A network disintegration method and system considering the cost of node removal

Abstract

The present invention belongs to the technical field of transportation network disintegration, and discloses a network disintegration method and system considering the cost of node removal. The method includes: inputting the transportation network to be disintegrated; obtaining the removal cost of each node in the transportation network; using the number of each operating vehicle as the cost of removing the node; sorting the removal costs of the nodes in ascending order and removing the nodes in sequence; using the index NGCC to evaluate the effectiveness of the above disintegration strategy, including: introducing the number of removed nodes as a penalty term into the objective function; introducing the DF algorithm to detect the leaves of GCC and removing them as the target in the initial stage of network disintegration; outputting the disintegrated transportation network. This application significantly reduces the scale of GCC without destroying the overall structure of the network; the DF algorithm is introduced to remove the tree-like structure in GCC.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic network disintegration, and particularly relates to a network disintegration method and system considering node removal cost. Background Art

[0002] In the interconnected world, network systems are crucial for communication, resource sharing, and collaboration. However, some networks, such as disease transmission networks, transportation networks, protein interaction networks, etc., are harmful. Therefore, corresponding means need to be taken to disintegrate them, and this problem is called the complex network disintegration problem.

[0003] Optimal percolation or network dismantling (ND) aims to maximize network collapse by removing nodes or edges, which is crucial for combating adverse networks. The effect of network disintegration is evaluated by an objective function customized for a specific scenario. Currently, there is no consensus on how to evaluate system health or define the objective of network disintegration. When evaluating the disintegration effect, the main method is to evaluate from the perspective of network connectivity. The most common method is to use the size of the giant connected component (GCC) to describe the network disintegration process and stop the attack when the GCC size reaches the target value. Some studies also use network metrics, such as efficiency or nestedness, as the objective of network disintegration. For the optimization objective, some studies aim to identify the smallest node set or the optimal order of node removal, which is called the classical network disintegration problem. Other studies focus on minimizing the removal cost, which is called the generalized network disintegration problem.

[0004] Achieving the optimal disintegration of the entire network is a classic NP-hard problem that requires a balance between policy effectiveness and efficiency. Due to the lack of polynomial algorithms for large-scale networks, scholars have adopted approximation algorithms to obtain approximate optimal solutions. Among them, some studies have transformed this problem into a node importance ranking problem and used methods of node centrality measurement to solve the network disintegration problem, such as degree centrality, betweenness centrality, H-index, and k-core centrality. Since the network disintegration problem is essentially a combinatorial optimization problem, some studies have proposed using heuristic algorithms to solve it, such as CI, BPD, EGP, GND, etc. Inspired by machine learning methods for solving combinatorial optimization problems, some frameworks such as FINDER (Fan, C., Zeng, L., Sun, Y. & Liu, Y.-Y. Finding key players in complex networks through deep reinforcement learning. Nature Machine Intelligence 2, 317-324 (2020). https: / / doi.org / 10.1038 / s42256-020-0177-2) and GDM have also been proposed to solve the network disintegration problem.

[0005] Most studies minimize the number of removed nodes, assuming equal removal costs. However, nodes vary in structure, function, and importance, which invalidates the above assumption. Ren (Generalized network dismantling. Proceedings of the National Academy of Sciences of the United States of America 116, 6554-6559 (2019)) et al. generalized the classic network disintegration problem by considering different costs of node removal and proposed a new method (called the GND algorithm) to solve it. Inspired by the use of reinforcement learning for solving combinatorial optimization problems, the FINDER framework adopted two node cost schemes for the study: degree cost and random cost. The goal is to find an effective strategy to minimize the total cost of node removal and the size of the GCC. Currently, FINDER is the optimal algorithm for this problem.

[0006] For a long time, most researchers have used the size of the GCC to describe the maximum capacity of the network system. This metric is easy to calculate and has a clear physical meaning. Therefore, it is one of the most commonly used metrics in the network disintegration problem. However, in the context of the generalized network disintegration problem, we found its serious defect. It fails to measure the damage at the network structure level, so unrealistic strategies can be adopted to achieve the most effective disintegration result.

