Key Node Identification Method for River Network Based on Complex Network

Abstract

The present invention discloses a method for identifying key nodes of river network water systems based on complex networks. The method of the present invention first constructs a water connection network, then conducts structural importance mining based on betweenness centrality, and conducts functional importance mining based on weighted betweenness centrality to calculate the importance of each node in the river network water system, which is a weighted function of structural importance and functional importance; the importance of each node in the river network water system is sorted from small to large to obtain a sequence set, and the elements in the sequence set are divided into multiple subsets in order, and each subset corresponds to an importance level. The method of the present invention comprehensively evaluates the importance of nodes through a weighting method, is flexibly applicable to the mining of important nodes in river network water systems with different densities, helps to ensure important nodes in case of emergencies, and lays a foundation for the overall robustness evaluation of water networks. The present invention is reasonably designed and convenient to operate, and deepens the application of complex network theory in river network water systems.

Description

Technical Field

[0001] The present invention belongs to the field of network information technology and the field of river network water system security technology, and relates to a method for identifying key nodes of river network water systems based on complex networks. Background Art

[0002] With the continuous improvement of the requirements for national water security and water guarantee, the research on the security (or robustness) of river network water systems has become one of the current hot research topics, and the identification of key nodes in the river network is an important part of the evaluation of its robustness.

[0003] Using complex network theory to evaluate the robustness of river network water system network structure is an effective method for the overall security performance test of the system and the planning and prevention of emergency accident measures. Key node identification refers to the excavation of nodes in the network based on a certain specific functional standard according to the importance degree, forming a sorting or classification of node importance, aiming to improve the protection and management level of key nodes. Especially when dealing with emergencies / deliberate attacks, the operation of key nodes can be guaranteed preferentially. Betweenness centrality is an important method for depicting the importance of nodes in a traffic network. In this method, it is assumed that the network traffic between any two nodes passes through the shortest path, and then it is considered that the greater the proportion of paths passing through a node, the greater the importance of the node, so as to reflect the importance and influence of different nodes in the whole network.

[0004] However, when the current key node identification based on betweenness centrality is applied to the water system network, two problems need to be solved. One is that the premise of the betweenness centrality method is to assume that the paths between nodes are the shortest, which is inconsistent with the actual water flow paths in the river network. The other is that the assumption that the traffic transfer between nodes only passes through the shortest path does not conform to the actual situation. Therefore, for large river network water systems with a large number of nodes and complex communication link relationships, there is no precedent for using traditional means to effectively identify key nodes that objectively reflect the network robustness of the network based on complex networks. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for identifying key nodes of river network water systems based on complex networks for the two problems faced by the current application of key node identification based on betweenness centrality in the water system network.

[0006] On the one hand, the method of the present invention introduces water flow resistance as the edge weight based on the principle of hydrodynamics, assuming that the water flow passes through the path of the least resistance; on the other hand, it introduces flow betweenness as the calculation basis of structural importance. Based on betweenness centrality, flow betweenness considers the enhancement effect of all paths in the network on the importance of nodes. This method can be better applied to the security or robustness evaluation of plain river network water systems. The specific method of the present invention is as follows:

[0007] Step (1) The river network is crisscrossed and the water network G = (V, E, W) is constructed; the water network intersection node set V = {v 1 ,v 2 ,…,v N}, N is the number of water system intersection points in the water network; the river section set i,j∈{1,2,…,N} and i≠j,e i,j Indicates the direction of water flow from node v i To node v j Flow, e i,j ∈E and e j,i ∈E means that the water flow can be at node v i With node v j There is bidirectional flow between them; the river section edge weight set W = [w i,j ], such as node v i With v j The edge weight w i,j =0, indicating that node v i With v j Not adjacent, otherwise w i,j That is the node v i With v j The weight of the adjacent edge.

