A high-speed rail key node identification method fusing island effect under super network

Abstract

The application discloses a high-speed rail key node identification method fusing island effect under a super network, and relates to the technical field of complex network science. The method first constructs a high-speed rail super network according to a super network theory, calculates a correlation matrix and an adjacency matrix; then calculates static topological indexes such as node super degree and node betweenness by using the two matrices; subsequently, a super network closeness centrality index is calculated, and a super network efficiency is derived according to a global average value of reciprocal of the shortest path length between node pairs, so as to evaluate node criticality; then, node attack is simulated, network efficiency is calculated, and an island is detected; finally, a key node set is determined by comprehensively considering network topology, the centrality index and the island effect. The method realizes accurate identification of high-speed rail key nodes, and provides strong support for high-speed rail network planning and management.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of complex network science, and in particular to a high-speed rail key node identification method fusing island effect under a super network. BACKGROUND

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

[0003] The traditional complex network model abstracts high-speed rail stations as nodes and lines as binary edges, which cannot represent the high-order correlation of multi-station coordinated operation. For example, when a high-speed rail line contains multiple stations, it needs to be split into multiple binary edges, which leads to distortion of the topological structure and makes it difficult to reflect the contribution of the line as a whole to the network connectivity. At the same time, existing methods focus on static physical connections (such as tracks and stations), while actual traffic efficiency is highly dependent on the spatiotemporal organization of dynamic service units (such as trains and flights). When a line fails, not only the physical nodes are affected, but also all the dynamic service units covered by it, causing a systematic loss of traffic capacity. However, the traditional model lacks the depiction of the mapping relationship between dynamic services and infrastructure.

[0004] In terms of key node evaluation, existing methods rely on static topological indicators (such as node degree and betweenness centrality), ignoring the potential possibility of cascading failure effect caused by the failure of a single node, especially the "island" phenomenon caused by the destruction of key nodes. That is, the failure of a node may split the network topology, leading to two typical structural damages: one is "isolated node", such as the failure of a hub station, which makes its adjacent stations become isolated points due to the loss of connection path. This kind of node is not destroyed itself, but its service function is completely paralyzed due to the loss of accessibility. The second is "isolated connected subgraph", which is a local connected but globally unreachable subnetwork formed after the failure of a regional core hub, which maintains local connectivity but loses cross-regional connection ability, leading to a sharp decline in network efficiency as a whole.

[0005] To solve the above problems, the super-network modeling maps a high-speed rail line to a super-edge connecting multiple stations by introducing the concept of super-edge, and retains the high-order topological characteristics of the multi-station coordination relationship; meanwhile, the super-edge is associated with the infrastructure to realize the coupling modeling of the static physical layer and the dynamic service layer. For the identification of key nodes, the super-network uses the characteristic that the super-edge connects nodes, which can amplify the influence of the destruction of a node on the surrounding nodes and the whole network. This modeling method not only conforms to the nature of the transportation system operation, but also comprehensively evaluates the static properties and dynamic destruction effect of the nodes, and provides multi-dimensional quantitative basis for the identification of key nodes. SUMMARY

[0006] The purpose of the present application is to provide a high-speed rail key node identification method fusing island effect under super-network, by constructing a single-layer high-speed rail super-network model, combining static topological indexes and island effect, and comprehensively quantifying the keyness of nodes, to improve the identification accuracy and practicality of key nodes.

[0007] To achieve the above purpose, the present application provides a high-speed rail key node identification method fusing island effect under super-network, and the steps are as follows:

[0008] Step S1, according to the super-network theory, a high-speed rail super-network is constructed, and an association matrix and an adjacency matrix are calculated according to the constructed high-speed rail super-network;

[0009] Step S2, based on the adjacency matrix and the association matrix of the high-speed rail super-network, the calculation of static topological indexes is performed, including the node super-degree and the node betweenness of the high-speed rail super-network;

[0010] Step S3, the closeness centrality index of the super-network is calculated;

[0011] Step S4, the efficiency of the super-network is calculated according to the global average value of the reciprocal of the shortest path length between all node pairs, and the criticality of the node to the whole network is evaluated through the change of the super-network efficiency;

[0012] Step S5, the network efficiency calculation and island detection of the super-network under single node destruction are performed by simulating node attack;

[0013] Step S6, the network topology index, the centrality index and the island effect are comprehensively considered to obtain a key node set.

