Network disintegration method and system considering node removal cost

Abstract

The invention belongs to the technical field of traffic network disintegration, and discloses a network disintegration method and system considering node removal cost, and the method comprises the steps: inputting a traffic transportation network needing to be disintegrated; obtaining the removal cost of each node in the traffic transportation network; the number of vehicles in each operation is used as the cost of node removal; sorting the removal cost of the nodes in an ascending order, and removing the nodes in sequence; evaluating the effectiveness of the disintegration strategy by using an index NGCC, wherein the method comprises the following steps: introducing the number of removed nodes as a penalty term into a target function; a DF algorithm is introduced to detect GCC leaves, and the GCC leaves are removed as targets in the initial stage of network disintegration; and outputting the disintegrated traffic transportation network. According to the invention, the scale of the GCC is obviously reduced without damaging the overall structure of the network; a DF algorithm is introduced to remove a structure similar to a tree in the GCC.

Description

Technical Field

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

[0002] In an interconnected world, network systems are essential for communication, resource sharing, and collaboration. However, some networks, such as disease transmission networks, transportation networks, and protein interaction networks, are harmful. Therefore, corresponding measures 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 the collapse of the network by removing nodes or edges, which is crucial to combat adverse networks. The effect of network dismantling is evaluated by an objective function tailored for a specific scenario. Currently, there is no consensus on how to evaluate system health or define the goal of network dismantling. When evaluating the effect of dismantling, the main approach is to evaluate it from the perspective of network connectivity. The most common approach is to use the size of the giant connected component (GCC) to describe the disintegration process of the network and stop the attack when the GCC size reaches a target value. Some studies also use network metrics, such as efficiency or nestedness, as the goal of network disintegration. For the optimization objective, some studies aim to identify the minimum set of nodes 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 optimal collapse of the entire network is a classic NP-hard problem that requires a balance between strategy effectiveness and efficiency. Due to the lack of polynomial algorithms for large-scale networks, scholars use approximate algorithms to obtain approximate optimal solutions. Among them, some studies transform this problem into a node importance ranking problem and use node centrality metrics to solve the network collapse problem, such as degree centrality, betweenness centrality, H index, and k-core centrality. Since the network collapse 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 collapse problem.

[0005] Most studies minimize the number of removed nodes, assuming that the removal cost is equal. However, nodes vary in structure, function, and importance, which makes the above assumption invalid. 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 reinforcement learning for solving combinatorial optimization problems, the FINDER framework adopts two node cost schemes for research: degree cost and stochastic cost. The goal is to find an effective strategy that minimizes the total cost of node removal and the size of GCC. Currently, FINDER is the optimal algorithm for this problem.

[0006] For a long time, most researchers have used the size of GCC to describe the maximum capacity of a 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 collapse problem. However, in the context of the generalized network collapse problem, we found its serious flaws. It fails to measure damage at the network structure level, allowing unrealistic strategies to be adopted to achieve the most effective collapse results.

[0007] Existing network collapse problems that consider the cost of node removal have obvious evaluation problems. Figure 1 ,By observing the results of FINDER, it tends to remove a large number of low-cost,edge nodes to make the scale of GCC decrease rapidly. Figure 2 It also shows the change in the node degree each time FINDER removes a node, showing a clear 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 the transportation network, which deletes nodes in ascending order according to the cost of the nodes.

[0009] The network disintegration method considering the node removal cost disclosed in the first aspect of the present application comprises the following steps: 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; The GCC leaf structure is detected and removed as a target in the initial stage of network collapse; when the network's GCC has no leaves, the GND algorithm is applied to dismantle the remaining network and obtain the removal order of the remaining nodes.

[0010] Preferably, 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.

[0011] Preferably, the ANC indicator is also used to calculate the area under the curve to evaluate the removal strategy, specifically 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.

[0012] Preferably, the objective function of the network collapse model considering cost constraints is as follows: ; .