[0008] Step (2) Structural importance mining based on flow betweenness centrality:

[0009] Node v k The structural importance value of g i,j Represents node v i With v j The number of all paths between i,j (k) represents node v i With v j Through node v k The number of all paths, k∈{1,2,…,N} and i≠k≠j; if the node v k If it is passed by multiple other paths, it means that node v k It is important in the network.

[0010] Step (3) Mining the function importance based on weighted betweenness centrality:

[0011] Node v k The function importance value of D i,j Represents node v i With v j The number of all shortest paths between i,j (k) represents node v i With v j By node v kThe number of all shortest paths; if node v k is passed through by multiple other shortest paths, it indicates that node v k is important in the network.

[0012] Step (4) calculates the importance of each node in the river network water system, which is a weighted function of structural importance and functional importance;

[0013] The node importance value C(k) of node v k is C(k)=μC F (k)+ωC B (k); where μ and ω are distribution coefficients, 0 < μ < 1, 0 < ω < 1, and μ + ω = 1.

[0014] Step (5) sorts the importance of each node in the river network water system from smallest to largest to obtain the sequence set P = rank(C(k)); the elements in the sequence set P are divided into multiple subsets P' in order, and each subset corresponds to an importance level.

[0015] Furthermore, the number of all shortest paths D i between node v j and v i,j , and the number of all shortest paths D i between node v j and v k passing through node v i,j (k) are specifically determined as follows:

[0016] Taking the water flow resistance w between adjacent nodes as the edge weight value, determine that the number of paths from node v i to v j is m, 1 ≤ m ≤ (N - 1)×(N - 2), and the water flow resistance of each path Node v p is the water flow confluence node passed through on the path from node v i to v j ; the water flow resistance of the shortest path

[0017] D i,j The solution function is D i,j =∑d i,j (x), d i,j (x) being 0 indicates a non-shortest path, and d i,j (x) being 1 indicates a shortest path;

[0018] The solution function of D i,j (k) is D i,j (k)=∑d' i,j (k(x)); Denote node v k Does not appear in node v i With v j In the shortest path of, v k ∈R denotes node v k Appears in node v i With v j In the shortest path of; d′ i,j (k(x)) being 0 indicates a non-shortest path or the shortest path does not contain node v k , d′ i,j (k(x)) being 1 indicates the shortest path and passes through node v k ;

[0019] Flow resistance Where l is the flow operation distance, n′ is the roughness coefficient, R is the hydraulic radius, S f Is the friction slope, C is a constant; for any w i,j ≠0,

[0020] The beneficial effects of the present invention include:

[0021] 1. The method of the present invention is applied to the excavation of important nodes in river network systems, aiming to identify the importance of the intersection points of each water system in the natural water network under different river network functions (taking flow resistance as an example in the present invention). The identification results will help to ensure important nodes in case of emergencies, lay a foundation for the overall robustness evaluation of the water network, and enrich the technical methods for identifying important nodes in river network systems.

[0022] 2. The present invention provides an idea for evaluating the importance of nodes based on the combination of structural and functional importance. The structural importance of nodes in the water network is characterized by flow betweenness, and the functional importance of nodes in the water network is characterized by weighted betweenness centrality. The importance of nodes is comprehensively evaluated by the weighting method, which is flexibly applicable to the excavation of important nodes in river network systems with different densities.

[0023] 3. The present invention combines river dynamics and the technology of excavating important nodes in complex networks. Taking flow resistance as the edge weight value, through the simulation of the shortest path between any nodes, the application of weighted betweenness important node evaluation in river network systems is realized.

