CN113285828A - Complex network key node identification method and power grid key node identification method - Google Patents

Complex network key node identification method and power grid key node identification method Download PDF

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CN113285828A
CN113285828A CN202110545468.9A CN202110545468A CN113285828A CN 113285828 A CN113285828 A CN 113285828A CN 202110545468 A CN202110545468 A CN 202110545468A CN 113285828 A CN113285828 A CN 113285828A
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nodes
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importance
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CN113285828B (en
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张惠芳
沈晓隶
李沛哲
李琴
徐志强
吴佩颖
陈娟
齐增清
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Hunan Jingyan Electric Power Design Co ltd
Economic and Technological Research Institute of State Grid Hunan Electric Power Co Ltd
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Economic and Technological Research Institute of State Grid Hunan Electric Power Co Ltd
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    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention discloses a complex network key node identification method, which comprises the steps of obtaining node connection relation data of a complex network to be analyzed and modeling; calculating local characteristic parameters of the nodes to obtain a local topological importance index; calculating global characteristic parameters of the nodes to obtain a global topological importance index; and calculating a comprehensive topological importance metric of the nodes and identifying key nodes of the complex network. The invention also discloses a power grid key node identification method comprising the complex network key node identification method. The method provided by the invention can objectively determine the weights of the local characteristics and the global characteristics of the nodes according to the internal information quantity of the indexes and the relevance between the indexes by using a multi-attribute decision theory, so that the fused importance identification indexes are more reasonable, and the method is high in reliability, good in practicability and higher in accuracy.

Description

Complex network key node identification method and power grid key node identification method
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a complex network key node identification method and a power grid key node identification method.
Background
In real life, almost all complex systems can be described in the form of networks, such as power networks, the internet, and the like. With the rapid development of network information technologies represented by the internet, the networking trend is very obvious, and people increasingly rely on the safe and reliable operation of various complex network systems in daily life. The scaleless and small-world characteristics of a real complex network make some special nodes in the network have a great influence on the structure and function of the network, and therefore the nodes are called as key nodes. When this part of the critical nodes in the network fails, its impact will quickly spread to the entire network. The method effectively identifies key nodes in the network, and can provide data support for network planning and risk management: these critical nodes may be heavily protected to improve overall network reliability. Therefore, how to accurately quantify the importance of the network nodes and dig out the key nodes in the network nodes is significant.
In recent years, research on node importance measurement has attracted wide attention of scholars at home and abroad, and identification of key nodes in complex networks has made great progress. At present, the importance degree of network nodes is mainly analyzed from two aspects of system science and social network. The core idea of the system scientific analysis method is that the importance of a node is equivalent to the destructiveness of the node or a plurality of nodes on a network after the node is deleted: for example, in the node deletion method, after a node in a network is deleted, the importance degree of the node is determined by using the change of indexes such as network connectivity and the like; the method has a problem that if the deletion of a plurality of nodes makes the network disconnected, the importance of the nodes is consistent, so that the evaluation result is inaccurate. The node contraction method is used for evaluating the importance of the nodes by analyzing the change of the network condensation degree before and after the contraction of the relevant nodes in the network; when the method is used for solving the network cohesion degree, the average shortest path of the whole network is calculated, the method is only considered from the global perspective as the node deletion method, the global information of the network nodes is calculated, and the importance of the nodes in local connection is ignored. The other type of social network analysis method starts from the contribution degree of nodes to the network, and has the core idea that the importance is equivalent to the significance; the method uses the degree centrality, betweenness, feature vector and other feature attributes of the nodes as evaluation indexes for distinguishing the importance of the nodes; these evaluation indexes describe the importance of a single node in the network from both the local attribute and the global attribute of the network: for example, the importance evaluation method based on degree centrality is a simple and effective local algorithm, which only emphasizes the number of edges connecting the nodes and the adjacent nodes; the betweenness-based method needs to use network global information, and the betweenness describes the control capability of nodes or edges on information or flow in the network; the feature vector fully considers the importance of establishing a connection node with the target node, and determines the position of the target node through the importance of adjacent nodes. In addition, researchers think that the importance of the node is related to the degree of the node and the degree of the neighbor node, and provide an evaluation index based on the degree of the node and the degree of the neighbor node, namely, the larger the degree of the node and the neighbor node is, the higher the importance of the node is; the researcher considers the node degree and the topological overlap ratio of the neighbor nodes, considers that the node degree is larger, and the topological overlap ratio of the neighbor nodes is smaller and more important, and accordingly provides a node importance evaluation algorithm based on the neighborhood similarity.
