A method for identifying key nodes in multi-layer transportation networks based on complex networks

Abstract

The present invention discloses a method for identifying key nodes of a transport multilayer network based on a complex network, comprising the following steps: S1) designing a transport multilayer network based on a complex network; S2) setting edge weights and routes of the transport multilayer network; S3) setting edge capacity and congestion time of the transport multilayer network; S4) optimizing the betweenness identification method into a route identification method; S5) optimizing the proximity centrality identification method into a single node cost identification method; S6) based on the topological structure, considering the characteristics of the transport multilayer network itself, integrating the route identification method and the single node cost identification method, identifying the key nodes of the transport multilayer network based on the complex network, and in the identification, it is considered that the higher the frequency of use of the edges around the node and the lower the cost of the node transporting materials to other nodes, the more critical the node is. This scheme takes into account the characteristics of the transport multilayer network itself and is suitable for the transport multilayer network based on the complex network.

Description

Technical Field

[0001] The invention relates to the technical field of computer application, and in particular to a method for identifying key nodes of a transport multi-layer network based on a complex network. Background Art

[0002] With the development of network science and technology, the study of node criticality has received more and more attention, not only because of its important theoretical research significance, but also because of its wide application value. Most traditional key node identification methods are based on the topological structure of a single-layer network for key node identification, and only consider the structure of the network, such as degree identification method, betweenness identification method, closeness centrality identification method and residual closeness centrality identification method. These methods only consider the topological characteristics of the network, but not the load of the network, edge weights, etc., which leads to certain one-sidedness and limitations in the identification of key nodes in actual networks. In fact, transport multi-layer networks have dynamic characteristics and multi-layer characteristics, and the edges in transport multi-layer networks have transport cost characteristics and edge capacity characteristics. When identifying key nodes, the topological structure cannot be considered alone. Therefore, traditional key node identification methods are not suitable for transport multi-layer networks. Summary of the invention