[0007] There are obvious evaluation problems in the existing network disintegration problem considering the cost of node removal. Refer to Figure 1 , by observing the results of FINDER, it tends to remove a large number of low-cost, peripheral nodes to rapidly reduce the scale of the GCC. Figure 2 It also shows the change in the degree of each node removed by FINDER, presenting an obvious upward trend. In the case of degree cost, the degree represents the removal cost of the node. Summary of the Invention

[0008] In view of this, the present application proposes a Minimum Cost (MC) algorithm for the network disintegration technology of transportation networks, which deletes nodes in ascending order according to the cost of the nodes.

[0009] The network disintegration method considering the cost of node removal disclosed in the first aspect of the present application includes the following steps:

[0010] Input the transportation network to be disintegrated;

[0011] Obtain the removal cost of each node in the transportation network; the number of each operating vehicle is used as the cost of removing the node;

[0012] Sort the removal costs of the nodes in ascending order and remove the nodes in sequence;

[0013] Use the index NGCC to evaluate the effectiveness of the above disintegration strategy, including: introducing the number of removed nodes as a penalty term into the objective function;

[0014] Introduce the DF algorithm to detect the leaves of the GCC and remove them as the target in the initial stage of network disintegration;

[0015] Output the disintegrated transportation network;

[0016] Among them, the disintegration strategy of the DF algorithm is as follows:

[0017] Delete the tree-like structure in the GCC;

[0018] Detect the leaf structure of the GCC and remove it as the target in the initial stage of network disintegration; when there are no leaves in the GCC of the network, apply the GND algorithm to demolish the remaining network and obtain the demolition order of the remaining nodes.

[0019] Preferably, the NGCC index is as follows:

[0020] ;

[0021] Among them, is the scale of the largest connected component of the network, is the remaining number of nodes in the network, is the total number of all nodes in the network.

[0022] Preferably, the ANC index is also used to evaluate the removal strategy by calculating the area under the curve, specifically including:

[0023] Given a network , where the node set is , the edge set is , the network connectivity metric is and the sequence of deleted nodes is , N is the total number of deleted nodes, and ANC is defined as follows:

[0024] ;

[0025] For the network disintegration problem considering cost constraints, the definition of ANC is:

[0026] ;

[0027] For the GCC scale, the physical meaning of the ANC curve is the average scale of the network GCC during the disintegration process to reflect the effectiveness of the disintegration strategy.

[0028] Preferably, the objective function of the network disintegration model considering cost constraints is as follows:

[0029] ;

[0030] .

[0031] Preferably, in the disintegration strategy of the DF algorithm, there is only one node with a 2-core or higher in the connected subgraph where the root node is located, and all other nodes are 1-core nodes. These connected subgraphs are the leaves of the GCC; the k-core node is defined as: if a node is part of a k-core network but not a k + 1-core network, then the node is a k-core node.

[0032] Preferably, the specific DF algorithm is as follows:

[0033] Only merge 1-core nodes and their neighbors, and finally merge them into the root node;

[0034] Establish two dictionaries: one stores the root node ID of each leaf node, and the other maintains the number of nodes within each leaf node;

[0035] Based on this, calculate the ratio of the leaf node size to the root node removal cost;

[0036] Sort all leaf nodes in descending order of the ratio to obtain the first batch of nodes to be removed;

[0037] Iteratively execute the above operations until there are no leaf nodes in the GCC or the size of the GCC is smaller than the preset threshold.

