networks, and transportation networks to measure the role of nodes as intermediaries in the network. With the emergence of temporal networks, the calculation method of betweenness centrality has faced new challenges; a significant feature of temporal networks is that nodes and edges change dynamically over time, and traditional static network models cannot effectively handle these timeliness characteristics, which brings great difficulties to the calculation and update of betweenness centrality. Most existing methods for calculating betweenness centrality rely on global calculations, which are particularly challenging in temporal networks; since nodes and edges in temporal networks are dynamic, the value of betweenness centrality also changes over time. Traditional methods usually require recalculating the betweenness centrality of all nodes every time the topology changes, resulting in extremely high computational complexity, especially in large-scale temporal networks. To address this issue, in recent years, some researchers have proposed incremental update algorithms, but these methods usually still face a trade-off between computational accuracy and efficiency and are difficult to be widely applied in large-scale dynamic networks.

[0003] In addition, most existing methods for calculating betweenness centrality based on temporal networks ignore the dynamic characteristics of nodes and edges changing over time, as well as the temporal dependence of temporal paths, and also lack effective processing of timeliness information. For example, many methods use simple historical data statistical models that cannot reflect the latest importance of nodes in the network in real time; in practical applications, especially in dynamic scenarios such as communication, transportation, and social networks, for example, in delay-tolerant networks, the betweenness centrality of nodes changes significantly with the update of temporal data. Whether the betweenness centrality of nodes can be updated in a timely manner to adjust the selection of message forwarding nodes is an important condition for the effective and timely transmission of network messages. Therefore, a more efficient and real-time update calculation method is needed. Additionally, some methods in the prior art can effectively update betweenness centrality in certain scenarios, but often ignore the additional complexity brought by the introduction of temporal edges; in temporal networks, the timeliness of edges and the dynamic changes of network topology need to be fully considered in the calculation process, while traditional static graph methods cannot effectively handle these complex temporal information.

[0004] Most existing methods for calculating betweenness centrality in temporal networks rely on recomputing the entire graph. Whenever the network topology changes, the betweenness centrality of all nodes needs to be recalculated. This method has excessive computational complexity and time overhead when dealing with large-scale temporal networks and cannot meet the requirements of real-time updates. In recent years, some researchers have tried to use the graph increment method for betweenness centrality updates, but some methods in the existing technology have not fully considered the characteristics of edges and nodes changing over time in temporal networks, ignoring the direct impact of temporal edges on the importance of nodes, thus unable to accurately reflect the real-time importance of nodes. At the same time, the impact brought by the deletion and modification of edges in the temporal graph is also ignored. Meanwhile, many methods need to store a large amount of historical data or the entire temporal graph. Facing large-scale networks, this storage requirement brings huge resource consumption and management complexity. Moreover, the update and storage operations of existing methods for temporal networks are usually not optimized enough, resulting in waste of storage space and computing resources. Although some technologies have improved the computing efficiency through optimized algorithms, they often make an unsatisfactory compromise between accuracy and efficiency and are difficult to provide sufficient efficiency while ensuring high accuracy. Summary of the Invention

[0005] In view of the above, the present invention provides a method for updating and calculating betweenness centrality based on a complex temporal network, which can effectively improve the computing efficiency and support flexible real-time updates, so as to cope with the scenario where the network topology and timeliness information change frequently, and on this basis, realize efficient and accurate evaluation of the importance of nodes in the temporal network.

[0006] A method for updating and calculating betweenness centrality based on a complex temporal network includes the following steps:

[0007] (1) Obtain the initial graph structure and timeliness data of the complex temporal network, initialize the temporal graph and the betweenness centrality calculation framework for each node in the graph, and complete the construction of the basic structure for calculating betweenness centrality in the complex temporal network;

[0008] (2) Obtain the edge information to be inserted, deleted, and updated, and perform insertion, deletion, and update operations on the edges in the temporal graph respectively to update the temporal graph structure and complete the dynamic update of the basic structure for calculating betweenness centrality in the complex temporal network;

[0009] (3) Update the betweenness centrality of nodes in the temporal graph by combining incremental calculation and global calculation to optimize the update efficiency of the betweenness centrality of nodes in the temporal graph;

[0010] (4) Evaluate the importance of nodes according to the changes in the complex temporal network and output the betweenness centrality values of each node after update.

[0011] Further, the specific implementation manner of step (1) is as follows:

[0012] S1-1: Obtain the initial graph structure, node timeliness data, and edge timeliness data of the complex temporal network;

[0013] S1-2: Filter out the nodes and edges that meet the timeliness according to the node timeliness data and edge timeliness data, initialize the temporal graph and define the temporal optimal path (for example, the latest departure and the earliest arrival);

[0014] S1-3: For any node in the temporal graph, take it as the source node, and initialize the betweenness centrality calculation framework for this node: set the initial value of betweenness centrality to zero, initialize the set of temporal optimal paths from the source node to other nodes, and initialize the set Q for storing the triples of temporal optimal paths (node, departure timestamp, and arrival timestamp);

[0015] S1-4: Initialize the state information of other nodes including the number of temporal optimal paths from the source node to other nodes and the optimal path length, and initialize the state information of each split point of the node including the number of temporal optimal paths from the source node to the split point and the optimal path length, whether the split point is the end point of the temporal optimal path from the source node to the corresponding node, and the set of predecessor split points of the split point; Initialize the local optimal timestamp lastbest for recording the out-edge of the source node selected last time, and initialize the out-edge pruning set of the source node;

[0016] S1-5: Starting from any successor node i of the source node, if the out-edge set of the successor node is empty, directly retain the maximum-time edge from the source node to the successor node and store it in the out-edge pruning set of the source node;

[0017] S1-6: If the out-edge set of the successor node is not empty, after selecting an out-edge by traversing the out-edge set of the successor node in descending order of time sequence, then traverse any edge j between the source node and the successor node i in ascending order of time sequence;

[0018] S1-7: If there is no edge between the source node and the successor node i in the out-edge pruning set of the source node, store the edge j in the out-edge pruning set of the source node, update lastbest to the timestamp of the edge j, and return to step S1-6 to continue traversing the next edge between the source node and the successor node i;

[0019] S1-8: If the out-edge timestamp of the selected successor node is greater than the timestamp of the edge j and the out-edge timestamp of the selected successor node is less than the current lastbest, store the edge j in the out-edge pruning set of the source node, update lastbest to the timestamp of the edge j, and return to step S26 to continue traversing the next out-edge of the successor node i; If the out-edge timestamp of the selected successor node is greater than the value of the current lastbest, return to step S1-6 to continue traversing the next out-edge of the successor node i;

[0020] S1-9: If the timestamp of the selected edge j is equal to the timestamp of the previous edge j - 1, it indicates that the timestamp of edge j is relatively small. Return to step S1-6 to traverse the next edge between the source node and the successor node i;

[0021] S1-10: If no eligible edge is found in steps S1-7 to S1-9, return to step S1-5 to traverse the next successor node until all the outgoing edges of all successor nodes are traversed, completing the pruning of the outgoing edges of the source node;

[0022] S1-11: Perform a breadth-first traversal of the successor nodes of the source node, traverse the set of outgoing edges of each successor node in descending order of time sequence, find the one-hop temporal optimal path and update it, and store the generated triples in the set Q;

[0023] S1-12: Pop a triple from the set Q, traverse its successor nodes, traverse the set of outgoing edges of each successor node in ascending order of time sequence, find the new temporal optimal path and compare and update it with the current temporal optimal path;

[0024] S1-13: Calculate the temporal optimal path from the source node to other nodes, calculate the splitting point betweenness centrality of each node in descending order of the number of hops. If the splitting point is the end point of the temporal optimal path, traverse its child nodes and successor nodes, calculate the contribution value of the splitting point to them, and sum up the contribution values of the splitting points of all nodes to complete the preliminary calculation of the betweenness centrality of the source node;

[0025] S1-14: Repeat steps S1-3 to S1-13 until the betweenness centrality calculation of all nodes in the temporal graph is completed, that is, the betweenness centrality calculation of the source node;

[0026] S1-15: Combine the pruning of the outgoing edges of the source node and the calculation of the betweenness centrality of the source node under all traversals to obtain the basic structure for calculating the betweenness centrality of the complex temporal network.