[0003] The present invention is mainly to solve the problem that the traditional key node identification method only considers the topological structure of the network and is not suitable for the transportation multi-layer network. A key node identification method for the transportation multi-layer network based on a complex network is provided. Firstly, the traditional betweenness identification method and the closeness centrality identification method are optimized respectively to obtain a routing identification method and a single node cost identification method. Then, the characteristics of the transportation multi-layer network itself are considered based on the topological structure, and the routing identification method and the single node cost identification method are integrated to form a key node identification method that is easy to implement, has good performance and takes into account the characteristics of the transportation multi-layer network. The method is suitable for the transportation multi-layer network based on the complex network.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] The method for identifying key nodes of a multi-layer transportation network based on a complex network includes the following steps: step S1) designing a multi-layer transportation network based on a complex network; step S2) setting edge weights and routes of the multi-layer transportation network; step S3) setting edge capacity and congestion time of the multi-layer transportation network; step S4) optimizing the betweenness identification method into a route identification method; step S5) optimizing the proximity centrality identification method into a single node cost identification method; step S6) based on the topological structure, considering the characteristics of the multi-layer transportation network itself, integrating the route identification method and the single node cost identification method, and obtaining a method for identifying key nodes of a multi-layer transportation network based on a complex network; in the method for identifying key nodes of a multi-layer transportation network based on a complex network, the higher the frequency of use of the edges around the node and the lower the cost of the node transporting materials to other nodes, the more critical the node is. The multi-layer transportation network has dynamic characteristics and multi-layer characteristics, and the edges in the multi-layer transportation network have transportation cost characteristics and edge capacity characteristics. Therefore, when identifying key nodes of the multi-layer transportation network, the structure of the network cannot be considered alone. However, the traditional key node identification method only considers the topological structure of the network, without considering the network load, edge weights, etc., which has limitations and is not suitable for transportation multi-layer networks. Therefore, the present invention proposes a key node identification method for transportation multi-layer networks based on complex networks, taking into account the characteristics of the transportation multi-layer network itself, including multi-layer characteristics, dynamic characteristics, transportation costs of connecting edges, and edge capacity characteristics.The specific process is as follows: first, a multi-layer transportation network based on a complex network is designed. The multi-layer transportation network includes an upper aviation network and a lower railway network. The upper aviation network is a BA network. Its main feature is that the scale of the network is constantly expanding, and newly added nodes tend to connect to nodes with high connectivity. The lower railway network is a spatial network. Its main feature is that whether nodes are connected depends on the distance between the nodes; then, the edge weights and routes of the multi-layer transportation network are set. The edge weights refer to the cost corresponding to each edge when transporting materials in the multi-layer transportation network. The route refers to the route for transporting materials. The routing addressing for transporting materials in the multi-layer transportation network is based on the Floyd algorithm to find the route with the lowest transportation cost; then, the edge capacity and congestion time of the multi-layer transportation network are set. The edge capacity is proportional to the initial transportation route. The congestion time refers to the time when the load of an edge in the multi-layer transportation network exceeds its capacity. Excessive load leads to an increase in the time cost on the edge; then, the traditional betweenness identification method is optimized into a routing identification method. The traditional The betweenness identification method considers the shortest path in topology. The higher the frequency of using a node in all shortest paths, the more critical the node is. The optimized route identification method believes that the higher the frequency of using the edges around the node in the initial transportation route, the more critical the node is. Then the traditional closeness centrality identification method is optimized into a single node cost identification method. The traditional closeness centrality identification method considers the shortest distance in topology. The closer the node is to other nodes, the more critical the node is. The optimized single node cost identification method visualizes the shortest distance in topology as the lowest cost path for transporting materials. The lower the cost of transporting materials from the node to other nodes, the more critical the node is. Finally, based on the topological structure, considering the characteristics of the multi-layer transportation network itself, the route identification method and the single node cost identification method are combined to obtain a key node identification method for the multi-layer transportation network based on a complex network. This method believes that the higher the frequency of using the edges around the node and the lower the cost of transporting materials from the node to other nodes, the more critical the node is. The formula is as follows:.

[0006]

[0007] Where KC(i) represents the criticality of node i in the key node identification method of multi-layer transportation network based on complex network, u ij represents the usage frequency of the edge between node i and node j in the transport multilayer network, w ij Represents the cost of transporting materials from node i to node j in a multi-layer transportation network.

[0008] This scheme takes into account the multi-layer nature of the transport multi-layer network, as well as the transport cost and edge capacity characteristics of the connecting edges. It is suitable for transport multi-layer networks based on complex networks. It is not only easy to implement but also performs well.

[0009] Preferably, in the route identification method, the higher the frequency of use of the edges surrounding the node in the initial transportation route, the more critical the node is. The traditional key node identification method is improved to make it suitable for transporting multi-layer networks, and the betweenness identification method is optimized into a route identification method. The traditional betweenness identification method considers the shortest path in topology. The more a node is used in all shortest paths, the more critical the node is; in the present invention, the improved route identification method considers that in the initial transportation route, the higher the frequency of use of the edges surrounding the node, the more critical the node is.

[0010] Preferably, the single node cost identification method visualizes the shortest distance in topology as the lowest cost path for transporting materials. The lower the cost of transporting materials from a node to other nodes, the more critical the node is. The traditional key node identification method is improved to make it suitable for transporting multi-layer networks, and the proximity centrality identification method is optimized into a single node cost identification method. The traditional proximity centrality identification method focuses on the shortest distance in topology. The closer a node is to other nodes, the more critical the node is. In the present invention, the improved single node cost identification method visualizes the shortest distance in topology as the lowest cost path for transporting materials. The lower the cost of transporting materials from a node to other nodes, the more critical the node is.