[0014] Preferably, in step S1, the high-speed rail super-network , wherein, is a node set composed of high-speed rail stations, is the first station of a high-speed rail line, is a super-edge set composed of high-speed rail operation trains, is the first station of a high-speed rail line, is a super-edge set composed of high-speed rail operation trains, Train number for each trip; the specific steps for creating this information are as follows:

[0015] Step S11: Map high-speed rail stations as nodes of the hypernet and map a complete high-speed rail trip as a hyperedge, which includes all high-speed rail stations that the train stops at.

[0016] Step S12: Define the set of nodes in the hypernetwork as follows The set of hyperedges is The adjacency matrix of a hypernetwork is defined as follows: Its size is Define the hypernetwork correlation matrix as Its size is ;in, M , N It is a positive integer;

[0017] Step S13: Traverse a high-speed rail train route, obtain the station information, and combine these stations together to form a superedge;

[0018] Step S14: Repeat step S13 until all stations and high-speed rail train services have been retrieved.

[0019] Step S15: Based on the structure of the high-speed rail supernetwork, construct the adjacency matrix and correlation matrix of the high-speed rail supernetwork.

[0020] Preferably, in step S15, the adjacency matrix is ​​calculated using the following formula:

[0021] ;

[0022] in, yes The Middle Line number Column elements, , ;

[0023] The formula for calculating the correlation matrix is ​​as follows:

[0024] ;

[0025] in, yes The Middle Line number The elements of the column.

[0026] Preferably, in step S2, the specific steps for calculating the static topology index are as follows:

[0027] Step S21: The node's superdegree is the number of hyperedges that contain that node. The larger the node's superdegree, the more hyperedges are associated with that node. The calculation formula is as follows:

[0028] ;

[0029] wherein, is the node hyperdegree, according to the node hyperdegree, a key node set ranked in the front based on the node hyperdegree is screened out ;

[0030] Step S22, the node betweenness is the ratio of the number of the shortest hyper-paths passing through a node to the number of all the shortest hyper-paths in the network, and the calculation formula is as follows:

[0031] ;

[0032] wherein, is the node betweenness, is the node and the node , the number of the shortest hyper-paths passing through the node , is the number of all the shortest hyper-paths in the hyper-network, is the number of all the shortest hyper-paths in the hyper-network, p and q is the node;

[0033] According to the node betweenness, a key node set ranked in the front based on the node betweenness is screened out ;

[0034] Step S23, by calculation of the static topology index, based on the network structure index, the node hyperdegree and the node betweenness are comprehensively considered, the union set of and is taken to obtain a preliminary selection set of key nodes .

[0035] Preferably, in step S3, the hyper-network 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:

[0036] ;

[0037] wherein, is the closeness centrality, is the length of the shortest path connecting two nodes and ; according to the hyper-network closeness centrality index, a key node set based on paths is screened out .

[0038] Preferably, in step S4, the efficiency of the hyper-network is the global average value of the reciprocal of the length of the shortest path between all node pairs, and the formula is as follows:

[0039] ;

[0040] Wherein, The efficiency of the supernetwork.

[0041] Preferably, in step S5, the simulation node attack is performed, and the network efficiency calculation of the supernetwork under single node destruction and island detection are performed, and the specific steps are as follows:

[0042] Step S51, island detection is performed by using an island detection model;

[0043] Step S52, a node set which has a greater influence on the supernetwork efficiency after being attacked is screened out ;

[0044] Step S53, the number of islands generated in the supernetwork after node destruction and the number of nodes contained in each island are counted, and a node set which is ranked in the front based on the total number of nodes contained in the islands is screened out .

[0045] Preferably, in step S51, island detection is performed by using an island detection model, and the specific operation is as follows:

[0046] Step S511, the correlation matrix of the built high-speed rail supernetwork is inputted;

[0047] Step S512, a single node is randomly attacked, the correlation matrix after deleting the invalid node and the supernode where the invalid node is located is imported, and the union-find set algorithm is used for island identification;

[0048] Step S513, initialization, each node is initialized as an independent set;

[0049] Step S514, supernode merging, all nodes in the same supernode are merged into the same set;

[0050] Step S515, connected component extraction, the root nodes of all nodes are counted, and the same root node belongs to the same connected component;

[0051] Step S516, the largest connected component which contains the most nodes after being destroyed is defined as the main network, and other connected components are regarded as islands.

[0052] Preferably, in step S6, the 、 、 、 The intersection is taken, and a key node set which comprehensively considers the network topology index, the centrality index and the island effect is obtained .

[0053] Therefore, the application provides a high-speed rail key node identification method which fuses the island effect under the supernetwork, and the beneficial effects are as follows:

[0054] (1) The application uses the super network theory, utilizes the characteristics that the super network can not only represent the complex relationship between multiple nodes but also effectively represent the super edge relationship between multiple nodes, constructs the high-speed rail super network, and makes the model more close to the complex connection between the high-speed rail network stations and running lines in reality.