[0038] The network disintegration system considering node removal cost disclosed in the second aspect of the present application includes:

[0039] Input module: Input the transportation network to be disintegrated;

[0040] Obtaining module: Obtain the removal cost of each node in the transportation network; the number of each operating vehicle is used as the cost of removing the node;

[0041] Removal module: Sort the removal costs of the nodes in ascending order and remove the nodes in sequence;

[0042] Evaluation module: Use the metric NGCC to evaluate the effectiveness of the above disintegration strategy, including: introducing the number of removed nodes as a penalty term into the objective function;

[0043] Detection module: Introduce the DF algorithm to detect the GCC leaves and remove them as the target in the initial stage of network disintegration;

[0044] Output module: Output the disintegrated transportation network.

[0045] The present application proposes the minimum cost MC algorithm, which removes nodes in ascending order according to the cost of the nodes and does not calculate the cost. However, the performance of the MC algorithm is even better than that of the intelligent agent FINDER of deep reinforcement learning. Inspired by the MC algorithm, the complex network disintegration problem considering cost constraints is rethought. It ignores the number of removed nodes and only considers the total cost of removal. Therefore, by removing a large number of low-cost nodes, the size of the GCC can be significantly reduced without destroying the overall structure of the network. To solve the above problems, a new metric NGCC is proposed to evaluate the effectiveness of the disintegration strategy. It introduces the number of removed nodes as a penalty term into the objective function; its computational complexity is consistent with the size of the GCC, and it shows consistent results with the size of the GCC in the classical network disintegration problem. Inspired by the CoreHD algorithm, the closer the network structure is to a tree, the more fragile it is. Therefore, the present application introduces the DF algorithm, which first removes the tree-like structure in the GCC. In nine real-world network experiments, the average ANC value of DF is 0.319, while the average ANC value of other algorithms (except the minimum cost) is 0.489. The disassembly effect is improved by 0.17. Two specific cases are further used to prove that NGCC is more suitable than GCC for comprehensively evaluating the network disintegration strategy considering removal cost. Description of the Drawings

[0046] Figure 1Nodes removed by FINDER when the removal cost degree-cost = 0.2;

[0047] Figure 2 Degree trend of nodes during the network disintegration process;

[0048] Figure 3 Comparison of the disintegration effects of this application and the FIDNER algorithm on real networks;

[0049] Figure 4 There are evaluation problems in the generalized network disintegration problem;

[0050] Figure 5 Redefine the generalized network disintegration problem;

[0051] Figure 6 Schematic diagram of the disintegration process of the DF algorithm;

[0052] Figure 7 Comparison of the disintegration effects of a certain local airport network, where the cost of a node is the number of flights at that airport. a-c are three metrics used to evaluate the DF, GND, and MC algorithms. d-i are the GCC topologies of the remaining networks, where (d) is the GCC topology of the remaining network when the DF algorithm reduces the GCC scale to 0.5. Detailed implementation manners

[0053] The following further describes the present invention with reference to the accompanying drawings, but does not limit the present invention in any way. Any transformation or replacement made based on the teachings of the present invention falls within the protection scope of the present invention.

[0054] The technical solution provided by the embodiment of this application relates to technologies such as network disintegration, and is specifically introduced and described through the following embodiments. The minimum cost MC algorithm proposed in this application is as follows:

[0055] ;

[0056] FINDER is a deep reinforcement learning algorithm, and its algorithm complexity and computational cost are very high. In contrast, the MC algorithm has the lowest complexity and no computational cost. For example, in the Flickr network, the MC algorithm takes 0.9 seconds to obtain a policy, while FINDER takes 7734.6 seconds. However, as Figure 3 shown, the performance of FINDER and the MC algorithm is almost the same, and the MC algorithm even shows better results. This itself is an unconventional result. To intuitively understand this unconventional phenomenon, this application conducts experiments on the Figure 4 network.

[0057] Through the MC algorithm, a disintegration strategy can be obtained: deleting square nodes in sequence. Through observation, this application specifies a strategy for removing hexagonal nodes. In the degree-cost scenario, these two disintegration strategies produce networks with the same GCC size, but the cost of removing hexagonal nodes is higher. Therefore, if the GCC scale is used as the only indicator to measure the true ability of the network system, then the cost of removing square nodes is lower, so removing square nodes is more optimal. However, from the resulting graphs after executing the two strategies, the result of removing square nodes does not match the goal of this application. Because it removes a large number of low-value edge nodes, does not remove the key nodes in the network, and does not damage the overall structure of the network.