In summary, the above indexes for evaluating the node importance degree are all used for describing the structural characteristics of the network from a single local or global angle, if the structure of the target network has significant characteristics in this respect, a better effect can be obtained, but the single-angle evaluation of the network node importance degree often has certain defects and limitations, and different node importance degree ranking results can be generated by adopting different evaluation indexes.
Disclosure of Invention
One of the objectives of the present invention is to provide a method for identifying key nodes of a complex network, which has high reliability, good practicability and high accuracy.
The invention also provides a method for identifying key nodes of a power grid, which comprises the method for identifying key nodes of a complex network.
The method for identifying the key nodes of the complex network comprises the following steps:
s1, acquiring node connection relation data of a complex network to be analyzed, and modeling network topology;
s2, calculating local characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a local topology importance index;
s3, calculating global characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a global topology importance index;
s4, calculating a comprehensive topological importance metric value of the node according to the local topological importance index obtained in the step S3 and the global topological importance index obtained in the step S4;
and S5, identifying the key nodes of the complex network according to the comprehensive topological importance metric value of the nodes obtained in the step S4.
Step S1, obtaining data of node connection relationships of the complex network to be analyzed, and modeling a network topology, specifically, modeling by using the following steps:
A. acquiring node connection relation data of a complex network to be analyzed, and constructing the network into a directionless and unweighted network G (V, E) containing N nodes and M edges according to the number of the nodes and the edges; wherein V is a network node set, and E is an edge set of the network;
B. constructing a network adjacency matrix A ═ a according to the connection relation between nodesij}; wherein a isijIs the element in the ith row and jth column of the network adjacency matrix A, and a if there is a connection between node i and node jij1, otherwise aij＝0。
Step S2, calculating local characteristic parameters of the nodes according to the network topology model established in step S1 to obtain a local topology importance index, specifically, obtaining the local topology importance index by the following steps:
a. calculating the degree centrality index DC of the node i by adopting the following formulai：
Figure BDA0003073351380000041
In the formula DiNumber of neighbor nodes of node i and Di＝∑j∈GaijIf a connection exists between node i and node j then aij1, otherwise aij0; n is the total number of nodes;
b. calculating the clustering coefficient C of the node i by adopting the following formulai：
Figure BDA0003073351380000042
In the formula PiTo D connected to node iiThe actual number of edges that exist for each node; agglomeration coefficient CiUsed for reflecting the degree of closeness among node neighbors;
c. c, the degree centrality index DC obtained in the step aiAnd the agglomeration coefficient C obtained in step biNormalization is carried out, so that a local topological importance index LD of the node i is obtainediAnd LCi：
Figure BDA0003073351380000043
Figure BDA0003073351380000044
In the formula
Figure BDA0003073351380000045
The minimum value of the centrality index of the medium number in all the nodes is obtained;
Figure BDA0003073351380000046
the maximum value of the centrality index of the medium number in all the nodes is obtained;
Figure BDA0003073351380000047
the maximum value of the clustering coefficients in all the nodes;
Figure BDA0003073351380000048
is the minimum value of the cluster coefficients in all nodes.
Step S3, calculating global feature parameters of the nodes according to the network topology model established in step S1 to obtain a global topology importance index, specifically calculating the global topology importance index by the following steps:
(1) calculating the betweenness B of the node i by adopting the following formulai：
Figure BDA0003073351380000051
In the formula sigmast(i) Is the number of shortest paths from node s to node t through node i; sigmastIs the number of pieces of shortest path from node s to node t;
(2) for the betweenness B obtained in the step (1)iNormalization is carried out, so that a global topological importance index GB of the node i is obtainedi：
Figure BDA0003073351380000052
In the formula
Figure BDA0003073351380000053
The minimum value of the intermediary number for all nodes;
Figure BDA0003073351380000054
the maximum number of intermediaries for all nodes.