[0055] (2) The application can more accurately express the complex interaction and mutual dependence between the running trains and stations in the real high-speed rail network, the propagation of node failure will start from the failed station along the interaction and dependence between the running trains and stations, so that the failure model is more close to the actual situation.

[0056] (3) The application considers the identification method of the key node in reality, proposes a new key node method, and comprehensively integrates the network structure index, the centrality index and the number of generated isolated islands to identify the key node in the super network.

[0057] (4) Through the analysis of the isolated island effect generated after single node failure, the key station of the high-speed rail network can be found out, the resilience of the high-speed rail network is explored, the high-speed rail network with more resilience is helped to be designed, and the planning of the high-speed rail network has reference significance.

[0058] The technical scheme of the application will be further described in detail below with the help of the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 The flow chart of the application is a super network under the fusion isolated island effect high-speed rail key node identification method;

[0060] Figure 2 The flow chart of the application is a super network construction;

[0061] Figure 3 The attack flow chart in the application is;

[0062] Figure 4 The flow chart of the isolated island detection model in the application is. DETAILED DESCRIPTION

[0063] In order to make the technical scheme, advantages and purposes of the application clearer, the technical scheme of the embodiment of the application will be described clearly and completely below. The described embodiment is a part of the embodiment of the application, not all the embodiments. Based on the described embodiment of the application, all other embodiments obtained by those skilled in the art without creative labor belong to the protection scope of the application.

[0064] Unless otherwise defined, the technical terms or scientific terms used in the application should be understood as the usual meaning understood by those skilled in the art in the field of the application.

[0065] AsFigure 1 The diagram shows a flowchart of a method for identifying key high-speed rail nodes that incorporates islanding effects under a hypernetwork, according to the present invention. The specific steps are as follows:

[0066] S1. Construct a high-speed rail hypernetwork based on hypernetwork theory, and calculate the correlation matrix and adjacency matrix based on the constructed high-speed rail hypernetwork;

[0067] like Figure 2 As shown, high-speed rail super network ,in, , is a set of nodes consisting of high-speed rail stations. For the first high-speed rail line One site, , is a superedge set consisting of high-speed rail train numbers. For the first high-speed rail Train number; specific steps are as follows:

[0068] S11, Mapping: Map high-speed rail stations as nodes of a super network, and map a complete high-speed rail trip as a super edge, which includes all the high-speed rail stations that the train stops at.

[0069] S12. Initialization: Define the set of nodes in the hypernetwork as follows: The set of hyperedges is The adjacency matrix of a hypernetwork is defined as follows: Its size is Define the hypernetwork correlation matrix as Its size is ;in, M , N It is a positive integer;

[0070] S13. Relationship between nodes and hyperedges: Traverse a high-speed rail line, obtain the station information, and combine these stations together to form a hyperedge; for example, if a train stops at a certain high-speed rail station... and Then the node and Add to the corresponding hyperedge;

[0071] S14, Looping Process: Repeat step S13 until all stations and high-speed rail train services have been searched.

[0072] S15. Constructing the Adjacency Matrix and Incidence Matrix: After mapping, construct the adjacency matrix and incidence matrix based on the hypernetwork structure. The adjacency matrix reflects the connections between nodes, while the incidence matrix represents the relationships between hyperedges and nodes. The formula for calculating the adjacency matrix is ​​as follows:

[0073] ;

[0074] wherein, is the element in the i-th row and j-th column of matrix A, the element in the i-th row and j-th column of matrix A, the element in the i-th row and j-th column of matrix A, , ;

[0075] The calculation formula of the incidence matrix is as follows:

[0076] ;

[0077] wherein, is the element in the i-th row and j-th column of matrix A, the element in the i-th row and j-th column of matrix A, the element in the i-th row and j-th column of matrix A;

[0078] The algorithm ends here, and the high-speed rail super network is constructed.

