High-speed rail key node identification method fusing islanding effect under super network

Abstract

The invention specifically discloses a high-speed rail key node identification method fusing an islanding effect under a super network, and relates to the technical field of complex network science. The method comprises the following steps: firstly, constructing a high-speed rail super network according to a super network theory, and calculating an incidence matrix and an adjacent matrix; calculating static topology indexes such as node excess and node betweenness by using the two matrixes; then, calculating a super-network proximity centrality index, and obtaining super-network efficiency according to a global average value of reciprocal lengths of shortest paths between node pairs so as to evaluate node criticality; simulating node attacks, calculating network efficiency and detecting islands; and finally, integrating the network topology, the centrality index and the islanding effect, and determining a key node set. According to the method, accurate identification of the key nodes of the high-speed rail is realized, and powerful support is provided for high-speed rail network planning and management.

Description

Technical Field

[0001] The present invention relates to the technical field of complex network science, and particularly to a method for identifying key nodes of high-speed railways that integrates the island effect under a hypernetwork. Background Art

[0002] As an important national transportation infrastructure, the topological characteristics and anti-destruction ability of the high-speed railway network directly affect transportation efficiency and safety. Through graph theory and network analysis methods, complex network science reveals the organizational structure of nodes and edges in complex systems, providing a systematic framework for the study of the high-speed railway network (hereinafter referred to as the high-speed railway network). This method can not only quantify topological features such as the degree distribution, clustering coefficient, and average path length of the network, but also simulate the network response under emergencies through dynamic simulation, evaluate the network robustness, and identify key vulnerable nodes. However, current traffic network modeling is mainly based on traditional complex network methods, which have significant limitations.

[0003] Traditional complex network models abstract high-speed railway stations as nodes and lines as binary edges, and cannot represent the high-order correlation of multi-station collaborative operation. For example, when a high-speed railway line contains multiple stations, it needs to be split into multiple binary edges, resulting in distorted topological structures and making it difficult to reflect the contribution of the overall line to network connectivity. At the same time, existing methods focus on static physical connections (such as railway tracks and stations), while actual traffic efficiency highly depends on the spatio-temporal organization of dynamic service units (such as train numbers and flights). When a certain line fails, not only the physical nodes are affected, but also all dynamic service units covered by it are affected, resulting in a systematic loss of traffic capacity. However, traditional models lack the description of the mapping relationship between dynamic services and infrastructure.

[0004] At the level of key node evaluation, existing methods rely on static topological indicators (such as node degree and betweenness centrality), ignoring the potential possibility of cascade failure effects caused by the failure of a single node. In particular, they cannot quantify the "island" phenomenon caused by the destruction of key nodes - that is, the failed nodes may split the network topology, resulting in two types of typical structural damages: one is the "isolated node". For example, after the failure of a hub station, its adjacent stations become isolated points due to the loss of connection paths. Although these nodes are not damaged themselves, their service functions are completely paralyzed due to the loss of reachability. The other is the "isolated connected subgraph". After the failure of the regional core hub, the entire regional network is disconnected from the main network, forming a sub-network that is locally connected but globally unreachable. Although this structure maintains local connectivity, the overall network efficiency drops sharply due to the loss of cross-regional connection ability.

[0005] In view of the above deficiencies, hypernetwork modeling maps a high-speed rail line as a hyperedge connecting multiple stations by introducing the concept of hyperedges, preserving the high-order topological features of the multi-station collaboration relationship; at the same time, it realizes the coupled modeling of the static physical layer and the dynamic service layer by associating infrastructure with hyperedges. For critical node identification, the hypernetwork uses the characteristic of connecting nodes with hyperedges, which can amplify the impact of a node being damaged on surrounding nodes and the overall network. This modeling method not only better fits the essence of the operation of the transportation system but also can comprehensively evaluate the static attributes and dynamic damage effects of nodes, providing a multi-dimensional quantitative basis for critical node identification. Summary of the Invention

[0006] The purpose of the present invention is to propose a method for identifying critical nodes of high-speed rail under a hypernetwork that integrates the island effect. By constructing a single-layer high-speed rail hypernetwork model, combining static topological indicators and the island effect, the criticality of nodes is comprehensively quantified, and the accuracy and practicality of critical node identification are improved.