Step S4, calculating a comprehensive topology importance metric of the node according to the local topology importance index obtained in step S3 and the global topology importance index obtained in step S4, specifically, calculating a comprehensive topology importance metric of the node by using the following steps:
1) the information entropy weight we of the jth index is calculated by adopting the following formulaj：
Figure BDA0003073351380000055
Wherein m is the total number of indexes; en is a radical ofjIs the entropy of the jth index and
Figure BDA0003073351380000056
n is the total number of nodes, pijIs the specific gravity of the ith node under the jth index
Figure BDA0003073351380000057
rijAn index value of a j index of the ith node;
2) calculating the integral Kendel correlation coefficient gamma of the jth index and other indexes by adopting the following formulaj：
Figure BDA0003073351380000058
Wherein m is the total number of indexes; tau isjtThe Kendel correlation coefficient of the j index and the t index is obtained;
3) calculating the Kendel coefficient weight wk of the j index by adopting the following formulajIs composed of
Figure BDA0003073351380000061
4) Calculating the objective weight w of the jth index by the following formulajIs composed of
Figure BDA0003073351380000062
5) The weighted node index matrix S is calculated by the following formula
Figure BDA0003073351380000063
6) Calculating a positive ideal solution F by adopting the following formula according to the weighting node index matrix S obtained in the step 5)+Negative ideal solution F-Is composed of
Figure BDA0003073351380000064
7) The ith node is calculated to the positive ideal solution F by the following formula+Is a distance of
Figure BDA0003073351380000065
Sum node i to negative ideal solution F-Is a distance of
Figure BDA0003073351380000066
Is composed of
Figure BDA0003073351380000067
8) Calculating the comprehensive topological importance metric value T of the ith node by adopting the following formulaiIs composed of
Figure BDA0003073351380000068
The Kendel correlation coefficient in the step 2) is specifically calculated by adopting the following steps:
for two node importance indicators, each having N elements, X ═ X (X) is set1,x2,...,xn) And Y ═ Y1,y2,...,yn) (ii) a When x isi＞xjAnd y isi＞yjOr is or，xi＜xjAnd y isi＜yjWhen, identify (x)i,yi) And (x)j,yj) This is a correlation for the data, otherwise (x) is assertedi,yi) And (x)j,yj) This is irrelevant to the data; thus, the Kendel correlation coefficient τ of the two node importance indicatorsXYThe calculation formula of (A) is as follows:
Figure BDA0003073351380000071
in the formula NcThe number of the related data pairs; n is a radical ofdNumber of unrelated data pairs; the same elements in X and Y form a small set, s1The number of elements belonging to X in the small set; s2The number of elements belonging to Y in the small set; n is0Is an intermediate number and
Figure BDA0003073351380000072
in step S5, the key nodes of the complex network are identified according to the comprehensive topology importance metric of the nodes obtained in step S4, specifically, the key nodes of the complex network are determined to be more critical according to the comprehensive topology importance metric of the nodes obtained in step S4, where the larger the comprehensive topology importance metric of the nodes is, the more critical the nodes are to the complex network.
The invention also provides a power grid key node identification method comprising the complex network key node identification method, which specifically comprises the following steps:
i, determining a power grid to be analyzed;
and II, taking the power grid to be analyzed determined in the step I as a complex network to be analyzed, and identifying the key nodes of the power grid to be analyzed by adopting the steps S1-5.
The complex network key node identification method and the power grid key node identification method provided by the invention eliminate the influence of specific services in different networks on the nodes from the common topological structure characteristic of the complex network, and provide a universal complex network key node identification method; the invention comprehensively considers the local characteristics and the global characteristics of the nodes, provides a comprehensive method for reflecting the local and global importance of the nodes, and can more reasonably and effectively identify key nodes in a complex network; the method provided by the invention can objectively determine the weights of the local characteristics and the global characteristics of the nodes according to the internal information quantity of the indexes and the relevance between the indexes by using a multi-attribute decision theory, so that the fused importance identification indexes are more reasonable, and the method is high in reliability, good in practicability and higher in accuracy.
Drawings
Fig. 1 is a schematic flow chart of a method for identifying a key node of a complex network according to the present invention.