[0011] Preferably, the routing identification method is expressed by the following formula:

[0012]

[0013] Among them, RC(i) represents the criticality of node i under the routing identification method, u ij Represents the usage frequency of the edge between node i and node j in the transport multilayer network.

[0014] The biggest difference between the optimized key node identification method and the traditional method is that it takes into account the actual situation in the network and can effectively distinguish the upper aviation network edges from the lower railway network edges, avoiding the drawback of the traditional method that only considers the network topology structure but cannot distinguish the two layers of the network.

[0015] Preferably, the single node cost identification method is expressed by the following formula:

[0016]

[0017] Where NC(i) represents the criticality of node i under the single node cost identification method, and w ij Represents the cost of transporting materials from node i to node j in a multi-layer transportation network.

[0018] The biggest difference between the optimized key node identification method and the traditional method is that it takes into account the actual situation in the network and can effectively distinguish the upper aviation network edges from the lower railway network edges, avoiding the drawback of the traditional method that only considers the network topology structure but cannot distinguish the two layers of the network.

[0019] Preferably, the transport multi-layer network in step S1 includes an upper aviation network and a lower railway network, the upper aviation network is a BA network, and the lower railway network is a space network. The transport multi-layer network designed by the present invention includes an upper aviation network and a lower railway network, the upper aviation network is a BA network, and the main feature is that the scale of the network is constantly expanding, and the newly added nodes are more inclined to connect with nodes with high connectivity. The probability of a newly added node connecting to an existing node is:

[0020]

[0021] Among them, k represents the degree value of the node;

[0022] The lower-level railway network is a spatial network. Its main feature is that whether nodes are connected depends on the distance between them. The distance between nodes is:

[0023]

[0024] Among them, (x i ,y i ) and (x j ,y j ) represents the geographic coordinates of node i and node j;

[0025] The node connectivity range is:

[0026] R=πr 2

[0027] Among them, r is the maximum distance that a node can establish an edge with other nodes.

[0028] Preferably, the edge weight in step S2 is the cost of each edge in the multi-layer transport network when transporting materials. The edge weight refers to the cost of each edge when transporting materials in the multi-layer transport network. The edge weight of the edge in the upper aviation network is:

[0029]

[0030] in, They represent the time cost and economic cost of transporting materials from node i to node j in the upper aviation network, and m is the proportion of economic cost in the total cost;

[0031] The edge weights of the connecting edges in the lower railway network are:

[0032]

[0033] in, They respectively represent the time cost and economic cost of transporting materials from node i to node j in the lower-level railway network, and m is the proportion of economic cost in the total cost.

[0034] Preferably, in the multi-layer transport network, the routing addressing of transported materials is based on the Floyd algorithm to find the route with the lowest transport cost, and the formula is as follows:

[0035] w i→j =(1-m)*min(T i→j )+m*min(E i→j )

[0036] Among them, T i→j and E i→j They represent the time cost and economic cost of transporting materials from node i to node j, respectively, and m represents the proportion of economic cost in the total cost. Routing refers to the route of transporting materials. The routing addressing of transporting materials in a multi-layer transport network is based on the Floyd algorithm to find the route with the lowest transportation cost.

[0037] Preferably, the edge capacity in step S3 is proportional to the initial transport route, and the formula is as follows:

[0038] C ij ∝u ij

[0039] Among them, C ij represents the edge capacity of the transport multilayer network, u ij Represents the usage frequency of the edge between node i and node j in the transport multilayer network in the initial transport route.

[0040] Preferably, the congestion time in step S3 is the time when the load of the edge in the transport multi-layer network exceeds its capacity, and the formula is as follows:

[0041]

[0042] Among them, L ij is the load of the edge between node i and node j, T ij It is the time cost of transporting materials between nodes i and j in the initial transportation route. Congestion time refers to the time when the load of an edge in a multi-layer transportation network exceeds its capacity. The excessive load leads to an increase in the time cost of the edge.