[0024] The present invention is reasonably designed and easy to operate, making up for the deficiencies of the prior art, enriching the advantages of the method for identifying important nodes in river network systems, and deepening the application of complex network theory in river network systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Is the flow chart of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0026] The method of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0027] like Figure 1 As shown in the figure, a method for identifying key nodes of a river network based on a complex network is as follows:

[0028] Step (1) The river network is crisscrossed to form a water network, and a water network G = (V, E, W) is constructed; where the water system intersection node set V = {v 1 ,v 2 ,…,v N}, N is the number of water system intersection points in the water network; the river section set i,j∈{1,2,…,N} and i≠j,e i,j Indicates the direction of water flow from node v i To node v j Flow, e i,j ∈E and e j,i ∈E means that the water flow can be at node v i With node v j There is bidirectional flow between them; the river section edge weight set W = [w i,j ], such as node v i With v j The edge weight w i,j =0, indicating that node v i With v j Not adjacent, otherwise w i,j That is the node v i With v j The weight of the adjacent edge.

[0029] Step (2) Structural importance mining based on flow betweenness centrality: The flow simulation method is used to analyze the important node positions of the network. Information transmission does not follow the shortest path principle, but adopts a free flow method to allow water to propagate freely throughout the network.

[0030] Node v k The structural importance value of g i,j Represents node v i With v j The number of all paths between i,j (k) represents node v i With v j By node v k The number of all paths, k∈{1,2,…,N} and i≠k≠j. If a node v k If it is passed by multiple other paths, it means that node v k It is important in the network.

[0031] Step (3) Function importance mining based on weighted betweenness centrality: The method of shortest path is used to analyze the important node positions in the network. To save the cost of information transmission, the shortest path principle is adopted for information transmission between any nodes.

[0032] Node v k 's function importance value D i,j represents all the shortest path numbers between node v i and v j . D i,j (k) represents all the shortest path numbers between node v i and v j passing through node v k . If node v k is passed by multiple other shortest paths, it means that node v k is very important in the network.

[0033] In the river network system, the water flow resistance can be used as the information transmission cost. In the present invention, the water flow resistance is set as the edge weight value between two connected nodes. It is set that the path with the minimum sum of water flow resistances among all paths between v i and v j is the shortest path.

[0034] It should be noted that although the water flow can select the shortest path according to the minimum resistance, when different information transmission costs are selected, it is not limited to the "water flow resistance" as a way of selecting the edge weight value.

[0035] Taking the water flow resistance w between adjacent nodes as the edge weight value, it is determined that the number of paths from node v i to v j is m, 1 ≤ m ≤ (N - 1) × (N - 2). The water flow resistance of each path Node v p is the water flow confluence node passed on the path from node v i to v j . The water flow resistance of the shortest path

[0036] Node v i and v j The solution function of all the shortest path numbers D i,j between them is as follows:

[0037] D i,j = ∑d i,j (x), d i,j (x) being 0 indicates a non-shortest path, and d i,j (x) being 1 indicates a shortest path;

[0038] Node v i with v j through node v k the number D of all the shortest paths i,j (k) is solved by the following function:

[0039] D i,j (k)=∑d′ i,j (k(x)); indicating that node v k does not appear in the shortest path between node v i and v j in the shortest path, v k ∈R indicates that node v k appears in the shortest path between node v i and v j ; d′ i,j (k(x)) being 0 indicates a non-shortest path or a shortest path without node v k , d′ i,j (k(x)) being 1 indicates a shortest path and passing through node v k .

[0040] For an independent and open river channel, according to the Manning formula it can be known that the flow resistance of the river channel is affected by the channel geometry, roughness coefficient, and friction slope. Under the premise of constant energy, the flow resistance is inversely proportional to the flow velocity, and the flow resistance is also positively correlated with the flow distance. Thus, the flow resistance where l is the flow distance, n′ is the roughness coefficient, R is the hydraulic radius, S f is the friction slope, and C is a constant. For any w i,j ≠0,

[0041] Step (4) calculates the importance of the river network water system nodes, which is a weighted function of structural importance and functional importance;

[0042] The node importance value C(k) of node v k =μC F (k)+ωC B (k); where μ and ω are distribution coefficients, 0 < μ < 1, 0 < ω < 1, and μ + ω = 1. In this embodiment, μ = ω = 0.5 is adopted.