Fig. 2 is a schematic flow chart of a method for identifying a key node of a power grid according to the present invention.
Fig. 3 is a schematic diagram of a network topology according to an embodiment of the present invention.
Detailed Description
Fig. 1 is a schematic flow chart of a method for identifying a key node of a complex network according to the present invention: the method for identifying the key nodes of the complex network comprises the following steps:
s1, acquiring node connection relation data of a complex network to be analyzed, and modeling network topology; specifically, the modeling is carried out by adopting the following steps:
A. acquiring node connection relation data of a complex network to be analyzed, and constructing the network into a directionless and unweighted network G (V, E) containing N nodes and M edges according to the number of the nodes and the edges; wherein V is a network node set, and E is an edge set of the network;
B. constructing a network adjacency matrix A ═ a according to the connection relation between nodesij}; wherein a isijIs the element in the ith row and jth column of the network adjacency matrix A, and a if there is a connection between node i and node jij1, otherwise aij＝0；
S2, calculating local characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a local topology importance index; specifically, the following steps are adopted to obtain a local topological importance index:
a. calculating the degree centrality index DC of the node i by adopting the following formulai：
Figure BDA0003073351380000081
In the formula DiNumber of neighbor nodes of node i and Di＝∑j∈GaijIf a connection exists between node i and node j then aij1, otherwise aij0; n is the total number of nodes;
b. calculating the clustering coefficient C of the node i by adopting the following formulai：
Figure BDA0003073351380000091
In the formula PiTo D connected to node iiThe actual number of edges that exist for each node; agglomeration coefficient CiUsed for reflecting the degree of closeness among node neighbors;
c. c, the degree centrality index DC obtained in the step aiAnd the agglomeration coefficient C obtained in step biNormalization is carried out, so that a local topological importance index LD of the node i is obtainediAnd LCi：
Figure BDA0003073351380000092
Figure BDA0003073351380000093
In the formula
Figure BDA0003073351380000094
The minimum value of the centrality index of the medium number in all the nodes is obtained;
Figure BDA0003073351380000095
the maximum value of the centrality index of the medium number in all the nodes is obtained;
Figure BDA0003073351380000096
the maximum value of the clustering coefficients in all the nodes;
Figure BDA0003073351380000097
the minimum value of the clustering coefficients in all the nodes is obtained;
s3, calculating global characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a global topology importance index; specifically, the global topology importance index is calculated by the following steps:
(1) calculating the betweenness B of the node i by adopting the following formulai：
Figure BDA0003073351380000098
In the formula sigmast(i) Is the number of shortest paths from node s to node t through node i; sigmastIs the number of pieces of shortest path from node s to node t;
(2) for the betweenness B obtained in the step (1)iNormalization is carried out, so that a global topological importance index GB of the node i is obtainedi：
Figure BDA0003073351380000101
In the formula
Figure BDA0003073351380000102
The minimum value of the intermediary number for all nodes;
Figure BDA0003073351380000103
maximum value of intermediary number for all nodes;
s4, calculating a comprehensive topological importance metric value of the node according to the local topological importance index obtained in the step S3 and the global topological importance index obtained in the step S4; specifically, the comprehensive topological importance metric of the node is calculated by adopting the following steps:
1) comprehensively considering the local characteristics and the global characteristics of the nodes by utilizing a multi-attribute decision theory, and calculating the information entropy weight of each index by an entropy weight method; the information entropy weight we of the jth index is calculated by adopting the following formulaj：
Figure BDA0003073351380000104
Wherein m is the total number of indexes; en is a radical ofjIs the entropy of the jth index and
Figure BDA0003073351380000105
n is the total number of nodes, pijIs the specific gravity of the ith node under the jth index
Figure BDA0003073351380000106
rijAn index value of a j index of the ith node;
2) kennel's coefficient is usually used to measure the correlation between the index and the index; calculating the integral Kendel correlation coefficient gamma of the jth index and other indexes by adopting the following formulaj：
Figure BDA0003073351380000107