[0058] In real life, the ability of a network system depends not only on the number of connected nodes but also on the network structure. The ideal disintegration result should lead to network fragmentation, that is, include many smaller connected components or a large number of isolated nodes, while reducing the scale of the GCC. Therefore, comparing Figure 4 b in Figure 4 with c in Figure 4 it can be seen that the true ability of the network in c is significantly lower, indicating that removing hexagonal nodes is more beneficial. Although removing hexagonal nodes incurs a higher cost, it also causes greater structural damage to the network.

[0059] In the generalized network disintegration problem, the GCC scale metric cannot measure the impact of the network structure. Therefore, this application attempts to use other common metrics, such as pairwise connectivity (PWC), Herfindahl-Hirschman Index (HHI), and the number of connected components (NCC), to replace the GCC scale to address its limitations. However, Figure 4 d-g shows that in all four metrics, the dark lines are below the light lines, indicating that deleting square nodes is better than deleting hexagonal nodes. Although, by comparing the average shortest path of the network, it can be considered that removing hexagonal nodes is more optimal, but the computational complexity of this metric is too high to be used for large networks. Therefore, a new metric that can accurately capture the expected disassembly effect is needed.

[0060] The essence of FINDER is an agent trained through reinforcement learning. Therefore, the effectiveness of the algorithm mainly depends on the reward function. For the generalized network problem, the reward for each step is:

[0061] ;

[0062] where, is the size of the largest connected component of the remaining network after removing the th node, and represents removing the The cost required for each node. For a combinatorial optimization problem, this application hopes that the reward value at each step can comprehensively consider two factors ( and ), so as to maximize the final reward. However, the comparative experiment between the MC algorithm of this application and FINDER shows that FINDER believes that the cost factor plays a decisive role in the reward function. Therefore, as long as the cost of each removed node is minimized, the final reward can be maximized. The MC and FINDER algorithms can cause the rapid decline of the GCC scale, only because a large number of edge nodes are removed at a lower cost. In the real scenario, without considering the quantity limit, simply disintegrating the network by removing a large number of edge nodes is an unrealistic strategy.

[0063] (2)Refer to Figure 5 , and redefine the network disintegration problem considering the cost of node removal;

[0064] Based on the above analysis, this application proposes a new metric, namely NGCC (Normalized GCC: Proportion of GCC in the residual network), to evaluate the effectiveness of the strategy for the generalized network disintegration problem:

[0065] ;

[0066] where is the scale of the largest connected component of the network, is the number of remaining nodes in the network, is the total number of all nodes in the network.

[0067] Physically, NGCC reflects the proportion of the largest connected component in the network. When the number of nodes is the same, the larger the value of NGCC, the larger the scale of GCC, indicating that more nodes are in a connected state, and thus the greater the role that the network can play; on the contrary, when the number of nodes is the same, the smaller the value of NGCC, the smaller the scale of GCC, indicating a higher degree of network fragmentation. Compared with the GCC scale, NGCC not only considers the number of node connections in the largest connected component but also considers the structural information in the network. In addition, the calculation cost of NGCC is the same as the computational complexity of the GCC scale, so it can be applied to large-scale networks. Since , it is impossible to quickly reduce NGCC by deleting a large number of nodes. Under the guidance of NGCC, a good strategy should be to minimize the removal of nodes while minimizing the GCC scale.