[0007] To achieve the above purpose, the present invention proposes a method for identifying critical nodes of high-speed rail under a hypernetwork that integrates the island effect, and the steps are as follows: Step S1: According to hypernetwork theory, construct a high-speed rail hypernetwork, and calculate the incidence matrix and adjacency matrix based on the constructed high-speed rail hypernetwork; Step S2: Calculate static topological indicators based on the adjacency matrix and incidence matrix of the high-speed rail hypernetwork, including the node degree and node betweenness of the high-speed rail hypernetwork; Step S3: Calculate the closeness centrality index of the hypernetwork; Step S4: Calculate the efficiency of the hypernetwork according to the global average value of the reciprocals of the shortest path lengths between all node pairs, and evaluate the critical degree of the node for the overall network through the change in the hypernetwork efficiency; Step S5: Simulate node attacks, and calculate the network efficiency and island detection of the hypernetwork under the destruction of a single node; Step S6: Comprehensively consider network topological indicators, centrality indicators, and the island effect to obtain a set of critical nodes.

[0008] Preferably, in step S1, the high-speed rail hypernetwork , where , is a set of nodes composed of high-speed rail stations, is the th station of the high-speed rail line, , is a set of hyperedges composed of high-speed rail operation trips, is the th operation trip of the high-speed rail; the specific construction steps are as follows: Step S11: Map high-speed rail stations to the nodes of the hypernetwork, and map a complete high-speed rail operation trip to a hyperedge, including all high-speed rail stations passed by this trip. Step S12: Define the node set in the hypernetwork as , and the hyperedge set as . Define the adjacency matrix of the hypernetwork as , with its size being . Define the incidence matrix of the hypernetwork as , with its size being ; where M , N are positive integers; Step S13: Traverse a high-speed rail operation train number, obtain the station information therein, and group these stations together to form a hyperedge; Step S14: Loop and execute Step S13 until all stations and high-speed rail operation train numbers are retrieved; Step S15: Construct the adjacency matrix and incidence matrix of the high-speed rail hypernetwork according to the structure of the high-speed rail hypernetwork.

[0009] Preferably, in Step S15, the calculation formula of the adjacency matrix is as follows: ; where is the element in the th row and the th column of , , ; The calculation formula of the incidence matrix is as follows: ; where is the element in the th row and the th column of .

[0010] Preferably, in Step S2, the specific steps for calculating the static topology index are as follows: Step S21: The node degree is the number of hyperedges containing the node. The larger the node degree, the more hyperedges are associated with this node. The calculation formula is as follows: ; where is the node degree. According to the node degree, screen out the set of key nodes ranked among the top based on the node degree ; Step S22: The node betweenness is the ratio of the number of shortest hyperpaths passing through a certain node to all shortest hyperpaths in the network. The calculation formula is as follows: ; where is the node betweenness, For a node and a node the number of the shortest hyperpaths passing through a node therebetween; is the number of all shortest hyperpaths in the hypernetwork, p and q are nodes; According to the node betweenness, a set of key nodes ranked among the top based on the node betweenness is selected ; Step S23, through the calculation of static topology indicators, based on network structure indicators, comprehensively considering the node degree and the node betweenness, take and the union of the sets to obtain a primary set of key nodes .

[0011] Preferably, in step S3, the hypernetwork closeness centrality is represented by the reciprocal of the average distance from a node to other nodes in the network, and the formula is as follows: ; wherein, is the closeness centrality, is the length of the shortest path connecting two nodes and ; According to the hypernetwork closeness centrality index, a set of key nodes based on the path is selected .

[0012] Preferably, in step S4, the efficiency of the hypernetwork is the global average of the reciprocals of the shortest path lengths between all node pairs, and the formula is as follows: ; wherein, is the efficiency of the hypernetwork.

[0013] Preferably, in step S5, simulate node attacks, and calculate the network efficiency and detect islands in the hypernetwork under the destruction of a single node. The specific steps are as follows: Step S51, use the island detection model to detect islands; Step S52, select a set of nodes that have a greater impact on the hypernetwork efficiency after being attacked ; Step S53, count the number of islands generated in the hypernetwork after node destruction, and the number of nodes included in each island, and select a set of nodes ranked among the top based on the total number of nodes included in the islands .

[0014] Preferably, in step S51, when using the island detection model to detect islands, the specific operation is: Step S511: Input the incidence matrix of the constructed high-speed rail hypernetwork; Step S512: Randomly attack a single node, import the incidence matrix after deleting the failed nodes and the hyperedges where the failed nodes are located, and use the union-find algorithm for island identification; Step S513: Initialize by initializing each node as an independent set; Step S514: Hyperedge merging, merge all nodes within the same hyperedge into the same set; Step S515: Connected component extraction, count the root nodes of all nodes, and the nodes with the same root node belong to the same connected component; Step S516: Define the largest connected component containing the most nodes after failure as the main network, and regard other connected components as islands.