Wherein m is the total number of indexes; tau isjtThe Kendel correlation coefficient of the j index and the t index is obtained; when gamma isjThe larger the index is, the larger the correlation between the index and other indexes is, and the weaker the contribution to identifying important nodes is; the Kendel correlation coefficient is calculated as follows:
for two node importance indicators, each having N elements, X ═ X (X) is set1,x2,...,xn) And Y ═ Y1,y2,...,yn) (ii) a When x isi＞xjAnd y isi＞yjOr, xi＜xjAnd y isi＜yjWhen, identify (x)i,yi) And (x)j,yj) This is a correlation for the data, otherwise (x) is assertedi,yi) And (x)j,yj) This is irrelevant to the data; thus, the Kendel correlation coefficient τ of the two node importance indicatorsXYThe calculation formula of (A) is as follows:
Figure BDA0003073351380000111
in the formula NcThe number of the related data pairs; n is a radical ofdNumber of unrelated data pairs; the same elements in X and Y form a small set, s1The number of elements belonging to X in the small set; s2The number of elements belonging to Y in the small set; n is0Is an intermediate number and
Figure BDA0003073351380000112
3) calculating the Kendel coefficient weight wk of the j index by adopting the following formulajIs composed of
Figure BDA0003073351380000113
4) The information entropy weight and the Kendall coefficient weight can objectively quantify the internal information content of the indexes and the relevance between the indexes, so the objective weight w of the jth index is calculated by the following formulajIs composed of
Figure BDA0003073351380000114
When the jth index can provide larger information quantity and the relevance of the jth index and other node importance indexes is smaller, the objective weight w of the jth indexjThe larger;
5) the weighted node index matrix S is calculated by the following formula
Figure BDA0003073351380000115
6) Calculating a positive ideal solution F by adopting the following formula according to the weighting node index matrix S obtained in the step 5)+Negative ideal solution F-Is composed of
Figure BDA0003073351380000121
7) The ith node is calculated to the positive ideal solution F by the following formula+Is a distance of
Figure BDA0003073351380000122
Sum node i to negative ideal solution F-Is a distance of
Figure BDA0003073351380000123
Is composed of
Figure BDA0003073351380000124
8) Calculating the comprehensive topological importance metric value T of the ith node by adopting the following formulaiIs composed of
Figure BDA0003073351380000125
S5, identifying key nodes of the complex network according to the comprehensive topological importance metric value of the nodes obtained in the step S4; specifically, according to the comprehensive topology importance metric of the node obtained in step S4, the larger the comprehensive topology importance metric of the node is, the more critical the node is considered to be to the complex network.
Fig. 2 is a schematic flow chart of a method for identifying a key node of a power grid according to the present invention: the method for identifying the key nodes of the power grid, which comprises the method for identifying the key nodes of the complex network, provided by the invention specifically comprises the following steps:
i, determining a power grid to be analyzed;
taking the power grid to be analyzed determined in the step I as a complex network to be analyzed, acquiring node connection relation data of the complex network to be analyzed, and modeling network topology; specifically, the modeling is carried out by adopting the following steps:
A. acquiring node connection relation data of a complex network to be analyzed, and constructing the network into a directionless and unweighted network G (V, E) containing N nodes and M edges according to the number of the nodes and the edges; wherein V is a network node set, and E is an edge set of the network;
B. constructing a network adjacency matrix A ═ a according to the connection relation between nodesij}; wherein a isijIs the element in the ith row and jth column of the network adjacency matrix A, and a if there is a connection between node i and node jij1, otherwise aij＝0；
According to the network topology model established in the step II, local characteristic parameters of the nodes are calculated to obtain a local topology importance index; specifically, the following steps are adopted to obtain a local topological importance index:
a. calculating the degree centrality index DC of the node i by adopting the following formulai：
Figure BDA0003073351380000131
In the formula DiNumber of neighbor nodes of node i and Di＝∑j∈GaijIf a connection exists between node i and node j then aij1, otherwise aij0; n is the total number of nodes;
b. calculating the clustering coefficient C of the node i by adopting the following formulai：
Figure BDA0003073351380000132
In the formula PiTo D connected to node iiThe actual number of edges that exist for each node; agglomeration coefficient CiUsed for reflecting the degree of closeness among node neighbors;