[0068] (3)The network disintegration model considering the cost of node removal;

[0069] The most classic evaluation system for network disintegration problems is the number of nodes removed when a disintegration strategy reduces the size (normalized) of the GCC of the target network to 0.01. The lower the number of nodes removed, the more effective the strategy. This application believes that the network disintegration strategy should reflect the complete removal process, so it is necessary to evaluate the whole process. Based on this, this application uses the area under the ANC (accumulated normalized connectivity) curve to evaluate the strategy. Given a network , where the node set is , the edge set is , the network connectivity metric is and the sequence of deleted nodes is , the definition of ANC is as follows:

[0070] ;

[0071] For the network disintegration problem considering cost constraints, the definition of ANC is:

[0072] ;

[0073] Taking the size of GCC as an example, the physical meaning of the ANC curve is the average size of the network GCC during the disintegration process, which can be used as a measure of network resilience and thus reflect the effectiveness of the disintegration strategy. Specifically for the NGCC index:

[0074] ;

[0075] Thus, the network disintegration model considering cost constraints is redefined as follows:

[0076] ;

[0077] .

[0078] Compared with before, this model incorporates the constraint of the number of removed nodes into the evaluation index, enabling decision-makers to balance the relationship among the number of removed nodes, the total removal cost, and the size of GCC, which is more in line with the actual constraint situation.

[0079] Disintegration strategy based on the Defoliation (DF) algorithm: The closer the structure of the network is to a tree, the more vulnerable it is. Therefore, first target and delete the tree-like structures in the GCC. Such as Figure 6As shown, the square node is called the root node. It is defined that if a node is part of a k-core network but not a (k + 1)-core network, then the node is called a k-core node. Therefore, in the connected subgraph where these root nodes are located, only one node is a 2-core or higher, and all other nodes are 1-core nodes. Such connected subgraphs are called GCC leaves. This application proposes a DF algorithm to detect these structures and remove them as targets in the initial stage of network breakdown. When there are no leaves in the GCC of the network, the GND algorithm is applied to dismantle the remaining network and obtain the removal order of the remaining nodes.

[0080] To improve the algorithm efficiency, this application introduces the Disjoint Set to search for the leaf nodes of the GCC. Specifically, only 1-core nodes and their neighbors are merged, and finally they are merged into the root node. Subsequently, two dictionaries are established: one stores the root node ID of each leaf node, and the other maintains the number of nodes within each leaf node. Based on this, the ratio of the leaf node size to the root node removal cost is calculated. All leaf nodes are sorted in descending order of the ratio to obtain the first batch of nodes to be removed. The above operations are iteratively executed until there are no leaf nodes in the GCC or the size of the GCC (normalized) is less than 0.01. Since the removal process of the DF algorithm starts from the leaf nodes of the GCC, that is, it ensures that the removed nodes are always within a cycle structure, and the destruction of the cycle structure can damage the structure of the network;

[0081] 。

[0082] Reference Figure 7 Referring to, this application conducts experiments on different real networks and compares the DF algorithm with classical network breakdown algorithms. Under the NGCC metric, the performance of the MC algorithm becomes the worst. The effectiveness of the GND algorithm has decreased, but generally speaking, it is still sub-optimal among all algorithms. The DF algorithm is always superior to other methods on most networks. In the case where the node degree is used as the cost, when considering a 18% removal cost, the removal strategy provided by DF is the most effective. During the entire breakdown process, the ANC value of DF is lower than that of other algorithms on most networks, indicating that the breakdown strategy is more effective. On the Epinions network, it only lags behind the GND algorithm by 0.066. The performance of DF in terms of average ANC is more than 10% higher than that of other algorithms. The average ANC value of DF is 0.319, while the average ANC of other algorithms (except for the minimum cost) is 0.489. The disassembly effect has increased by 0.17.