[0013] Preferably, in the collapse strategy of the DF algorithm, only one node in the connected subgraph where the root node is located is 2-core or higher, and all other nodes are 1-core nodes, and 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.

[0014] Preferably, 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.

[0015] The network disintegration system considering the node removal cost disclosed in the second aspect of the present application includes: 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 collapsed transportation network.

[0016] This application proposes a minimum cost MC algorithm, which removes nodes in ascending order according to their cost and has no computational cost. But the performance of the MC algorithm is even better than that of the deep reinforcement learning agent FINDER. Inspired by the MC algorithm, the problem of complex network disintegration considering cost constraints is rethought, which ignores the number of nodes deleted and only considers the total cost of deletion. Therefore, by removing a large number of low-cost nodes, the size of GCC can be significantly reduced without destroying the overall structure of the network. In order to solve the above problems, a new indicator 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 classic 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 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 used to further prove that NGCC is more suitable than GCC for comprehensive evaluation of network disintegration strategies that take removal costs into consideration. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The nodes removed by FINDER when the removal cost degree-cost = 0.2; Figure 2 The degree trend of nodes during network collapse; Figure 3 Comparison of the disintegration effects of this application and the FIDNER algorithm on real networks; Figure 4 There are evaluative problems with the generalized network disintegration problem; Figure 5 Redefine the generalized network disintegration problem; Figure 6 Schematic diagram of the collapse process of the DF algorithm; Figure 7 Comparison of the disintegration effect of a certain airport network. The cost of a node is the number of flights at the airport. ac, are three metrics used to evaluate the DF, GND and MC algorithms. di, is the GCC topology of the remaining network, where (d) is the GCC topology of the remaining network when the DF algorithm reduces the GCC size to 0.5. DETAILED DESCRIPTION

[0018] The present invention is further described below in conjunction with the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention belong to the protection scope of the present invention.

[0019] The technical solution provided in the embodiment of the present application involves network disintegration and other technologies, which are specifically introduced and explained through the following embodiments. The minimum cost MC algorithm proposed in the present application is as follows: ; FINDER is a deep reinforcement learning algorithm with very high algorithmic complexity and computational cost. In contrast, the MC algorithm has minimal 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, Figure 3 As shown in Figure 2, the performance of the FINDER and MC algorithms is almost the same, and the MC algorithm even shows better results. This is an unconventional result in itself. In order to intuitively understand this unconventional phenomenon, this application Figure 4 The experiment was conducted on the network.

[0020] Through the MC algorithm, a disintegration strategy can be obtained: delete square nodes one by one. Through observation, this application specifies a strategy for removing hexagonal nodes. In the degree cost scenario, the two disintegration strategies produce networks with the same GCC size, but the cost of deleting hexagonal nodes is higher. Therefore, if the GCC scale is used as the only indicator to measure the true capacity of the network system, the cost of removing square nodes is lower, so removing square nodes is better. However, judging from the result graph after the execution of the two strategies, the result of removing square nodes does not meet the goals of this application. Because it removes a large number of low-value edge nodes, does not remove key nodes in the network, and does not damage the overall structure of the network.

[0021] In real life, the capacity of a network system depends not only on the number of connected nodes but also on the structure of the network. The ideal disruption result should lead to network fragmentation, that is, including many smaller connected components or a large number of isolated nodes, while reducing the size of the GCC. Figure 4 Middle b and Figure 4 For comparison, Figure 4 The true capacity of the network in c is significantly lower, indicating that removing the hexagonal nodes is more beneficial. Although removing the hexagonal nodes will incur higher costs, it will also cause greater structural damage to the network.

[0022] In the generalized network collapse problem, the GCC scale metric cannot measure the impact of network structure. Therefore, this application attempts to replace the GCC scale with other common metrics such as pairwise connectivity (PWC), Herfindahl-Hirschman index (HHI), and number of connected patches (NCC) to address its limitations. However, Figure 4 DG shows that in all four indicators, the dark line is below the light line, which indicates that removing square nodes is better than removing hexagonal nodes. Although, by comparing the average shortest path of the network, it can be considered that removing hexagonal nodes is better, but the computational complexity of this indicator is too high to be used for large networks. Therefore, a new indicator that can accurately capture the expected removal effect is needed.