[0043] Therefore, the advantages of the present invention are:

[0044] (1) Considering the topological structure, multi-layered nature, dynamics and edge characteristics of the transport multi-layer network, the key nodes of the transport multi-layer network based on the complex network are effectively identified;

[0045] (2) It is suitable for transporting multi-layer networks and is not only easy to implement but also performs well. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the structure of the upper aviation network in an embodiment of the present invention.

[0047] Figure 2 Schematic diagram of the structure of the lower railway network in an embodiment of the present invention.

[0048] Figure 3 It is a schematic diagram of the structure of a multi-layer transport network in an embodiment of the present invention.

[0049] Figure 4 This is a diagram showing changes in the transportation cost of each piece of material in a multi-layer transportation network after attacking the most critical node according to the betweenness identification method in an embodiment of the present invention.

[0050] Figure 5 This is a diagram showing changes in the transportation cost of each piece of material in a multi-layer transportation network after attacking the least critical node according to the betweenness identification method in an embodiment of the present invention.

[0051] Figure 6 This is a diagram showing changes in the transportation cost of each piece of material in a multi-layer transportation network after attacking the most critical node according to different key node identification methods in an embodiment of the present invention.

[0052] Figure 7 This is a diagram showing changes in the transportation cost of each piece of material in a multi-layer transportation network after attacking the least critical node according to different key node identification methods in an embodiment of the present invention.

[0053] Figure 8 It is a performance diagram of each key node identification method (the most critical node is attacked) under different economic cost proportions m in an embodiment of the present invention.

[0054] Fig. 9 It is a performance diagram of each key node identification method (the least critical node is attacked) under different economic cost proportions m in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0056] The method for identifying key nodes of a multi-layer transportation network based on a complex network includes the following steps: step S1) designing a multi-layer transportation network based on a complex network; step S2) setting edge weights and routes of the multi-layer transportation network; step S3) setting edge capacity and congestion time of the multi-layer transportation network; step S4) optimizing the betweenness identification method into a routing identification method; step S5) optimizing the proximity centrality identification method into a single node cost identification method; step S6) based on the topological structure, considering the characteristics of the multi-layer transportation network itself, integrating the routing identification method and the single node cost identification method, and identifying the key nodes of the multi-layer transportation network based on the complex network. During the identification process, it is considered that the higher the frequency of use of the edges around the node and the lower the cost of the node to transport materials to other nodes, the more critical the node is. The specific process is as follows:

[0057] Step S1: Design a multi-layer transport network based on a complex network, such as Figure 1-Figure 3 As shown in Figure 1, the multi-layer transportation network includes an upper aviation network and a lower railway network. The upper aviation network is a BA network. Its main feature is that the scale of the network continues to expand. Newly added nodes are more inclined to connect with nodes with high connectivity. The probability of a newly added node connecting to an existing node is:

[0058]

[0059] Among them, k represents the degree value of the node;

[0060] The lower-level railway network is a spatial network. Its main feature is that whether nodes are connected depends on the distance between them. The distance between nodes is:

[0061]

[0062] Among them, (x i ,y i ) and (x j ,y j ) represents the geographic coordinates of node i and node j;

[0063] The node connectivity range is:

[0064] R=πr 2

[0065] Among them, r is the maximum distance that a node can establish an edge with other nodes.

[0066] Step S2: Set the edge weights and routes of the multi-layer transport network. The edge weights refer to the cost of each edge in the multi-layer transport network when transporting materials. The edge weights of the edges in the upper aviation network are:

[0067]

[0068] in, They represent the time cost and economic cost of transporting materials from node i to node j in the upper aviation network, and m is the proportion of economic cost in the total cost;

[0069] The edge weights of the connecting edges in the lower railway network are:

[0070]

[0071] in, They represent the time cost and economic cost of transporting materials from node i to node j in the lower-level railway network, respectively, and m is the proportion of economic cost in the total cost;

[0072] Routing refers to the route of transporting materials. In a multi-layer transport network, the routing addressing of transporting materials is based on the Floyd algorithm to find the route with the lowest transportation cost. The formula is as follows:

[0073] w i→j =(1-m)*min(T i→j )+m*min(E i→j )

[0074] Among them, T i→j and E i→j They represent the time cost and economic cost of transporting materials from node i to node j respectively, and m represents the proportion of economic cost in the total cost.