[0083] In terms of real data, the transportation network used is the airport network of a certain place (https: / / toreopsahl.com / datasets / #usairports.) for experiments, and the number of flights operated by each airport is used as the cost of deleting nodes. Although the MC algorithm reduces the GCC scale to 0.5 and 0.3 at the lowest cost, its structural damage is much less than that of the DF and GND algorithms. The DF and GND algorithms consume more costs in destroying the network structure to reduce the function of the real-world network system. The GCC scale metric cannot reflect the damage to the network structure. Therefore, in the context of network disintegration considering cost constraints, the GCC scale metric cannot comprehensively evaluate the effectiveness of the removal strategy. NGCC takes into account the number of removed nodes and indirectly reflects the damage to the network structure. Therefore, it is considered that NGCC is more suitable for the network disintegration problem considering cost constraints. When the disintegration cost is 0.3, the DF algorithm reduces the NGCC of the network to 0.570, while the GND algorithm reduces it to 0.876. At the same time, the DF algorithm reduces the GCC size of the network to 0.519, while the GND algorithm reduces the GCC size to 0.618. Therefore, at the same cost, the DF algorithm makes the GCC drop more while removing fewer nodes.

[0084] By observing the removal strategy of FINDER, it is found that it preferentially removes a large number of low-cost square nodes. Therefore, this application proposes the minimum cost MC algorithm, which removes nodes in ascending order according to the cost of the nodes and does not calculate the cost. However, the performance of the MC algorithm is even better than that of the intelligent agent FINDER of deep reinforcement learning. Inspired by the MC algorithm, the complex network disintegration problem considering cost constraints is rethought. It ignores the number of removed nodes and only considers the total cost of deletion. Therefore, by removing a large number of low-cost nodes, the scale of GCC can be significantly reduced without destroying the overall structure of the network. To solve the above problems, a new metric NGCC is proposed to evaluate the effectiveness of the disintegration strategy. It introduces the number of removed nodes as a penalty term into the objective function; its computational complexity is consistent with the GCC scale, and it shows consistent results with the GCC scale in the classical network disintegration problem. Inspired by the CoreHD algorithm, the closer the network structure is to a tree, the more fragile it is. Therefore, this application introduces the DF algorithm, which first removes the tree-like structure in the GCC. In nine real-world network experiments, the average ANC value of DF is 0.319, while the average ANC value of other algorithms (except the minimum cost) is 0.489. The disassembly effect is improved by 0.17. Two specific cases are further used to prove that NGCC is more suitable than GCC for comprehensively evaluating the network disintegration strategy considering the removal cost.

[0085] As used herein, the term "preferred" is meant to be used as an example, illustration, or exemplification. Any aspect or design described herein as "preferred" should not necessarily be construed as more advantageous than other aspects or designs. Instead, the use of the term "preferred" is intended to present concepts in a concrete manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X uses A or B" is meant to naturally include any one of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing instances.

[0086] Moreover, although the present disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the drawings. The present disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular with respect to the various functions performed by the above-described components (e.g., elements, etc.), the terms used to describe such components are intended to correspond to any component (unless otherwise indicated) that performs the specified function of the described component (e.g., which is functionally equivalent), even if not structurally equivalent to the disclosed structure that performs the function in the exemplary implementations of the present disclosure shown herein. Additionally, although a particular feature of the present disclosure has been disclosed with respect to only one of several implementations, such feature may be combined with one or other features of other implementations as may be desired and advantageous for a given or particular application. Also, insofar as the terms "comprise", "have", "include", or variants thereof are used in the detailed description or claims, such terms are intended to include in a manner similar to the term "include".

[0087] Each functional unit in the embodiments of the present invention may be integrated into one processing module, or each unit may exist physically alone, or multiple or more than multiple units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The above-mentioned storage medium may be a read-only memory, a magnetic disk, or an optical disc, etc. The above-mentioned various devices or systems may execute the storage method in the corresponding method embodiments.

[0088] In summary, the above embodiments are one implementation manner of the present invention, but the implementation manner of the present invention is not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement manners and are all included within the protection scope of the present invention.