[0027] Furthermore, for the edge information to be inserted in step (2), the specific implementation method is as follows:

[0028] S21-1: Obtain the edge information to be inserted, including the timeliness data such as the start node, end node, and timestamp of the inserted edge, and obtain the current basic structure for calculating the betweenness centrality of the complex temporal network;

[0029] S21-2: Insert a new edge into the temporal graph, update the graph structure according to the timeliness data of the edge, and ensure that the newly added edge conforms to the timeliness constraints of the complex temporal network;

[0030] S21-3: Update the status information of the nodes related to the inserted edge, including the number of temporal optimal paths and the optimal path lengths from the source node to other nodes, the number of temporal optimal paths and the optimal path lengths of the split points, whether the nodes related to the inserted edge affect the original paths, and determine whether it is necessary to update the original paths or recalculate the temporal optimal paths;

[0031] S21-4: Analyze the impact of the inserted edge on the betweenness centrality of the nodes in the complex temporal network, especially whether the inserted edge generates new temporal optimal paths, whether it changes the selection of the existing temporal optimal paths, and thus affects the betweenness centrality values of the nodes;

[0032] S21-5: For each node affected by the inserted edge, recalculate its temporal optimal paths to other nodes and update the optimal path set;

[0033] S21-6: If the inserted edge affects the split point, update the contribution value of the split point to the original node betweenness centrality, check the change in its importance in the complex temporal network, ensure that the new contribution value correctly reflects this change, and update the contribution values of the corresponding nodes;

[0034] S21-7: Save the new temporal optimal paths and ensure that the information of all nodes is updated in a timely manner;

[0035] S21-8: After completing the update of the temporal graph structure and the betweenness centrality calculation framework for the inserted edge, recalculate and adjust the temporal graph structure to ensure that the topology of the complex temporal network and the importance evaluation of the nodes are consistent.

[0036] Furthermore, for the edge information to be deleted in step (2), the specific implementation method is as follows:

[0037] S22-1: Obtain the edge information to be deleted, including the timeliness data such as the start node, end node, and timestamp of the deleted edge;

[0038] S22-2: Delete the specified edge in the temporal graph, ensure that the graph structure still complies with the timeliness constraints of the complex temporal network after the edge is deleted, and update the topology of the network;

[0039] S22-3: Update the status information of the nodes related to the deleted edge, including the number of temporal optimal paths and the optimal path lengths from the source node to other nodes, the number of temporal optimal paths and the optimal path lengths of the split points, whether the nodes related to the deleted edge affect the original paths, and determine whether it is necessary to update the original paths or recalculate the temporal optimal paths;

[0040] S22-4: Recalculate the impact of the deleted edge on the betweenness centrality of nodes in the complex temporal network, especially whether the deleted edge disrupts the original temporal optimal path, resulting in the need to calculate new optimal paths or the abandonment of old paths;

[0041] S22-5: For nodes affected by the deleted edge, recalculate their temporal optimal paths to other nodes and update the set of optimal paths;

[0042] S22-6: If the deleted edge affects the split point, update the contribution value of the split point to the betweenness centrality of the original node, check its importance change in the complex temporal network, ensure that the new contribution value correctly reflects this change, and update the contribution values of the corresponding nodes;

[0043] S22-7: Save the updated temporal optimal paths, ensure that all affected node information is updated in a timely manner, and make necessary path corrections;

[0044] S22-8: Complete the update of the temporal graph structure and the betweenness centrality calculation framework after deleting the edge, ensure the consistency of the topology and node importance evaluation of the complex temporal network, and avoid calculation errors caused by the deletion operation.

[0045] Furthermore, for the edge information to be updated in step (2), the specific implementation method is as follows:

[0046] S23-1: Obtain the edge information to be updated, including the start node, end node, and new edge weight of the updated edge;

[0047] S23-2: Find the edge to be updated in the temporal graph, update the status information of the edge according to the new edge weight, and ensure that the timeliness constraint after updating the temporal graph structure is satisfied;

[0048] S23-3: Update the status information of the nodes related to the updated edge, especially the number and length of the temporal optimal paths from the source node to other nodes, and the number and length of the temporal optimal paths of the split point;

[0049] S23-4: Re-evaluate the betweenness centrality of the nodes affected by the updated edge, especially whether the updated edge weight affects the calculation of the temporal optimal path, and determine whether the path needs to be adjusted;

[0050] S23-5: For nodes affected by the updated edge, recalculate their temporal optimal paths to other nodes and update the set of optimal paths;

[0051] S23-6: If the updated edge affects the splitting point, check its impact on the contribution value of the splitting point, recalculate the contribution value of the splitting point to the betweenness centrality of the original node, check its importance change in the complex temporal network, ensure that the new contribution value correctly reflects this change, and update the contribution values of the corresponding nodes;

[0052] S23-7: Save the updated temporal optimal paths to ensure that the information of all affected nodes is updated in a timely manner;

[0053] S23-8: Complete the update of the temporal graph structure and the betweenness centrality calculation framework after updating the edge weights to ensure the consistency of the topology and node importance evaluation of the complex temporal network.

[0054] Furthermore, in step (3), the betweenness centrality of nodes in the temporal graph is updated through incremental calculation, and the specific implementation method is as follows:

[0055] S31-1: Obtain the initial values of the betweenness centrality of all nodes in the temporal graph, and establish an incremental calculation framework to prepare for incremental update operations to cope with local changes in nodes and edges;

[0056] S31-2: When local changes occur in the network topology (such as edge insertion, deletion, or weight update), use the incremental calculation method to update the affected nodes and edges, and only calculate the temporal optimal paths and betweenness centrality between those node pairs directly affected by the change, without having to recalculate the entire temporal graph;

[0057] S31-3: For the incrementally updated nodes, calculate the new temporal optimal paths and adjust the corresponding betweenness centrality values to ensure that local updates do not affect the calculation results of the entire network;

[0058] S31-4: Update the optimal path set and betweenness centrality values, only update the parts related to the change, and avoid recalculating the entire graph, thereby significantly improving the calculation efficiency;

[0059] S31-5: After completing the incremental calculation, return the betweenness centrality values of the updated nodes, and prepare to handle possible global calculation requirements.

[0060] Furthermore, in step (3), the betweenness centrality of nodes in the temporal graph is updated through global calculation, and the specific implementation method is as follows:

[0061] S32-1: When large-scale structural changes occur in the complex temporal network (such as large-scale node insertion, deletion, update, or network topology change), switch to the global calculation mode;

[0062] S32-2: Perform a full network traversal and recalculate the temporal optimal paths from all nodes to other nodes;

[0063] S32-3: Update the betweenness centrality values of all nodes according to the new global calculation results, and ensure the integrity of the temporal graph structure to avoid omission or incorrect calculation;

[0064] S32-4: After completing the global calculation, re-initialize the incremental calculation framework to provide a basis for the incremental calculation update of the next local change;

[0065] S32-5: Combine the global calculation results with the incremental calculation results to ensure the accuracy of the betweenness centrality values of each node in the complex temporal network, and provide an accurate calculation basis for subsequent dynamic changes.