[0075] Step S3: Set the edge capacity and congestion time of the transport multi-layer network. The edge capacity is proportional to the initial transport route. The formula is as follows:

[0076] C ij ∝u ij

[0077] Among them, C ij represents the edge capacity of the transport multilayer network, u ij represents the usage frequency of the edge between node i and node j in the transport multilayer network in the initial transport route;

[0078] Congestion time refers to the time when the load on the edges in a transport multi-layer network exceeds its capacity. The formula is as follows:

[0079]

[0080] Among them, L ij is the load of the edge between node i and node j, T ij is the time cost of transporting materials between nodes i and j in the initial transportation route. Excessive load leads to an increase in the time cost on this edge.

[0081] Step S4: Optimize the traditional betweenness identification method into a route identification method, improve the traditional key node identification method to make it suitable for transporting multi-layer networks, and optimize the betweenness identification method into a route identification method. The traditional betweenness identification method considers the shortest path in topology. The more a node is used in all shortest paths, the more critical the node is; in the present invention, the improved route identification method considers that in the initial transport route, the higher the frequency of use of the edges around the node, the more critical the node is. The route identification method can be expressed by the following formula:

[0082]

[0083] Among them, RC(i) represents the criticality of node i under the routing identification method, u ij Represents the usage frequency of the edge between node i and node j in the transport multilayer network.

[0084] Step S5: Optimize the traditional proximity centrality identification method into a single node cost identification method, improve the traditional key node identification method to make it suitable for transporting multi-layer networks, and optimize the proximity centrality identification method into a single node cost identification method. The traditional proximity centrality identification method focuses on the shortest distance in topology. The closer the node is to other nodes, the more critical the node is; in the present invention, the improved single node cost identification method visualizes the shortest distance in topology as the lowest cost path for transporting materials. The lower the cost of transporting materials from the node to other nodes, the more critical the node is. The single node cost identification method can be expressed by the following formula:

[0085]

[0086] Where NC(i) represents the criticality of node i under the single node cost identification method, and w ij Represents the cost of transporting materials from node i to node j in a multi-layer transportation network.

[0087] Step S6: Based on the topological structure, the characteristics of the multi-layer transport network are considered, and the route identification method and the single node cost identification method are integrated to identify the key nodes of the multi-layer transport network based on the complex network. The above method believes that the higher the frequency of use of the edges around the node and the lower the cost of transporting materials from the node to other nodes, the more critical the node is, which can be expressed by the following formula:

[0088]

[0089] Where KC(i) represents the criticality of node i in the key node identification method of multi-layer transportation network based on complex network, u ij represents the usage frequency of the edge between node i and node j in the transport multilayer network, w ijRepresents the cost of transporting materials from node i to node j in a multi-layer transportation network.

[0090] After the key nodes of the multi-layer transport network are attacked, the initial transport route will no longer be the optimal transport route. In order to save transport costs and maximize transport benefits, the transport route needs to be replanned. In this embodiment, in order to solve the dynamic characteristics of the multi-layer transport network, a new route planning method is proposed based on the greedy algorithm. The materials to be transported are divided into M parts. The larger M is, the better the route planning effect is. The route of each material is planned separately and orderly: the first material R 1 According to the network after the attack with empty load, the second material R 2 A new round of planning is carried out based on the previous planning until the material R M The route is planned.