Claims

1. A network disintegration method considering the cost of node removal, characterized in that: The following steps are involved: Input transportation networks need to be dismantled; Get the removal cost of each node in the transportation network; the number of each operating vehicle is used as the cost of removing the node; Sort the removal costs of the nodes in ascending order and remove the nodes one by one; The NGCC indicator is used to evaluate the effectiveness of the above collapse strategy, including: introducing the number of removed nodes as a penalty term into the objective function; The DF algorithm is introduced to detect GCC leaves and remove them as targets at the initial stage of network collapse; exporting a disintegrated transportation network; Among them, the collapse strategy of the DF algorithm is as follows: Delete the tree structure in GCC; Detect GCC leaf structures and remove them as targets at the initial stage of network collapse; when the network's GCC has no leaves, apply the GND algorithm to dismantle the remaining network and obtain the removal order of the remaining nodes; The DF algorithm is specifically: Only 1-core nodes and their neighbors are merged, and finally they are merged into the root node; Create two dictionaries: one to store the root node ID of each leaf node, and the other to maintain the number of nodes in each leaf node; Based on this, the ratio of leaf node size to root node removal cost is calculated; Sort all leaf nodes in descending order by ratio to get the first batch of nodes to be removed; The above operation is iterated until there are no leaf nodes in the GCC or the size of the GCC is smaller than a preset threshold.

2. The network disintegration method considering node removal cost according to claim 1, characterized in that: The NGCC indicators are as follows: ； in, is the size of the largest connected piece of the network, is the number of nodes remaining in the network, is the number of all nodes in the network.

3. The network disintegration method considering node removal cost according to claim 1, characterized in that: The ANC indicator is also used to calculate the area under the curve to evaluate the removal strategy, including: Given a network , where the node set is , the edge set is , the network connectivity metric is And the sequence of deleted nodes is , N is the total number of deleted nodes, and ANC is defined as follows: ； For the network collapse problem considering cost constraints, ANC is defined as: ； For the GCC size, the physical meaning of the ANC curve is the average size of the network GCC during the disintegration process, which reflects the effectiveness of the disintegration strategy.

4. The network disintegration method considering node removal cost according to claim 3, characterized in that: The objective function of the network disintegration model considering cost constraints is as follows: ； 。 5. The network disintegration method considering node removal cost according to claim 4, characterized in that: In the collapse strategy of the DF algorithm, the root node is located in a connected subgraph in which only one node is 2-core or higher, and all other nodes are 1-core nodes. These connected subgraphs are GCC leaves; a k-core node is defined as: if a node is part of a k-core network but not a k+1-core network, then the node is a k-core node.

6. A network disintegration system considering node removal cost using the method according to any one of claims 1 to 5, characterized in that: include: Input module: input the transportation network that needs to be dismantled; Acquisition module: obtain the removal cost of each node in the transportation network; the number of each operating vehicle is used as the cost of removing the node; Removal module: sort the removal costs of the nodes in ascending order and remove the nodes one by one; Evaluation module: Use the NGCC indicator to evaluate the effectiveness of the above collapse strategy, including: introducing the number of removed nodes as a penalty term into the objective function; Detection module: Introducing the DF algorithm to detect GCC leaves and removing them as targets at the initial stage of network collapse; Output module: Output the disintegrated transportation network; Among them, the collapse strategy of the DF algorithm is as follows: Delete the tree structure in GCC; Detect GCC leaf structures and remove them as targets at the initial stage of network collapse; when the network's GCC has no leaves, apply the GND algorithm to dismantle the remaining network and obtain the removal order of the remaining nodes; The DF algorithm is specifically: Only 1-core nodes and their neighbors are merged, and finally they are merged into the root node; Create two dictionaries: one to store the root node ID of each leaf node, and the other to maintain the number of nodes in each leaf node; Based on this, the ratio of leaf node size to root node removal cost is calculated; Sort all leaf nodes in descending order by ratio to get the first batch of nodes to be removed; The above operation is iterated until there are no leaf nodes in the GCC or the size of the GCC is smaller than a preset threshold.

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