[0015] Preferably, in step S6, for , , , Take the intersection to obtain the set of key nodes that comprehensively consider network topology indicators, centrality indicators, and island effects .

[0016] Therefore, the present invention proposes a method for identifying key nodes of high-speed rail under a hypernetwork that integrates island effects, and its beneficial effects are as follows: (1) The present invention uses hypernetwork theory and constructs a high-speed rail hypernetwork by utilizing the characteristics that a hypernetwork can not only represent the complex relationships between multiple nodes but also effectively represent the hyperedge relationships between multiple nodes, making the model more in line with the complex connections between high-speed rail network stations and operation lines in reality.

[0017] (2) The present invention can more accurately express the complex interactions and interdependencies between running trains and stations in the real high-speed rail network. The propagation of node failures will start from the failed station and spread along the interactions and dependencies between running trains and stations, making the failure model more in line with the actual situation.

[0018] (3) The present invention considers the identification method of key nodes in reality and proposes a new method for key nodes, comprehensively incorporating network structure indicators, centrality indicators, and the number of generated islands to identify key nodes in the hypernetwork.

[0019] (4) Through the analysis of the island effect generated after the failure of a single node, the key stations of the high-speed rail network can be found, the resilience of the high-speed rail network can be explored, which helps to design a more resilient high-speed rail network and has reference significance for the planning of the high-speed rail network.

[0020] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0021] Figure 1 Flow chart of a method for identifying key nodes of high - speed rail integrating island effect under a hyper - network according to the present invention; Figure 2 Flow chart of hyper - network construction according to the present invention; Figure 3 Flow chart of the attack in the present invention; Figure 4 Flow chart of the island detection model in the present invention. Detailed implementation manners

[0022] To make the technical solutions, advantages and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention without creative efforts belong to the protection scope of the present invention.

[0023] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those of ordinary skill in the art to which the present invention belongs.

[0024] As Figure 1 shown, it is a flow chart of a method for identifying key nodes of high - speed rail integrating island effect under a hyper - network according to the present invention, and the specific steps are as follows: S1. According to the hyper - network theory, construct a high - speed rail hyper - network, and calculate the incidence matrix and adjacency matrix based on the constructed high - speed rail hyper - network; As Figure 2 shown, the high - speed rail hyper - network , where , is a node set composed of high - speed rail stations, is the th station of the high - speed rail line, , is a hyper - edge set composed of high - speed rail operation trips, is the th operation trip of the high - speed rail; the specific steps are as follows: S11. Mapping: Map high - speed rail stations to nodes of the hyper - network, and map a complete high - speed rail operation trip to a hyper - edge, which includes all high - speed rail stations passed by this trip; S12. Initialization: Define the node set in the hyper - network as , the hyper - edge set as , define the adjacency matrix of the hyper - network as , its size is , define the incidence matrix of the hyper - network as , its size is ; where M 、N is a positive integer; S13. Association between nodes and hyperedges: Traverse a high-speed rail operation train number, obtain the station information therein, and group these stations together to form a hyperedge. For example, if a certain train number stops at high-speed rail stations and , then add the nodes and to the corresponding hyperedge; S14. Loop process: Loop and execute step S13 until all stations and high-speed rail operation train numbers are retrieved; S15. Construct the adjacency matrix and incidence matrix: After the mapping is completed, construct the adjacency matrix and incidence matrix according to the structure of the hypernetwork. The adjacency matrix reflects the connection situation between nodes, while the incidence matrix represents the association relationship between hyperedges and nodes. Among them, the calculation formula of the adjacency matrix is as follows: ; where is the element in the th row and th column of , ; The calculation formula of the incidence matrix is as follows: ; where is the element in the th row and th column of At this point, the algorithm ends and the high-speed rail hypernetwork is constructed.