[0079] S2, based on the adjacency matrix and the incidence matrix of the high-speed rail super network, the calculation of the static topology index is carried out, including the node super degree and the node betweenness of the high-speed rail super network, and the specific steps are as follows:

[0080] S21, the node super degree is the number of super edge strips containing the node, the larger the node super degree is, the more super edges associated with the node, indicating that the node is more important, and the calculation formula is as follows:

[0081] ;

[0082] wherein, is the node super degree, and according to the node super degree, the key node set ranked in the front row based on the node super degree is screened out ;

[0083] S22, the node betweenness is the ratio of the number of shortest super paths passing through a node to the number of all shortest super paths in the network, the larger the node betweenness is, the more shortest paths passing through the node, the greater the influence of the node on the network connectivity and network efficiency, and the stronger the node importance is, and when the node cannot complete the task given by the system, the greater the influence on the stability of the entire network is, and the calculation formula is as follows:

[0084] ;

[0085] wherein, is the node betweenness, is the number of shortest super paths passing through node i between node j and node k, is the number of shortest super paths passing through node i between node j and node k, is the number of all shortest super paths in the super network, is the number of all shortest super paths in the super network, is the number of all shortest super paths in the super network, and p is the number of all shortest super paths in the super network, and q is the number of all shortest super paths in the super network.

[0086] According to the node betweenness, a key node set ranked in the front based on the node betweenness is screened out ;

[0087] S23, by calculation of the static topology index, based on the network structure index, considering the node super degree and the node betweenness, taking and The union set of the union set is obtained .

[0088] S3, the closeness centrality index of the super network is calculated, which is represented by the reciprocal of the average distance from the node to other nodes in the network, and the formula is as follows:

[0089] ;

[0090] Wherein, is the closeness centrality, is the length of the shortest path connecting two nodes and According to the closeness centrality index of the super network, a path-based key node set is screened out ;

[0091] S4, the efficiency of the super network is calculated according to the global average value of the reciprocal of the length of the shortest path between all node pairs, and the key degree of the node to the whole network is evaluated through the change of the super network efficiency, wherein the calculation formula of the super network efficiency is as follows:

[0092] ;

[0093] Wherein, is the efficiency of the super network;

[0094] S5, as shown in Figure 3 , simulate node attack, and perform network efficiency calculation and island detection of the super network under single node destruction, and the specific steps are as follows:

[0095] Step S51, as shown in Figure 4 , island detection is performed by using an island detection model, and the specific operation is as follows:

[0096] Step S511, input the correlation matrix of the built high-speed rail super network;

[0097] Step S512, randomly attack a single node, import the correlation matrix after deleting the invalid node and the super edge where the invalid node is located, and use the union-find set algorithm to identify the island;

[0098] Step S513, initialization, initialize each node as an independent set;

[0099] Step S514, super-edge merging, merging all nodes in the same super-edge into the same set, reflecting the logical connectivity formed by the super-edge; assuming that the super-edge currently processed is , any one node in is selected as the initial representative point, and other nodes are merged into the set where is located;

[0100] Step S515, connected component extraction, counting the root nodes of all nodes, and the same root node belongs to the same connected component;

[0101] Step S516, defining the largest connected component containing the most nodes after failure as the main network, and other connected components as islands.

[0102] Step S52, screening out a node set that has a greater impact on the super-network efficiency after being attacked ;

[0103] Step S53, counting the number of other connected components-islands generated in the network after the node is destroyed, and the number of nodes contained in each island, and screening out a node set ranked in the front based on the total number of nodes contained in the island ;

[0104] S6, taking the intersection of , , , to obtain a key node set considering the network topology index, centrality index and island effect .

[0105] It should be noted that the contents not elaborated in the present application are all prior art and are well known to those skilled in the art.

[0106] Therefore, the present application provides a high-speed rail key node identification method under a super-network that fuses island effects, uses super-network theory to construct a high-speed rail super-network, fuses static topology and island effect related indexes to identify key nodes, makes the model more realistic and the node identification more accurate, and is of great significance to high-speed rail network safety evaluation, emergency management and planning optimization.

[0107] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application and not to limit them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: it can still modify or equivalently replace the technical solutions of the present application, 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 application.​