[0066] Furthermore, the specific implementation manner of the step (4) is as follows:

[0067] S4-1: Finally, output the updated betweenness centrality values of each node to ensure the accurate evaluation of the importance of all nodes after the change of the complex temporal network, and provide support for subsequent network optimization and decision-making;

[0068] S4-2: Save the updated betweenness centrality values of each node to the temporal graph as the basis for the next round of calculation and analysis, and ensure the real-time and accuracy of the importance evaluation of nodes in the complex temporal network.

[0069] A computer device includes a memory and a processor. A computer program is stored in the memory, and the processor is configured to execute the computer program to implement the above-mentioned betweenness centrality update calculation method based on a complex temporal network.

[0070] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the above-mentioned betweenness centrality update calculation method based on a complex temporal network.

[0071] The present invention successfully constructs a temporal network betweenness centrality calculation framework, which can handle the timeliness changes of nodes and edges, and supports efficient betweenness centrality update calculation. In particular, the present invention designs an optimization strategy that combines incremental calculation and global calculation, significantly improving the efficiency of betweenness centrality update in the temporal network while avoiding the high computational overhead in traditional methods. By dynamically updating the graph structure and node states, the present invention can reflect the topological changes of the temporal network in real time, thereby providing an accurate evaluation of node importance for network optimization, routing selection, etc. In addition, for the insertion, deletion, and update of edges in the temporal network, the present invention provides flexible and efficient operation methods to ensure that the temporal graph can be updated efficiently and accurately in a frequently changing environment, solving the contradiction between computational accuracy and efficiency in the prior art. Therefore, the technical solution of the present invention provides an efficient and accurate calculation method for evaluating the importance of nodes in the temporal network, and can be widely applied to multiple fields such as communication networks, transportation networks, and social networks. Brief Description of the Drawings

[0072] Figure 1 This is a schematic flow diagram of the method for updating the betweenness centrality based on a complex temporal network according to the present invention. Detailed Embodiments

[0073] In order to describe the present invention more specifically, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0074] As Figure 1 shown, the method for updating the betweenness centrality based on a complex temporal network according to the present invention includes the following steps:

[0075] S11: Obtain the initial graph structure and timeliness data of the complex temporal network, construct a temporal graph model, and initialize the calculation framework for the betweenness centrality of all timeliness nodes in the temporal graph, so as to complete the construction of the basic structure for calculating the betweenness centrality of the complex temporal network.

[0076] S12: Obtain the edge information to be inserted, deleted, and updated, and perform insertion, deletion, and update operations on the edges in the temporal graph respectively, update the graph structure in the temporal network, and complete the dynamic update of the basic structure for calculating the betweenness centrality of the complex temporal network.

[0077] S13: Update the betweenness centrality of the complex temporal graph by combining incremental calculation and global calculation, and optimize the update efficiency of the betweenness centrality in the temporal graph.

[0078] S14: Evaluate the importance of nodes according to the changes in the temporal network, and output the updated betweenness centrality value.

[0079] The present invention designs a temporal graph model and combines a strategy of combining incremental calculation and global calculation, which significantly improves the update efficiency of the betweenness centrality in the temporal network. By dynamically updating the graph structure in the temporal network and timely processing the insertion, deletion, and update operations of nodes and edges, it effectively responds to the frequent changes in the topology of the temporal network. The present invention provides an efficient calculation framework for betweenness centrality by optimizing the calculation method, which can evaluate the importance of nodes in the temporal network in real time and ensure the balance between calculation accuracy and efficiency. In addition, the present invention designs a flexible dynamic update strategy, which can quickly and accurately complete the evaluation of node importance during the change of the temporal network, and solves the problems of calculation overhead and update lag in the existing methods.

[0080] The temporal graph model involved in the present invention can be constructed and initialized through multiple actual application scenarios. For example, in the application scenario of Delay Tolerant Network (DTN), the timeliness of nodes and edges is directly related to the transmission path and forwarding order of data packets. When calculating the betweenness centrality of nodes, the timeliness of edges needs to be considered. Especially when data packets are transmitted through multiple relay nodes, how to update the betweenness centrality value of each node using temporal information; in this scenario, the edges of the temporal graph not only represent the connection relationship between nodes, but also contain information such as timestamps and transmission delays, and the temporal graph model needs to be constructed based on these timeliness data. In addition, in the application scenario of social networks, the social relationships and interaction frequencies between users are important characteristics of the temporal network. The social relationships of each user change over time. The edges of the temporal graph can represent the interaction behaviors between users and are dynamically updated over time; in the temporal graph of social networks, the calculation of the betweenness centrality of nodes needs to be adjusted according to time factors to accurately reflect the users with greater influence within a specific time period. In the application scenario of traffic networks, the timeliness of information such as traffic flow and road conditions also affects the calculation of the betweenness centrality of nodes. The traffic state of each road changes over time. The edges in the temporal graph can represent the traffic state of the road (such as traffic capacity, congestion situation, etc.), while the nodes represent traffic hubs or intersections. At this time, the timeliness data of the edges in the temporal graph will determine how to calculate the importance of each node in the network. Especially when traffic congestion or emergencies occur, the role of which nodes as key intermediate nodes is particularly important. Step S11 of the present invention incorporates timeliness data into the calculation framework of nodes and edges through the construction of the temporal graph model, initializes the calculation of the betweenness centrality of all timeliness nodes in the temporal network, and completes the construction of the basic structure for calculating the betweenness centrality of complex temporal networks, providing support for subsequent temporal network updates and node importance evaluations. In the specific implementation process, step S11 includes the following sub-steps:

[0081] S21: Obtain the initial graph structure, node timeliness data, and edge timeliness data of the complex temporal network.

[0082] Specifically, collect and obtain the initial data of the temporal network, including the node connection relationships in the temporal network, and the timeliness information of nodes and edges. The node timeliness data indicates the active state and existence time of the nodes, while the edge timeliness data records the timeliness of the edges connecting these nodes (such as start time, end time, and edge information within the time period when the message is valid).

[0083] S22: Screen out the nodes and edges that meet the timeliness according to the node timeliness data and edge timeliness data, initialize the temporal graph model, and define the temporal optimal path.

[0084] Specifically, active nodes and edges that meet the timeliness requirements are filtered out according to the timeliness data of nodes and edges, and the temporal graph model is initialized. On this basis, criteria for the temporal optimal path are defined. For example, "departing latest and arriving earliest" is one of the optimal path definitions applicable to delay-tolerant networks. Other definitions such as "departing latest and having the shortest path" can also be selected according to the requirements of different application scenarios. These temporal path criteria make the path selection not only based on the topological structure but also consider the time dimension, ensuring that the path selection conforms to the temporal dependence relationship to achieve more accurate and efficient network optimization.

[0085] S23: Traverse each node of the temporal graph. Consider the currently traversed node as the source node, and initialize the betweenness centrality calculation framework for each node: set the initial betweenness centrality value to zero, initialize the set of optimal paths from the source node to other nodes, and initialize the set Q for storing temporal path triples.

[0086] Specifically, the initialized set Q is used to store the triples of temporal paths (including nodes, departure timestamps, and arrival timestamps). This set adjusts and controls the execution order of the entire top-down traversal algorithm.