[0091] The traditional key node identification method and the complex network-based transport multi-layer network key node identification method proposed by the present invention are respectively used to identify the key nodes in the transport multi-layer network, and then the identified key nodes (including the most critical nodes and the least critical nodes) are attacked. By comparing the changes in the transportation material costs of the transport multi-layer network after the attack, the optimal key node identification method is analyzed. Figure 4-Figure 9 As shown, the simulation results show that no matter whether the most critical node is damaged or the least critical node is damaged (the multi-layer transportation network actively reduces its own transportation costs by shutting down the transportation business of the least critical node), the key nodes identified by the key node identification method proposed in this scheme will be the most affected and the transportation cost will be increased the most after being attacked. Therefore, the recognition effect of the key node identification method proposed in this invention is significantly better than that of various traditional key node identification methods.

Claims

1. A method for identifying key nodes in multi-layer transportation networks based on complex networks. It is characterized in that The following steps are involved: Step S1: Design a multi-layer transportation network based on a complex network; Step S2: Setting edge weights and routing of the transport multi-layer network; Step S3: Setting the edge capacity and congestion time of the transport multi-layer network; Step S4: Optimizing the betweenness identification method into a routing identification method, the higher the usage frequency of the edges around the node, the more critical the node is; Step S5: Optimize the proximity centrality identification method into a single node cost identification method. The lower the cost of transporting materials from a node to other nodes, the more critical the node is. Step S6: Based on the topological structure, taking into account the characteristics of the transport multi-layer network itself, the routing identification method and the single node cost identification method are integrated to obtain a key node identification method of the transport multi-layer network based on a complex network; In the method for identifying key nodes in a multi-layer transport network based on a complex network, the higher the usage frequency of the edges around the node and the lower the cost of transporting materials from the node to other nodes, the more critical the node is. The formula is: Among them, u ij represents the usage frequency of the edge between node i and node j in the transport multilayer network, w ij Represents the cost of transporting materials from node i to node j in a multi-layer transportation network.

2. According to the complex network-based transportation multi-layer network key node identification method of claim 1, It is characterized in that In the route identification method, the higher the usage frequency of the edges surrounding a node in the initial transportation route, the more critical the node is.

3. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 1, It is characterized in that The single node cost identification method visualizes the shortest distance in topology as the lowest cost path for transporting materials.

4. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 2, It is characterized in that The formula of the routing identification method is: Among them, u ij Represents the usage frequency of the edge between node i and node j in the transportation multilayer network.

5. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 3, It is characterized in that The formula of the single node cost identification method is: Among them, w ij Represents the cost of transporting materials from node i to node j in a multi-layer transportation network.

6. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 1, It is characterized in that The multi-layer transportation network in step S1 includes an upper aviation network and a lower railway network, wherein the upper aviation network is a BA network and the lower railway network is a space network.

7. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 1, It is characterized in that The edge weight in step S2 is the cost corresponding to each edge in the multi-layer transport network when transporting materials.

8. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 7, It is characterized in that In the multi-layer transport network, the routing addressing of transported materials is based on the Floyd algorithm to find the route with the lowest transport cost. The formula is as follows: w i→j =(1-m)*min(T i→j )+m*min(E i→j ) Among them, T i→j and E i→j They represent the time cost and economic cost of transporting materials from node i to node j respectively, and m represents the proportion of economic cost in the total cost.

9. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 1, It is characterized in that The edge capacity in step S3 is proportional to the initial transport route, and the formula is as follows: C ij ∝u ij Among them, C ij represents the edge capacity of the transport multilayer network, u ij Represents the usage frequency of the edge between node i and node j in the transport multilayer network in the initial transport route.

10. The method for identifying key nodes of a multi-layer transport network based on a complex network according to claim 1 or 8, It is characterized in that The congestion time in step S3 is the time when the load of the edge in the transport multi-layer network exceeds its capacity, and the formula is as follows: Among them, L ij is the load of the edge between node i and node j, T ij It is the time cost of transporting materials between nodes i and j in the initial transportation route.

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