[0025] S2. Calculate the static topological indicators based on the adjacency matrix and incidence matrix of the high-speed rail hypernetwork, including the node degree and node betweenness of the high-speed rail hypernetwork. The specific steps are as follows: S21. The node degree is the number of hyperedges containing this node. The larger the node degree, the more hyperedges associated with this node, indicating that the importance of this node is stronger. The calculation formula is as follows: ; where is the node degree. According to the node degree, screen out the set of key nodes ranked among the top based on the node degree ; S22. The node betweenness is the ratio of the number of shortest hyperpaths passing through a certain node to all shortest hyperpaths in the network. The larger the node betweenness, the more shortest paths pass through this node, and the greater the impact of this node on the network connectivity rate and network efficiency, the stronger the node importance. When the node fails to complete the tasks given by the system, the impact on the stability of the entire network is also greater. The calculation formula is as follows: ; Among them, is the node betweenness, is the node and the node The number of shortest hyperpaths passing through the node between them, is the number of all shortest hyperpaths in the hypernetwork, p and q are nodes; According to the node betweenness, select the key node set ranked among the top based on the node betweenness ; S23. Through the calculation of static topology indicators, based on network structure indicators, comprehensively consider node degree and node betweenness, and take and The union of the sets to obtain the primary selection set of key nodes .

[0026] S3. Calculate the closeness centrality index of the hypernetwork, which is represented by the reciprocal of the average distance from a node to other nodes in the network. The formula is as follows: ; Among them, is the closeness centrality, is the length of the shortest path connecting two nodes and ; According to the hypernetwork closeness centrality index, select the key node set based on the path ; S4. Calculate the efficiency of the hypernetwork according to the global average value of the reciprocals of the shortest path lengths between all node pairs, and evaluate the criticality of this node to the overall network through the change of the hypernetwork efficiency. The hypernetwork efficiency calculation formula is as follows: ; Among them, is the efficiency of the hypernetwork; S5. As Figure 3 shown, simulate node attacks, calculate the network efficiency of the hypernetwork under the destruction of a single node and detect islands. The specific steps are as follows: Step S51. As Figure 4As shown in the figure, the island detection is carried out by using the island detection model, and the specific operation is as follows: Step S511: Input the association matrix of the constructed high-speed rail hypernetwork; Step S512: Randomly attack a single node, import the association matrix after deleting the failed nodes and the hyperedges where the failed nodes are located, and use the union-find algorithm for island identification; Step S513: Initialize, and initialize each node as an independent set; Step S514: Hyperedge merging, merge all the nodes within the same hyperedge into the same set, reflecting the logical connectivity formed by them through this hyperedge; Assume that the currently processed hyperedge is , select a node from as the initial representative point, and take as the benchmark, and merge the other nodes into the set where is located; Step S515: Connected component extraction, count the root nodes of all nodes, and the nodes with the same root node belong to the same connected component; Step S516: Define the largest connected component with the largest number of nodes after failure as the main network, and regard other connected components as islands.

[0027] Step S52: Screen out the node set that has a greater impact on the hypernetwork efficiency after being attacked ; Step S53: Count the number of other connected components - islands generated in the network after node destruction, as well as the number of nodes included in each island, and screen out the node set ranked among the top based on the total number of nodes included in the islands ; S6: Take the intersection of , , , to obtain the key node set that comprehensively considers network topology indicators, centrality indicators and island effects .

[0028] It should be noted that the content not elaborated in detail in the present invention is all prior art and is well known to those skilled in the art.

[0029] Therefore, the present invention provides a method for identifying key nodes of high-speed rail integrating island effects under a hypernetwork, constructs a high-speed rail hypernetwork by using hypernetwork theory, and integrates static topology and island effect related indicators to identify key nodes, making the model more in line with reality and node identification more accurate, which is of great significance to high-speed rail network security assessment, emergency management and planning optimization.

[0030] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for identifying key nodes of high-speed railways that integrates the island effect under a super network, characterized in that, It includes the following steps: Step S1: According to the hypernetwork theory, construct a high-speed rail hypernetwork, and calculate the incidence matrix and adjacency matrix based on the constructed high-speed rail hypernetwork; Step S2: Calculate the static topological indices based on the adjacency matrix and incidence matrix of the high-speed rail hypernetwork, including the node degree and betweenness centrality of the high-speed rail hypernetwork; Step S3: Calculate the closeness centrality index of the hypernetwork; Step S4: Calculate the efficiency of the hypernetwork according to the global average of the reciprocals of the shortest path lengths between all node pairs, and evaluate the criticality of the node to the overall network through the change of the hypernetwork efficiency; Step S5: Simulate node attacks, and calculate the network efficiency of the hypernetwork and detect isolated islands under the destruction of a single node; Step S6: Comprehensively consider the network topological indices, centrality indices and isolated island effects to obtain a set of critical nodes.