[0087] S24: Initialize the state information of other nodes, including the number of temporal optimal paths from the source node to other nodes and the optimal path length. Initialize the state information of each split point of the node, including the number of temporal optimal paths from the source node to the split point and the optimal path length, whether the split point is the end point of the optimal path from the source node to the corresponding node, and the set of precursor split points of the split point. Initialize the local optimal timestamp lastbest for recording the out-edge of the source node selected last time (used to handle the case where the out-edge of the source node is greater than the out-edge of the successor node of the source node), and initialize the out-edge pruning set of the source node.

[0088] S25: Starting from any successor node i of the source node, if the out-edge set of the successor node is empty, directly retain the maximum temporal edge from the source node to the successor node and store it in the out-edge pruning set of the source node.

[0089] S26: If the out-edge set of the successor node is not empty, after selecting an out-edge of the successor node by traversing the out-edge set of the successor node in descending order of time sequence, then traverse any edge j between the source node and the successor node i in ascending order of time sequence.

[0090] S27: If there is no edge between the source node and the successor node i in the out-edge pruning set, store the edge j in the out-edge pruning set of the source node, update lastbest to the timestamp of the edge j, and return to step S26 to continue traversing the next edge between the source node and the successor node i.

[0091] S28: If the timestamp of the out-edge of the selected successor node is greater than the timestamp of edge j and the timestamp of the out-edge of the selected successor node is less than the current lastbest, then store edge j in the out-edge pruning set of the source node, update lastbest to the timestamp of edge j, and return to step S26 to continue traversing the next out-edge of successor node i; if the timestamp of the out-edge of the selected successor node is greater than the value of the current lastbest, then return to step S26 to continue traversing the next out-edge of successor node i.

[0092] S29: If the timestamp of the selected edge j is equal to the timestamp of the previous edge j - 1, it means that the timestamp of edge j is relatively small, and return to step 26 to traverse the next edge between the source node and successor node i.

[0093] S210: If no eligible edge is found in steps S27 to S29, repeat steps S25 - S29 until all the edges of the successor nodes are traversed, that is, complete the out-edge pruning of the source node.

[0094] Specifically, the out-edge pruning of the source node is to set the timestamp range through the types of timestamps of the out-edges of the successor nodes of the source node. Among the edge groups of the out-edges of the source node that fall within each range, only the edge with the largest timestamp is taken, and the remaining edges will all participate in the operation. The ignored edges will not enter the calculation, saving the calculation cost.

[0095] The remaining edges will definitely participate in at least one-hop DFS operation. Because the remaining edges are all the maximum timings in each range divided by the successor nodes according to the out-edges. Therefore, first consider the successor nodes of the source node that can be reached in one hop, and the one-hop path with the largest timing to the successor nodes of the source node can be determined. However, it is impossible to determine whether this one-hop path is better than the two-hop path. At the same time, if there are edges with larger timings or unreachable points, they can also be reached through the maximum timing edges in each range. So the types of departure times of the departure paths in the multi-hop paths can be covered by the maximum timing edges within the upper bound divided by the timings of the successor nodes of the successor nodes of the source node. The ignored edges do not need to be added. The ignored edges all have the characteristic that their timings are less than the maximum timing edge of the same upper bound. When selecting the same out-edge of the successor node, when the optimal path is defined as the latest departure and the earliest arrival, the optimal path must be composed of the maximum timing edges of the same upper bound, and the edges less than the maximum timing edge will be optimized.

[0096] S211: Perform a breadth-first traversal of the successor nodes of the source node, traverse the edge sets of each successor node in descending order of timestamps, find the one-hop temporal optimal path and update it, and add the generated triples to the set Q.

[0097] Specifically, breadth-first traverse the successor nodes of the source node. Each successor node traverses the edge set in descending order of time sequence (the optimal path in one hop can be found for the first time), update the optimal path, and add the corresponding triple to Q.

[0098] S212: Pop a triple from Q, traverse its successor nodes, traverse the edge set of each successor node in ascending order of time sequence, find the new temporal optimal path and compare and update it with the current temporal optimal path.

[0099] Specifically, pop the triple (n, ts, te) from Q, traverse the successor node m of n, and each m traverses the edge set in ascending order of time sequence (the optimal path in two hops can be found for the first time), compare this path with the optimal path and update it.

[0100] S213: Enter the second stage, calculate the optimal path from the source node to other nodes, calculate the splitting point betweenness centrality of each node in descending order of hop count. If the splitting point is the end point of the optimal path, traverse its child nodes and successor nodes, calculate the contribution value of the splitting point to them, and sum up the contribution values of the splitting points of all nodes to complete the preliminary calculation of the betweenness centrality of this source node.

[0101] Specifically, use a bottom-up approach to iteratively calculate the temporal betweenness centrality of all splitting points of each vertex, sort in descending order of the optimal path length from the source node to the successor node, and then calculate the contribution of the successor nodes and child nodes of the splitting point to its betweenness centrality.

[0102] S214: Repeat steps S23 - S213 until the betweenness centrality calculation of all nodes in the temporal graph is completed, that is, the betweenness centrality calculation of the source node.

[0103] Specifically, when all nodes have been traversed as the source node, the optimal paths between all node pairs will be counted. This process is an independently repeatable process, so an iterative calculation framework and a multi-threaded concurrency mechanism can be used to reduce the calculation amount.

[0104] S215: Merge the out-edge pruning of the source node under all traversals and the betweenness centrality calculation of the source node to obtain the basic structure for calculating the betweenness centrality of the complex temporal network.

[0105] The formula for calculating the betweenness centrality of nodes in a complex temporal graph is where σ sf (v) represents the number of temporal optimal paths from node s to f passing through node v, and σ sf represents the number of temporal optimal paths from node s to f, and δ s. (v, t) is the contribution value of all subsequent nodes of the splitting point (v, t) to it in the temporal optimal path where the source node u passes through the splitting point (v, t).

[0106] In practical application scenarios, such as in delay-tolerant networks, social networks, and transportation networks, operations such as data insertion (e.g., the addition of new nodes or new communication connections), deletion (e.g., the disconnection of nodes or connections), and update (e.g., changes in the weights of edges) are often extremely frequent. These operations will affect the network topology and node importance assessment. In the application scenario of delay-tolerant networks, when new nodes or communication connections are inserted, the edges in the temporal graph will be updated, and the optimal paths of relevant nodes will be recalculated based on the new timeliness data; if the timeliness or bandwidth of a certain edge changes (e.g., the transmission delay decreases or the bandwidth increases), the weight of the edge needs to be updated accordingly, which will affect the path selection of data packets transmitted through this edge in the network and the betweenness centrality of nodes; when an edge is deleted, the network topology will change, which may cause some paths to be disconnected, so it is necessary to recalculate the paths of relevant nodes and update the node importance. In the application scenario of social networks, the social relationships between users change as interactions increase or decrease. When new interactions occur between users, the weights of the social relationship edges will change (e.g., the interaction frequency increases), which will affect the social influence of nodes and the information dissemination path; on the contrary, when a social relationship breaks, the weight of the corresponding edge will decrease or be deleted, affecting the importance of nodes and the calculation of social paths. In addition, the weights of edges may be updated due to changes in the interaction frequency of users, and the temporal network will be adjusted in a timely manner according to these changes to ensure that the node importance assessment accurately reflects the real-time social state. In the application scenario of transportation networks, newly added road connections and deleted road connections will both affect the network topology, thereby affecting the calculation of the optimal path. If the traffic state of a road (e.g., traffic capacity or traffic flow) changes, the weight of the edge also needs to be updated. For example, when the traffic flow of a certain road increases or congestion occurs, the weight of the edge increases, affecting the path selection of vehicles; if the traffic capacity of the road improves, the weight of the edge decreases, and the traffic path will be readjusted; when a road is deleted, the relevant edges will be deleted, the network topology needs to be recalculated, and the paths of affected nodes will be updated.