[0023] The essence of FINDER is an intelligent agent trained through reinforcement learning. Therefore, the effectiveness of the algorithm mainly depends on the reward function. For generalized network problems, the reward for each step is: ; in, To remove The maximum size of the connected patch of the remaining network after nodes, Indicates removal of For a combinatorial optimization problem, this application hopes that the reward value of each step can comprehensively consider two factors ( and ), to maximize the final reward. However, the comparative experiments between the MC algorithm of this application and FINDER show that FINDER believes that the cost factor plays a decisive role in the reward function. Therefore, as long as the cost of each node removed is minimized, the final reward can be maximized. The MC and FINDER algorithms can rapidly reduce the scale of GCC simply because a large number of edge nodes are removed at a lower cost. In real scenarios, it is an unrealistic strategy to simply disintegrate the network by removing a large number of edge nodes without considering the quantity limit.

[0024] (2) Reference Figure 5 , redefine the network collapse problem considering the cost of node removal; Based on the above analysis, this application proposes a new indicator, namely NGCC (NormalizedGCC:Proportion of GCC in the residual network), to evaluate the effectiveness of the strategy for the generalized network collapse problem: ; 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.

[0025] In a physical sense, NGCC reflects the proportion of the largest connected piece in the network. When the number of nodes is the same, the larger the NGCC value is, the larger the GCC scale is, which means that more nodes are connected, and thus the network can play a greater role; on the contrary, when the number of nodes is the same, the smaller the NGCC value is, the smaller the GCC scale is, which means that the degree of network fragmentation is higher. Compared with the GCC scale, NGCC not only considers the number of node connections of the largest connected piece, but also the structural information in the network. In addition, the computational cost of NGCC is consistent with the computational complexity of the GCC scale, so it can be applied to large-scale networks. Due to , so 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 size of GCC while minimizing the number of nodes removed.

[0026] (3) Network collapse model considering the cost of node removal; The most classic network collapse problem evaluation system is the number of nodes removed when a collapse strategy reduces the GCC scale (normalized) of the target network to 0.01. The lower the number of nodes removed, the more effective the strategy is. This application believes that the network collapse strategy should reflect the complete removal process, so the whole process needs to be evaluated. 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: ; For the network collapse problem considering cost constraints, ANC is defined as: ; Taking the GCC scale as an example, the physical meaning of the ANC curve is the average scale 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 indicator: ; In this way, the network collapse model considering cost constraints is redefined as follows: ; .

[0027] Compared with the previous model, this model incorporates the constraint on the number of nodes to be removed into the evaluation indicators, requiring decision makers to balance the relationship between the number of removed nodes, the total cost of removal, and the scale of GCC, which is more in line with actual constraints.

[0028] Defoliation (DF) algorithm-based collapse strategy: The closer the network structure is to a tree, the more fragile it is. Therefore, we first target and remove the tree-like structure in GCC. Figure 6 As shown, the square nodes are called root nodes. Definition 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, these root nodes are located in a connected subgraph where only one node is 2-core or higher and all other nodes are 1-core nodes. These 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 collapse. When the GCC of the network has no leaves, the GND algorithm is applied to dismantle the remaining network and obtain the demolition order of the remaining nodes.

[0029] In order to improve the efficiency of the algorithm, this application introduces a disjoint set to search for the leaf nodes of GCC. Specifically, only 1-core nodes and their neighbors are merged, and finally they are merged into root nodes. Subsequently, two dictionaries are established: one stores the root node ID of each leaf node, and the other maintains the number of nodes in 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 by the ratio to obtain the first batch of nodes to be removed. Iterate the above operations until there are no leaf nodes in GCC or the GCC scale (normalized) is less than 0.01. Since the removal process of the DF algorithm starts from the leaf nodes of GCC, it ensures that the removed nodes are always within a circle structure, and the destruction of the circle structure can cause damage to the structure of the network; .