2. The method for identifying key nodes of high-speed rail integrating island effect under a super network according to claim 1, wherein In step S1, the high-speed rail super network , where is a node set composed of high-speed rail stations, is the th station of the high-speed rail line, is a hyperedge set composed of high-speed rail operation trips, is the th operation trip of the high-speed rail; the specific construction steps are as follows: Step S11: Map high-speed rail stations to the nodes of the hypernetwork, and map a complete high-speed rail operation trip to a hyperedge, which includes all high-speed rail stations passed by this trip; Step S12: Define the node set in the hypernetwork as , the hyperedge set as , and define the adjacency matrix of the hypernetwork as , with its size being . Define the incidence matrix of the hypernetwork as , with its size being ; where M , N are positive integers. Step S13: Traverse a high-speed rail operation trip, obtain the station information therein, and combine these stations together to form a hyperedge; Step S14: Loop and execute Step S13 until all stations and high-speed rail operation trips are retrieved; Step S15: According to the structure of the high-speed rail hypernetwork, construct the adjacency matrix and incidence matrix of the high-speed rail hypernetwork.

3. The method for identifying key nodes of high-speed rail integrating island effect under a super network according to claim 2, wherein In Step S15, the calculation formula of the adjacency matrix is as follows: ； Among them, is the th column element in the , are positive integers; The calculation formula of the incidence matrix is as follows: ； Among them, is the th element in the 4. The method for identifying key nodes of high-speed rail under a super network with integrated island effect according to claim 3, wherein In Step S2, the specific steps for calculating the static topological indices are as follows: Step S21: The node degree is the number of hyperedges containing this node. The larger the node degree, the more hyperedges are associated with this node. The calculation formula is as follows: ； Among them, is the node degree. Based on the node degree, a set of key nodes ranked among the top in terms of node degree is selected ; Step S22: The betweenness centrality of a node is the ratio of the number of shortest hyperpaths passing through this node to all shortest hyperpaths in the network. The calculation formula is as follows: ； Among them, is the node betweenness centrality, is the number of the shortest hyperpaths passing through node between node and node , is the number of all shortest hyperpaths in the hypernetwork, p and q are nodes; According to the node betweenness, screen out the set of key nodes ranked among the top based on the node betweenness ; Step S23: Through the calculation of static topological indices, based on network structure indices, comprehensively considering node degree and node betweenness, take the and union of the sets to obtain a preliminary set of key nodes .

5. The method for identifying key nodes of high-speed rail integrating island effect under a super network according to claim 4, wherein In Step S3, the hypernetwork closeness centrality is represented by the reciprocal of the average distance from a node to other nodes in the network. The formula is as follows: ； Among them, is the closeness centrality, is the length of the shortest path connecting two nodes and ; according to the hypernetwork closeness centrality index, a set of path-based key nodes is selected .

6. The method for identifying key nodes of high-speed rail under a super network with integrated island effect according to claim 5, wherein, In Step S4, the efficiency of the hypernetwork is the global average of the reciprocals of the shortest path lengths between all node pairs. The formula is as follows: ； Among them, is the efficiency of the super network.

7. A method for identifying key nodes of high-speed rail under a super network with integrated island effect according to claim 6, characterized in that, In Step S5, simulate node attacks, and calculate the network efficiency of the hypernetwork and detect isolated islands under the destruction of a single node. The specific steps are as follows: Step S51: Use the isolated island detection model to detect isolated islands; Step S52: Screen out the node set that has a greater impact on the efficiency of the super network after being attacked ; Step S53: Count the number of isolated islands generated in the hypernetwork after node failure, as well as the number of nodes contained in each isolated island, and filter out the node set ranked among the top in terms of the total number of nodes contained in the isolated islands 。 8. A method for identifying key nodes of high-speed railways that integrates the island effect under a super network according to claim 7, characterized in that, In Step S51, when using the isolated island detection model to detect isolated islands, the specific operation is as follows: Step S511: Input the incidence matrix of the constructed high-speed rail hypernetwork; Step S512: Randomly attack a single node, import the incidence matrix after deleting the failed node and the hyperedge where the failed node is located, and use the union-find algorithm to identify isolated islands; Step S513: Initialize, and initialize each node as an independent set; Step S514: Hyperedge merging, merge all nodes within the same hyperedge into the same set; Step S515: Connected component extraction, count the root nodes of all nodes, and the same root nodes belong to the same connected component; Step S516: Define the largest connected component containing the most nodes after failure as the main network, and other connected components are regarded as isolated islands.

9. The method for identifying key nodes of high-speed rail integrating island effect under a super network according to claim 8, wherein, In step S6, for , , , take the intersection to obtain a key node set that comprehensively considers network topology indicators, centrality indicators, and islanding effects .

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