[0107] In step S12, obtain the edge information to be inserted, update the graph structure in the complex temporal network, and complete the dynamic update of the basic structure for calculating the betweenness centrality of the complex temporal network, including:

[0108] S41: Obtain the edge information to be inserted, including the timeliness data such as the start node, end node, and timestamp of the inserted edge, and obtain the current basic structure for calculating the betweenness centrality of the complex temporal network.

[0109] S42: Insert a new edge in the temporal graph, update the graph structure according to the timeliness data of the edge, and ensure that the newly added edge meets the timeliness constraints of the complex temporal network.

[0110] Specifically, when a new edge is inserted, the edge directly affects the original optimal path, thus changing the calculation of betweenness centrality. In particular, the inserted edge may provide new optimal paths or shorter paths for some nodes, thereby changing the betweenness centrality of the nodes. For example, if a path that originally passed through multiple nodes can now reach the target node directly through the newly inserted edge, the betweenness centrality of the relevant nodes will decrease because their path participation has decreased; for each affected node, it is necessary to recalculate its optimal path to other nodes and update the betweenness centrality.

[0111] S43: Update the status information of the nodes related to the inserted edge, including the number of temporal optimal paths and the optimal path length from the source node to other nodes, the number of temporal optimal paths and the optimal path length of the split point, whether the nodes related to the inserted edge affect the original path, and determine whether it is necessary to update the original path or recalculate the temporal optimal path.

[0112] S44: Analyze the impact of the inserted edge on the betweenness centrality of nodes in the complex temporal network, especially whether the inserted edge generates new temporal optimal paths, whether it changes the selection of existing temporal optimal paths, and thus affects the betweenness centrality value of the nodes.

[0113] S45: For each node affected by the inserted edge, recalculate its temporal optimal path to other nodes and update the path set.

[0114] Specifically, for the source node (incoming point), if the inserted edge creates a new optimal path, the number of optimal paths from the source node to the target node will increase, and the path length may decrease, thus affecting the betweenness centrality of the source node. The betweenness centrality of the source node will be affected, especially when the new edge makes the source node a more important intermediate node, the betweenness centrality value of the source node will increase. At this time, the path set of the source node needs to be updated to ensure that the new optimal path is taken into account. For the end node, the inserted edge may provide it with a new path, changing its number of optimal paths and path length; if the new edge makes the end node more accessible to other nodes, or makes the end point an easier-to-reach target, then the betweenness centrality of the end node will be affected. Specifically, if the new edge makes the end point the end of the optimal paths of multiple source nodes, its betweenness centrality value will increase, and at this time, the status of the end node needs to be updated to recalculate its path and contribution value. For other intermediate nodes (neither source nodes nor end nodes), if the inserted edge creates new paths or optimizes existing paths, their betweenness centrality will also be affected because in the path calculation of these nodes, the inserted edge may exist as a new intermediate, changing the original set of optimal paths. The paths and betweenness centrality of these nodes need to be recalculated to ensure that the contributions of all paths and nodes in the network are accurately evaluated.

[0115] S46: If the inserted edge affects the splitting point, update the contribution value of the splitting point to the betweenness centrality of the original node, check the change in its importance in the complex temporal network, ensure that the new contribution value correctly reflects this change, and update the contribution values of the corresponding nodes.

[0116] Specifically, for the nodes affected by the inserted edge, especially the splitting points, their contribution values must be updated; splitting points refer to those nodes that play a key role in the temporal paths. When the path calculation changes, the contribution values of these nodes need to be re-evaluated. After inserting a new edge, the contributions of the splitting points may increase or decrease, so their betweenness centrality calculations also need to be adjusted according to the new optimal paths.

[0117] S47: Save the new temporal optimal path and ensure that the information of all nodes is updated in a timely manner.

[0118] S48: After completing the update of the temporal graph structure and betweenness centrality of the inserted edge, recalculate and adjust the graph structure to ensure that the topology of the complex temporal network and the importance evaluation of the nodes are consistent.

[0119] Specifically, if the inserted edge connects new nodes, then these new nodes will be incorporated into the temporal graph and become part of the new graph structure. The calculation of the betweenness centrality of the new nodes will depend on their connection relationships with other nodes. At this time, the new nodes may introduce new paths, which may affect the betweenness centrality of other nodes in the network; for example, the new nodes may become part of the optimal path between multiple nodes through the inserted edge, or become a new mediator between some nodes, which will directly affect the betweenness centrality values of it and other nodes. The new nodes need to recalculate the optimal paths and betweenness centrality according to their connection relationships with other nodes, and at the same time check whether they affect the paths and betweenness centrality of the existing nodes.

[0120] Obtain the information of the edge to be deleted in step S12, update the graph structure in the temporal network, and complete the dynamic update of the basic structure for calculating the betweenness centrality of the complex temporal network, including:

[0121] S51: Obtain the information of the edge to be deleted, including the timeliness data such as the start node, end node, and timestamp of the deleted edge.

[0122] S52: Delete the specified edge in the temporal graph, ensure that the graph structure still meets the timeliness constraints of the complex temporal network after deleting the edge, and update the topological structure of the network.

[0123] S53: Update the status information of the nodes related to the deleted edge, including the number of temporal optimal paths and the optimal path lengths from the source node to other nodes, the number of temporal optimal paths and the optimal path lengths of the split points, whether the related nodes of the deleted edge affect the original paths, and determine whether it is necessary to update the original paths or recalculate the temporal optimal paths.

[0124] S54: Recalculate the impact of the deleted edge on the betweenness centrality of the nodes in the complex temporal network, especially whether the deleted edge destroys the original temporal optimal paths, resulting in the need to calculate new optimal paths or discard the old paths.

[0125] S55: For the nodes affected by the deleted edge, recalculate their temporal optimal paths to other nodes and update the optimal path set.

[0126] Specifically, for the source node, the deleted edge may affect the optimal path from the source node to other nodes. If the deleted edge is part of the optimal path from the source node to the target node, then the betweenness centrality of the source node to the target node will change. The deleted edge may cause the number of paths of the source node to decrease, thus affecting the betweenness centrality value of the source node. The optimal path of the source node may need to be recalculated, especially when the original path is deleted or interrupted. For the end node (target node), the deleted edge may also cause changes in the optimal path of the end point, especially when the deleted edge is part of the path of the end node. The deleted edge may cause the betweenness centrality of the end point to decrease because some paths passing through this edge will no longer be valid. Therefore, the optimal path and betweenness centrality value of the end node need to be recalculated. For intermediate nodes (neither source nodes nor end nodes), the deleted edge may affect the optimal paths of these nodes, especially when the edge is part of the paths in which these nodes participate. After the edge is deleted, the betweenness centrality values of the affected nodes will change, and their paths may need to be re-evaluated, especially when the deleted edge makes the original path no longer valid.

[0127] S56: If the deleted edge affects the split point, update the contribution value of the split point to the betweenness centrality of the original node, check the change in its importance in the complex temporal network, ensure that the new contribution value correctly reflects this change, and update the contribution values of the corresponding nodes.

[0128] S57: Save the updated temporal optimal paths, ensure that all affected node information is updated in a timely manner, and make necessary path corrections.

[0129] S58: Complete the update of the temporal graph structure and the betweenness centrality calculation framework after the edge deletion, ensure the consistency of the topology and node importance evaluation of the complex temporal network, and avoid calculation errors caused by deletion operations.