[0030] refer to Figure 7, this application conducted experiments on different real networks, comparing the DF algorithm with the classic network disintegration algorithm. Under the NGCC metric, the performance of the MC algorithm becomes the worst. The effectiveness of the GND algorithm has declined, but overall it is still the second best among all algorithms. The DF algorithm consistently outperforms other methods on most networks. In the case of node degree as the cost, the demolition strategy provided by DF is the most effective when considering 18% of the demolition cost. Throughout the disintegration process, the ANC value of DF is lower than that of other algorithms on most networks, indicating that the disintegration strategy is more effective. On the Epinions network, it lags behind the GND algorithm by only 0.066. DF outperforms other algorithms by more than 10% in terms of average ANC. The average ANC value of DF is 0.319, while the average ANC of other algorithms (except the minimum cost) is 0.489. The disassembly effect is improved by 0.17.

[0031] 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 uses the lowest cost to reduce the GCC size to 0.5 and 0.3, 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 network system in reality. 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 fully evaluate the effectiveness of the removal strategy. NGCC considers the number of nodes removed and indirectly reflects the damage to the network structure. Therefore, it is believed that NGCC is more suitable for the problem of network disintegration 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 reduces GCC more while removing fewer nodes.

[0032] 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 a minimum cost MC algorithm, which removes nodes in ascending order according to the cost of the nodes, and has no computational cost. But the performance of the MC algorithm is even better than that of the deep reinforcement learning agent FINDER. Inspired by the MC algorithm, the problem of complex network collapse considering cost constraints is rethought, which ignores the number of deleted nodes and only considers the total cost of deletion. Therefore, by removing a large number of low-cost nodes, the size of GCC can be significantly reduced without destroying the overall structure of the network. In order to solve the above problems, a new indicator NGCC is proposed to evaluate the effectiveness of the collapse 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 classic network collapse 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 GCC. In nine real-world network experiments, DF has an average ANC value of 0.319, while the average ANC value of other algorithms (except minimum cost) is 0.489. The removal effect is improved by 0.17. Two specific cases further prove that NGCC is more suitable than GCC for comprehensive evaluation of network dismantling strategies considering removal costs.

[0033] As used herein, the word "preferred" is intended to be used as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as being more advantageous than other aspects or designs. On the contrary, the use of the word "preferred" is intended to present concepts in a specific way. The term "or" as used in this application 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" means any one of the naturally included 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 examples.

[0034] Moreover, although the present disclosure has been shown and described with respect to one or implementations, those skilled in the art will think of equivalent variations and modifications based on the reading and understanding of this specification and the accompanying 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-mentioned components (such as 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 component (such as it is functionally equivalent), even if the structure is not equivalent to the disclosed structure of the function in the exemplary implementation of the present disclosure shown herein. In addition, although the specific features of the present disclosure have been disclosed with respect to only one of several implementations, such features can be combined with one or other features of other implementations that may be desired and advantageous for a given or specific application. Moreover, insofar as the terms "including", "having", "containing" or their variations are used in specific embodiments or claims, such terms are intended to be included in a manner similar to the term "comprising".

[0035] The functional units in the embodiments of the present invention may be integrated into a processing module, or each unit may exist physically separately, or multiple or more 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. If 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 disk or an optical disk, etc. The above-mentioned devices or systems may execute the storage method in the corresponding method embodiment.

[0036] To sum up, the above embodiment is an implementation mode of the present invention, but the implementation mode of the present invention is not limited by the embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in 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; The GCC leaf structure is detected and removed as a target in the initial stage of network collapse; when the network's GCC has no leaves, the GND algorithm is applied to dismantle the remaining network and obtain the removal order of the remaining nodes.

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. The network disintegration method considering node removal cost according to claim 5, characterized in that: 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.

7. A network disintegration system considering node removal cost using the method according to any one of claims 1 to 6, 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 collapsed transportation network.

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