[0043] Step (5) Sort the importance of each node in the river network system from small to large to obtain a sequence set P = rank(C(k)); divide the elements in the sequence set P into multiple subsets P' in order, and each subset corresponds to an importance level. This method is set to 5 levels. That is, the nodes corresponding to the smallest 20% of the elements are Class V important nodes, the nodes corresponding to 20% - 40% of the elements are Class IV important nodes, the nodes corresponding to 40% - 60% of the elements are Class III important nodes; the nodes corresponding to 60% - 80% of the elements are Class II important nodes, that is, the sub-important nodes; the nodes corresponding to the largest 20% of the elements are Class I important nodes, that is, the most important nodes.

Claims

1. A method for identifying key nodes of river network water systems based on complex networks, characterized in that: Step (1): Since the river network water systems are crisscrossed, construct a water connection network G=(V, E, W); The set V of water system convergence nodes = {v 1 , v 2 , …, v N}, where N is the number of water system convergence points in the water connection network; River segment set For i, j ∈ {1, 2, …, N} and i ≠ j, e i,j represents the water flow direction from node v i to node v j flows, e i,j ∈ E and e j,i ∈ E means that the water flow can flow bidirectionally between node v i and node v j ; The set of edge weights W for a river section is W = [w i,j , such as for nodes v i and v j , the edge weight w i,j = 0, indicating that nodes v i and v j are not adjacent. Otherwise, w i,j is the weight of the adjacent edge between nodes v i and v j . Step (2): Mining of structural importance based on betweenness centrality; Node v k The structural importance value g i,j represents all the number of paths between node v i and v j ; g i,j (k) represents all the number of paths between node v i and v j through node v k , k ∈ {1, 2, …, N} and i ≠ k ≠ j; if node v k is passed by multiple other paths, it means that node v k is important in the network; Step (3): Mining of functional importance based on weighted betweenness centrality; Node v k Functional importance value D i,j Indicates all the shortest path numbers between node v i and v j ; D i,j (k) indicates node v i and v j All the shortest path numbers passing through node v k ; If node v k is passed by multiple other shortest paths, it indicates that node v k is important in the network; Node v i All shortest path numbers D j between v i,j and node v i All shortest path numbers D j through node v k between v i,j (k) The specific determination method is as follows: Determine the node v with the water flow resistance w between adjacent nodes as the edge weight i to v j The number of paths is m, where 1 ≤ m ≤ (N - 1) × (N - 2). The water flow resistance of each path Node v p is the water flow convergence node passed on the path from node v i to v j ; the water flow resistance of the shortest path x = 1, …, m; D i,j The solution function for D i,j = ∑d i,j (x), d i,j (x) being 0 indicates a non - shortest path, and d i,j (x) being 1 indicates the shortest path; D i,j The solution function of (k) is D i,j (k) = ∑d i ′ ,j (k(x)); Indicates that node v k Does not appear in the shortest path between node v i And v j , v k ∈R indicates that node v k Appears in the shortest path between node v i And v j ; d i ′ ,j (k(x)) being 0 indicates a non - shortest path or a shortest path that does not contain node v k , d i ′ ,j (k(x)) being 1 indicates a shortest path and passes through node v k ; Flow resistance where l is the flow distance, n′ is the roughness coefficient, R is the hydraulic radius, S f is the friction slope, C is a constant; for any w i,j ≠0, Step (4): Calculate the importance of each node in the river network water system, which is a weighted function of structural importance and functional importance; Node v k The node importance value C(k) of F is μC B (k) + ωC (k); where μ and ω are distribution coefficients, 0 < μ < 1, 0 < ω < 1, and μ + ω = 1; Step (5): After sorting the importance of each node in the river network water system from small to large, obtain a sequence set P = rank(C(k)); Divide the elements in the sequence set P into multiple subsets P' in order, and each subset corresponds to an importance level.

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