[0130] Specifically, if deleting an edge causes some nodes to become disconnected or a path to become unreachable, the betweenness centrality of nodes in the temporal network will be affected; in particular, the disconnected nodes in the network may no longer participate in any path calculation, so their betweenness centrality values should be updated or set to zero. In addition, the network topology after deleting an edge may cause the original split points and critical nodes to lose their importance, and the relevant contribution values also need to be updated.

[0131] In step S12, obtain the edge information to be updated, update the graph structure in the temporal network, and complete the dynamic update of the basic structure for calculating the betweenness centrality of the complex temporal network, including:

[0132] S61: Obtain the edge information to be updated, including the start node, end node, and new edge weight of the updated edge.

[0133] S62: Find the edge to be updated in the temporal graph, update the status information of the edge according to the new edge weight, and ensure that the timeliness constraint after the update of the temporal graph structure is satisfied.

[0134] S63: Update the status information of the nodes related to the updated edge, especially the number of temporal optimal paths and the optimal path length from the source node to other nodes, and the number of temporal optimal paths and the optimal path length of the split points.

[0135] S64: Re-evaluate the betweenness centrality of the nodes affected by the updated edge, especially whether the updated edge weight affects the calculation of the temporal optimal path, and determine whether the path needs to be adjusted.

[0136] S65: For the nodes affected by the updated edge, recalculate their temporal optimal paths to other nodes and update the optimal path set.

[0137] Specifically, for the source node, updating the edge weight may cause changes in its optimal paths to other nodes. Especially when the updated edge is part of the path from the source node to the target node, if the weight of the updated edge causes the source node to reach the target node through another path, the betweenness centrality of the source node may change. Specifically, if the weight of the original path decreases (i.e., the path becomes shorter after the weight update), the number of optimal paths and the betweenness centrality value of the source node will increase; if the path becomes longer or is no longer an optimal path, the betweenness centrality value of the source node may decrease. For the target node (out-node), the updated edge weight may affect the path selection from the source node to the target node. If the weight of the updated edge makes some paths shorter or longer, the betweenness centrality of the target node will be affected; especially if a certain path becomes more prominent (i.e., through the updated edge, the target node becomes the end point of more optimal paths), the betweenness centrality of the target node will increase; conversely, if the updated edge makes the path no longer an optimal path, the betweenness centrality of the target node may decrease. For the intermediate nodes in the network, updating the edge weight may affect their role as path mediators. If the weight of the updated edge changes the paths passing through these nodes, the betweenness centrality of these intermediate nodes will also change. For example, an intermediate node may become part of a new optimal path through the updated edge, thus increasing its betweenness centrality; on the contrary, if the updated edge makes the original path no longer optimal, the betweenness centrality of the intermediate node may decrease.

[0138] S66: If the updated edge affects the split point, check its impact on the contribution value of the split point, recalculate the betweenness centrality of the split point to the original node, check the change in its importance in the complex temporal network, ensure that the new contribution value correctly reflects this change, and update the contribution value of the corresponding node.

[0139] S67: Save the updated temporal optimal paths to ensure that the information of all affected nodes is updated in a timely manner.

[0140] S68: Complete the update of the temporal graph structure and the betweenness centrality calculation framework after updating the edge weight to ensure the consistency of the topology and node importance evaluation of the complex temporal network.

[0141] In practical application scenarios, such as in delay-tolerant networks, social networks, and transportation networks, the update of temporal graphs needs to cope with the challenges of frequent changes in nodes and edges. Therefore, combining incremental calculation and global calculation can effectively improve the efficiency and accuracy of updating betweenness centrality in temporal graphs. In the application scenario of delay-tolerant networks, the connections between nodes are often intermittent, and the network topology changes over time. Incremental calculation can be used to update the paths affected by newly added edges or nodes without having to recompute the entire network each time. For example, when a new relay node joins, only the paths related to this node need to be recomputed, and incremental calculation can efficiently handle such local changes. For large-scale topological changes, such as the extensive addition or deletion of nodes in the network, global calculation may be required to ensure that the betweenness centrality of all nodes remains accurate. In the application scenario of social networks, as user behaviors and social relationships change, the timeliness of nodes and edges changes. Incremental calculation can update only the affected part of the network paths when new connections are established or relationships are broken between users. For example, when a user establishes a new friendship with another person, incremental calculation only needs to update the betweenness centrality of the relevant nodes on this path without having to recompute all nodes. When the entire social network undergoes large-scale changes (such as extensive changes in the relationships of a group of users), global calculation can ensure that the betweenness centrality of all nodes is comprehensively updated. In the application scenario of transportation networks, the real-time changes in traffic flow and road conditions require frequent updates of temporal graphs. Incremental calculation is suitable for handling daily traffic flow changes, such as temporary congestion or traffic control on roads. It can quickly calculate and adjust the betweenness centrality of affected nodes. For long-term traffic pattern changes (such as the opening of new roads or the closure of old roads), global calculation is needed to re-evaluate the importance of nodes in the entire transportation network to ensure that the betweenness centrality of each node reflects the latest traffic conditions.

[0142] In step S13, the betweenness centrality of nodes in the complex temporal graph is updated through incremental calculation, including:

[0143] S81: Obtain the initial values of the betweenness centrality of all nodes in the temporal graph and establish an incremental calculation framework to prepare for incremental update operations to cope with local changes in nodes and edges.

[0144] S82: When local changes occur in the complex temporal network topology (such as edge insertion, deletion, or weight update), use the incremental calculation method to update the affected nodes and edges, and only calculate the temporal optimal paths and betweenness centrality between node pairs directly affected by the changes without having to recompute the entire temporal graph.

[0145] Specifically, when local changes occur to nodes and edges, the incremental calculation method only updates the paths and betweenness centrality of the affected nodes. For example, when a new edge is inserted or the weight of an edge is updated, only the path calculation and betweenness centrality of this edge and the nodes it connects (directly or indirectly) will be affected; incremental calculation avoids recalculating the entire graph, thus greatly improving the calculation efficiency.

[0146] S83: For the incrementally updated nodes, calculate the new optimal paths and adjust the corresponding betweenness centrality values to ensure that local updates do not affect the calculation results of the entire network.

[0147] S84: Update the set of optimal paths and betweenness centrality values, only update the parts related to the changes, and avoid recalculating the entire graph, thereby significantly improving the calculation efficiency.

[0148] Specifically, for the betweenness centrality of the source node, At this time, σ sf (v) and σ sf are updated specifically, that is, the number of temporal optimal paths between node pairs in the complex temporal graph and the number of temporal optimal paths passing through the source node v.

[0149] S85: After completing the incremental calculation, return the betweenness centrality of the updated nodes and prepare to handle possible global calculation requirements.

[0150] Specifically, after the incremental calculation is completed, return the updated betweenness centrality values of each node and be ready to handle possible large-scale structural changes. After the local update is completed, check whether there is a need for global calculation. If the incremental update is not sufficient to ensure the accuracy of the temporal network, the system will switch to the global calculation mode.

[0151] In step S13, the betweenness centrality of nodes in the complex temporal graph is updated through global calculation, including:

[0152] S91: When large-scale structural changes occur in the complex temporal network (such as large-scale node insertions, deletions, updates, or network topology changes), switch to the global calculation mode.

[0153] S92: Perform a full network traversal and recalculate the temporal optimal paths from all nodes to other nodes; global calculation will update the betweenness centrality values of all nodes to ensure that the temporal optimal paths of all nodes are correctly calculated.