Claims

1. A method for identifying key nodes in high-speed rail systems that incorporates islanding effects under a hypernetwork, characterized in that, Includes the following steps: Step S1: Construct a high-speed rail hypernetwork based on hypernetwork theory, and calculate the correlation matrix and adjacency matrix based on the constructed high-speed rail hypernetwork; Step S2: Calculate static topology indices based on the adjacency matrix and correlation matrix of the high-speed rail supernetwork, including node degree and node betweenness of the high-speed rail supernetwork. Step S3: Calculate the proximity centrality index of the hypernetwork; Step S4: Calculate the efficiency of the hypernetwork based on 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 by the change in the efficiency of the hypernetwork. Step S5: Simulate node attacks to calculate the network efficiency of the hypernetwork and detect isolated nodes under the condition of single node damage; Step S6: Taking into account network topology indicators, centrality indicators, and island effect, obtain the set of key nodes; In step S1, the high-speed rail super network ,in, , is a set of nodes consisting of high-speed rail stations. For the first high-speed rail line One site, , is a superedge set consisting of high-speed rail train numbers. For the first high-speed rail Train number for each trip; the specific steps for creating this information are as follows: Step S11: Map high-speed rail stations as nodes of the hypernet and map a complete high-speed rail trip as a hyperedge, which includes all high-speed rail stations that the train stops at. Step S12: Define the set of nodes in the hypernetwork as follows The set of hyperedges is The adjacency matrix of a hypernetwork is defined as follows: Its size is Define the hypernetwork correlation matrix as Its size is ;in, It is a positive integer; Step S13: Traverse a high-speed rail train route, obtain the station information, and combine these stations together to form a superedge; Step S14: Repeat step S13 until all stations and high-speed rail train services have been retrieved. Step S15: Based on the structure of the high-speed rail supernetwork, construct the adjacency matrix and correlation matrix of the high-speed rail supernetwork; In step S3, the hypernetwork proximity centrality is expressed as the reciprocal of the average distance from a node to other nodes in the network, as shown in the following formula: ； in, To approximate centrality, To connect two nodes and The length of the shortest path; based on the hypernetwork proximity centrality index, a set of key nodes based on the path is selected. .

2. The method for identifying key high-speed rail nodes under a hypernetwork based on the islanding effect, as described in claim 1, is characterized in that... In step S15, the adjacency matrix is ​​calculated using the following formula: ； in, yes The Middle Line number Column elements, , It is a positive integer; The formula for calculating the correlation matrix is ​​as follows: ； in, yes The Middle Line number The elements of the column.

3. The method for identifying key high-speed rail nodes under a hypernetwork based on the islanding effect, as described in claim 2, is characterized in that... In step S2, the specific steps for calculating the static topology index are as follows: Step S21: The node's superdegree is the number of hyperedges that contain that node. The larger the node's superdegree, the more hyperedges are associated with that node. The calculation formula is as follows: ； in, To achieve node expiration, based on node expiration, a set of key nodes ranking at the top is selected. ; Step S22: The node betweenness is the ratio of the number of shortest superpaths passing through a given node to the total number of shortest superpaths in the network. The calculation formula is as follows: ； in, For node betweenness, For nodes and nodes Between nodes The number of shortest superpaths, This represents the number of all shortest superpaths in the hypernetwork. and For nodes; Based on node betweenness, select the set of key nodes ranked at the top according to their node betweenness. ; Step S23: Through the calculation of static topology indicators, based on network structure indicators, and comprehensively considering node superdegree and node betweenness, take... and The union of the sets yields the initial selection set of key nodes. .

4. The method for identifying key high-speed rail nodes under a hypernetwork based on the islanding effect, as described in claim 3, is characterized in that... In step S4, the efficiency of the hypernetwork is the global average of the reciprocals of the shortest path lengths between all node pairs, as shown in the following formula: ； in, To improve the efficiency of supernetworks.

5. The method for identifying key high-speed rail nodes under a hypernetwork based on the islanding effect, as described in claim 4, is characterized in that... In step S5, a node attack is simulated to calculate the network efficiency of the hypernetwork and detect isolated nodes under the condition of single node damage. The specific steps are as follows: Step S51: Perform island detection using the island detection model; Step S52: Select the set of nodes that have a significant impact on the efficiency of the supernetwork after being attacked. ; Step S53: Count the number of isolated islands generated in the supernetwork after node failure, and the number of nodes contained in each isolated island. Select the set of nodes ranked highest based on the total number of nodes contained in each isolated island. .

6. The method for identifying key high-speed rail nodes under a hypernetwork based on the islanding effect, as described in claim 5, is characterized in that... In step S51, island detection is performed using an island detection model. The specific operation is as follows: Step S511: Input the correlation matrix of the constructed high-speed rail supernetwork; Step S512: Randomly attack a single node, import the correlation matrix after deleting the failed node and the hyperedge where the failed node is located, and use the disjoint set algorithm to identify isolated nodes; Step S513: Initialization, initialize each node as an independent set; Step S514: Merge hyperedges, merging 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 node belongs to the same connected component; Step S516: Define the largest connected component with the most nodes after failure as the main network, and treat other connected components as islands.

7. The method for identifying key high-speed rail nodes under a hypernetwork based on the islanding effect according to claim 6, characterized in that, In step S6, for , , , Taking the intersection yields the set of key nodes that comprehensively consider network topology metrics, centrality metrics, and the island effect. .

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