[0154] S93: Update the betweenness centrality of all nodes according to the new global calculation results and ensure the integrity of the temporal graph structure to avoid omission or incorrect calculation.

[0155] S94: After completing the global calculation, re-initialize the incremental calculation framework to provide a basis for updating the incremental calculation of the next local change.

[0156] S95: Combine the global calculation result with the incremental calculation result to ensure the accuracy of the betweenness centrality value of each node in the complex temporal network and provide an accurate calculation basis for subsequent dynamic changes.

[0157] Specifically, in the combination of global calculation and incremental calculation, ensure that the final betweenness centrality value reflects the latest state of the temporal network. By combining the results of global calculation and incremental calculation, accuracy can be maintained during large-scale changes, and calculation efficiency can be maintained during local changes, providing basic support for subsequent dynamic changes of the temporal network.

[0158] In step S14, evaluate the importance of nodes according to the changes in the temporal network and output the updated betweenness centrality value, including:

[0159] S101: Finally, output the betweenness centrality values of each updated node to ensure the accuracy of the importance evaluation of all nodes after the changes in the complex temporal network, providing support for subsequent network optimization and decision-making.

[0160] Specifically, the update of the betweenness centrality value of nodes can be used for optimization and decision support in various practical applications. For example, in the application scenario of the traffic network, the updated betweenness centrality value can help to adjust the traffic flow scheduling in real time, optimize the passing efficiency of traffic hubs, and avoid traffic congestion. In the application scenario of the social network, the update of the betweenness centrality value can help to identify key users in the social propagation process, thereby optimizing the information dissemination path and improving the accuracy of social advertising or recommendation systems. In the application scenario of the delay-tolerant network, the updated betweenness centrality value of nodes can optimize the message forwarding strategy and select relay nodes with stronger transmission capabilities, thereby improving the efficiency and reliability of data transmission. In addition, the update of the betweenness centrality value can also affect resource allocation. By identifying key nodes and paths in the temporal network, it can help to achieve load balancing, traffic scheduling, and optimization strategies for data transmission in the network; the updated betweenness centrality value can be used as a key parameter in decision-making systems such as network traffic optimization, route selection, and emergency scheduling to ensure the optimal use of network resources.

[0161] S102: Save the updated betweenness centrality value to the temporal graph as the basis for the next round of calculation and analysis, ensuring the real-time and accuracy of the importance evaluation of nodes in the network.

[0162] Specifically, after saving the updated betweenness centrality values, the temporal graph model can provide accurate basic data for future temporal network analysis. Through continuous updates and saving, each node and its importance in the temporal network can be accurately tracked and evaluated; these updated node betweenness centrality values will serve as the basis for network scheduling, routing strategy optimization, and load balancing, providing real-time and reliable data support for subsequent calculations and analyses. Through this continuous update and saving method, the important nodes in the temporal network can reflect their roles and importance in the network in real time, providing support for subsequent decision-making and optimization, and ensuring the continuous improvement of network performance and efficiency.

[0163] The above description of the embodiments is to facilitate the understanding and application of the present invention by those of ordinary skill in the technical field. It is obvious that those who are familiar with the technology in this field can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A method for calculating betweenness centrality update based on complex temporal networks, comprising the following steps: (1) Obtain the initial graph structure and timeliness data of the complex temporal network, initialize the temporal graph and the betweenness centrality calculation framework of each node in the graph, and complete the construction of the basic structure for calculating the betweenness centrality of the complex temporal network; (2) Obtain the edge information to be inserted, deleted, and updated, and perform insertion, deletion, and update operations on the edges in the temporal graph, respectively, update the temporal graph structure, and complete the dynamic update of the basic structure of the calculation of the betweenness centrality of the complex temporal network; (3) Update the betweenness centrality of nodes in the temporal graph by combining incremental calculation and global calculation, and optimize the updating efficiency of the betweenness centrality of nodes in the temporal graph; (4) According to the changes in the complex temporal network, the importance of the nodes is evaluated and the betweenness centrality value of each node after the update is output.

2. The betweenness centrality update calculation method based on complex temporal networks according to claim 1 is characterized by: The specific implementation of step (1) is as follows: S1-1: Obtain the initial graph structure, node timeliness data, and edge timeliness data of the complex temporal network; S1-2: Filter out nodes and edges that meet the timeliness requirements based on the node timeliness data and edge timeliness data, initialize the temporal graph, and define the temporal optimal path; S1-3: For any node in the temporal graph, take it as the source node and initialize the betweenness centrality calculation framework for the node: set the initial value of betweenness centrality to zero, initialize the temporal optimal path set from the source node to other nodes, and initialize the set Q for storing the temporal optimal path triples; S1-4: Initialize the status information of other nodes, including the number and length of the temporal optimal paths from the source node to other nodes. Initialize the status information of each split point of the node, including the number and length of the temporal optimal paths from the source node to the split point, whether the split point is the end point of the temporal optimal path from the source node to the corresponding node, and the set of predecessor split points of the split point; initialize the local optimal timestamp lastbest used to record the last selected outbound edge of the source node, and initialize the outbound edge pruning set of the source node; S1-5: Starting from any successor node i of the source node, if the outgoing edge set of the successor node is empty, directly retain the maximum temporal edge from the source node to the successor node and store it in the outgoing edge pruning set of the source node; S1-6: If the outgoing edge set of the successor node is not empty, traverse the outgoing edge set of the successor node in descending time order, select an outgoing edge from it, and then traverse any edge j between the source node and the successor node i in ascending time order; S1-7: If there is no edge between the source node and the successor node i in the outgoing edge pruning set of the source node, store the edge j in the outgoing edge pruning set of the source node, update lastbest to the timestamp of edge j, and return to step S1-6 to continue traversing the next edge between the source node and the successor node i; S1-8: If the outgoing edge timestamp of the selected successor node is greater than the timestamp of edge j and the outgoing edge timestamp of the selected successor node is less than the current lastbest, then store edge j in the outgoing edge pruning set of the source node, update lastbest to the timestamp of edge j, and return to step S26 to continue traversing the next outgoing edge of the successor node i; if the outgoing edge timestamp of the selected successor node is greater than the current lastbest value, return to step S1-6 to continue traversing the next outgoing edge of the successor node i; S1-9: If the timestamp of the selected edge j is equal to the timestamp of the previous edge j-1, it means that the timestamp of edge j is relatively small, and return to step S1-6 to traverse the next edge between the source node and the successor node i; S1-10: If no edge that meets the conditions is found in steps S1-7 to S1-9, return to step S1-5 to traverse the next successor node until all outgoing edges of the successor nodes are traversed, completing the outgoing edge pruning of the source node; S1-11: Breadth-first traverse the successor nodes of the source node, traverse the outgoing edge set of each successor node in descending time order, find the one-hop temporal optimal path and update it, and store the generated triples in the set Q; S1-12: Pop a triple from set Q, traverse its successor nodes, traverse the outgoing edge set of each successor node in ascending temporal order, find a new temporal optimal path, and compare and update it with the current temporal optimal path; S1-13: Calculate the temporal optimal path from the source node to other nodes, calculate the split point betweenness centrality of each node in descending order of hop count, and if the split point is the end point of the temporal optimal path, traverse its child nodes and successor nodes, calculate the contribution value of the split point to them, and sum the split point contribution values ​​of all nodes to complete the preliminary calculation of the betweenness centrality of the source node; S1-14: repeat steps S1-3 to S1-13 until the betweenness centrality calculation of all nodes of the temporal graph is completed, that is, the betweenness centrality calculation of the source node; S1-15: Combine the outgoing edge pruning of all source nodes under traversal and the betweenness centrality calculation of the source nodes to obtain the basic structure of betweenness centrality calculation of complex temporal networks.

3. The betweenness centrality update calculation method based on complex temporal networks according to claim 1 is characterized by: The specific implementation method of the side information to be inserted in step (2) is as follows: S21-1: Obtain the edge information to be inserted, including the timeliness data including the start node, end node, and timestamp of the inserted edge, and obtain the current complex temporal network betweenness centrality calculation infrastructure; S21-2: Insert new edges into the temporal graph, update the graph structure according to the temporal data of the edges, and ensure that the newly added edges meet the temporal constraints of the complex temporal network; S21-3: Update the status information of the nodes related to the inserted edge, including the number and length of the temporal optimal paths from the source node to other nodes, the number and length of the temporal optimal paths of the split points, whether the nodes related to the inserted edge affect the original path, and determine whether it is necessary to update the original path or recalculate the temporal optimal path; S21-4: Analyze the impact of inserting edges on the betweenness centrality of nodes in complex temporal networks, especially whether inserting edges generates new temporal optimal paths, changes the selection of existing temporal optimal paths, and thus affects the betweenness centrality values ​​of nodes; S21-5: For each node affected by the inserted edge, recalculate its temporal optimal path to other nodes and update the optimal path set; S21-6: If the inserted edge affects the split point, update the contribution value of the split point to the betweenness centrality of the original node, check its importance change in the complex temporal network, ensure that the new contribution value correctly reflects the change, and update the contribution value of the corresponding node; S21-7: Save the new temporal optimal path and ensure that the information of all nodes is updated in time; S21-8: After completing the update of the temporal graph structure of the inserted edge and the betweenness centrality calculation framework, recalculate and adjust the temporal graph structure to ensure that the topology of the complex temporal network and the importance evaluation of the nodes remain consistent.

4. The betweenness centrality update calculation method based on complex temporal networks according to claim 1 is characterized by: The specific implementation method for the side information to be deleted in step (2) is as follows: S22-1: Obtain the edge information to be deleted, including the timeliness data including the start node, end node, and timestamp of the deleted edge; S22-2: Delete the specified edge in the temporal graph to ensure that the graph structure still meets the timeliness constraints of the complex temporal network after deleting the edge, and update the topology of the network; S22-3: Update the status information of the nodes related to the deleted edge, including the number and length of the temporal optimal paths from the source node to other nodes, the number and length of the temporal optimal paths of the split points, whether the nodes related to the deleted edge affect the original path, and determine whether it is necessary to update the original path or recalculate the temporal optimal path; S22-4: Recalculate the impact of edge deletion on node betweenness centrality in complex temporal networks, especially whether the deleted edge destroys the original temporal optimal path, resulting in the need to calculate a new optimal path or the abandonment of the old path; S22-5: For the nodes affected by the deleted edge, recalculate their temporal optimal paths to other nodes and update the optimal path set; S22-6: If the deleted edge affects the split point, update the contribution value of the split point to the betweenness centrality of the original node, check its importance change in the complex temporal network, ensure that the new contribution value correctly reflects the change, and update the contribution value of the corresponding node; S22-7: Save the updated temporal optimal path, ensure that all affected node information is updated in a timely manner, and make necessary path corrections; S22-8: Complete the update of the temporal graph structure and betweenness centrality calculation framework after deleting edges, ensure the consistency of topology and node importance evaluation of complex temporal networks, and avoid calculation errors caused by deletion operations.

5. The betweenness centrality update calculation method based on complex temporal networks according to claim 1 is characterized by: In step (2), the side information to be updated is specifically implemented as follows: S23-1: Obtain the edge information to be updated, including the start node, end node and new edge weight of the updated edge; S23-2: Find the edge to be updated in the temporal graph, update the state information of the edge according to the new edge weight, and ensure that the timeliness constraint of the updated temporal graph structure is satisfied; S23-3: Update the status information of nodes related to the update edge, especially the number and length of the temporal optimal paths from the source node to other nodes, and the number and length of the temporal optimal paths of the split points; S23-4: Re-evaluate the betweenness centrality of nodes affected by the updated edges, especially whether the updated edge weights affect the calculation of the temporal optimal path, and determine whether the path needs to be adjusted; S23-5: For the nodes affected by the updated edge, recalculate their temporal optimal paths to other nodes and update the optimal path set; S23-6: If the updated edge affects the split point, check its impact on the contribution value of the split point, recalculate the contribution value of the split point to the betweenness centrality of the original node, check its importance change in the complex temporal network, ensure that the new contribution value correctly reflects the change, and update the contribution value of the corresponding node; S23-7: Save the updated temporal optimal path to ensure that all affected node information is updated in a timely manner; S23-8: Complete the update of the temporal graph structure and betweenness centrality calculation framework after updating edge weights to ensure the consistency of the topology and node importance evaluation of complex temporal networks.

6. The betweenness centrality update calculation method based on complex temporal networks according to claim 1 is characterized by: In step (3), the betweenness centrality of the nodes in the temporal graph is updated by incremental calculation, and the specific implementation method is as follows: S31-1: Obtain the initial values ​​of the betweenness centrality of all nodes in the temporal graph, and establish an incremental calculation framework to prepare for incremental update operations to cope with local changes in nodes and edges; S31-2: When a local change occurs in the network topology, an incremental calculation method is used to update the affected nodes and edges, and only the temporal optimal paths and betweenness centrality between those node pairs directly affected by the change are calculated without recalculating the entire temporal graph; S31-3: For the incrementally updated nodes, calculate the new temporal optimal path and adjust the corresponding betweenness centrality value to ensure that the local update does not affect the calculation results of the entire network; S31-4: Update the optimal path set and betweenness centrality values, only updating the parts related to the change, avoiding recalculation of the entire graph, thus significantly improving computational efficiency; S31-5: After completing the incremental calculation, return the betweenness centrality value of the updated node and prepare to handle possible global calculation needs.

7. The betweenness centrality update calculation method based on complex temporal networks according to claim 6 is characterized by: In step (3), the betweenness centrality of the nodes in the temporal graph is updated by global calculation, and the specific implementation method is as follows: S32-1: When a complex temporal network undergoes a large-scale structural change, switch to global computing mode; S32-2: perform a full network traversal and recalculate the temporal optimal path from all nodes to other nodes; S32-3: Update the betweenness centrality values ​​of all nodes according to the new global calculation results, and ensure the integrity of the temporal graph structure to avoid omissions or miscalculations; S32-4: After completing the global calculation, reinitialize the incremental calculation framework to provide a basis for the next incremental calculation update of local changes; S32-5: Combine the global calculation results with the incremental calculation results to ensure the accuracy of the betweenness centrality value of each node in the complex temporal network and provide an accurate calculation basis for subsequent dynamic changes.

8. The betweenness centrality update calculation method based on complex temporal networks according to claim 1 is characterized by: The specific implementation of step (4) is as follows: S4-1: Finally, the betweenness centrality value of each node after the update is output to ensure that the importance evaluation of all nodes after the changes in the complex temporal network is accurate, providing support for subsequent network optimization and decision-making; S4-2: Save the updated betweenness centrality value of each node in the temporal graph as the basis for the next round of calculation and analysis to ensure the real-time and accuracy of node importance evaluation in complex temporal networks.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor is used to execute the computer program to implement the betweenness centrality update calculation method based on a complex temporal network as claimed in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the betweenness centrality update calculation method based on a complex temporal network according to any one of claims 1 to 8.

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