c. c, the degree centrality index DC obtained in the step aiAnd the agglomeration coefficient C obtained in step biNormalization is carried out, so that a local topological importance index LD of the node i is obtainediAnd LCi：
Figure BDA0003073351380000133
Figure BDA0003073351380000134
In the formula
Figure BDA0003073351380000135
The minimum value of the centrality index of the medium number in all the nodes is obtained;
Figure BDA0003073351380000136
the maximum value of the centrality index of the medium number in all the nodes is obtained;
Figure BDA0003073351380000137
the maximum value of the clustering coefficients in all the nodes;
Figure BDA0003073351380000141
the minimum value of the clustering coefficients in all the nodes is obtained;
calculating the global characteristic parameters of the nodes according to the network topology model established in the step II to obtain a global topology importance index; specifically, the global topology importance index is calculated by the following steps:
(1) calculating the betweenness B of the node i by adopting the following formulai：
Figure BDA0003073351380000142
In the formula sigmast(i) Is the number of shortest paths from node s to node t through node i; sigmastIs the number of pieces of shortest path from node s to node t;
(2) for the betweenness B obtained in the step (1)iNormalization is carried out, so that a global topological importance index GB of the node i is obtainedi：
Figure BDA0003073351380000143
In the formula
Figure BDA0003073351380000144
The minimum value of the intermediary number for all nodes;
Figure BDA0003073351380000145
maximum value of intermediary number for all nodes;
calculating a comprehensive topological importance metric value of the node according to the local topological importance index obtained in the step III and the global topological importance index obtained in the step IV; specifically, the comprehensive topological importance metric of the node is calculated by adopting the following steps:
1) comprehensively considering the local characteristics and the global characteristics of the nodes by utilizing a multi-attribute decision theory, and calculating the information entropy weight of each index by an entropy weight method; the information entropy weight we of the jth index is calculated by adopting the following formulaj：
Figure BDA0003073351380000146
Wherein m is the total number of indexes; en is a radical ofjIs the entropy of the jth index and
Figure BDA0003073351380000147
n is the total number of nodes, pijIs the specific gravity of the ith node under the jth index
Figure BDA0003073351380000151
rijAn index value of a j index of the ith node;
2) kennel's coefficient is usually used to measure the correlation between the index and the index; calculating the integral Kendel correlation coefficient gamma of the jth index and other indexes by adopting the following formulaj：
Figure BDA0003073351380000152
Wherein m is the total number of indexes; tau isjtThe Kendel correlation coefficient of the j index and the t index is obtained; when gamma isjThe larger the size, the more the description isThe index has larger correlation with other indexes and weaker contribution to identifying important nodes; the Kendel correlation coefficient is calculated as follows:
for two node importance indicators, each having N elements, X ═ X (X) is set1,x2,...,xn) And Y ═ Y1,y2,...,yn) (ii) a When x isi＞xjAnd y isi＞yjOr, xi＜xjAnd y isi＜yjWhen, identify (x)i,yi) And (x)j,yj) This is a correlation for the data, otherwise (x) is assertedi,yi) And (x)j,yj) This is irrelevant to the data; thus, the Kendel correlation coefficient τ of the two node importance indicatorsXYThe calculation formula of (A) is as follows:
Figure BDA0003073351380000153
in the formula NcThe number of the related data pairs; n is a radical ofdNumber of unrelated data pairs; the same elements in X and Y form a small set, s1The number of elements belonging to X in the small set; s2The number of elements belonging to Y in the small set; n is0Is an intermediate number and
Figure BDA0003073351380000154
3) calculating the Kendel coefficient weight wk of the j index by adopting the following formulajIs composed of
Figure BDA0003073351380000155
4) The information entropy weight and the Kendall coefficient weight can objectively quantify the internal information content of the indexes and the relevance between the indexes, so the objective weight w of the jth index is calculated by the following formulajIs composed of
Figure BDA0003073351380000161
When the j index can provide a larger amount of information, at the same timeWhen the relevance of j indexes and other node importance indexes is small, the objective weight w of the jth indexjThe larger;
5) the weighted node index matrix S is calculated by the following formula
Figure BDA0003073351380000162
6) Calculating a positive ideal solution F by adopting the following formula according to the weighting node index matrix S obtained in the step 5)+Negative ideal solution F-Is composed of
Figure BDA0003073351380000163
7) The ith node is calculated to the positive ideal solution F by the following formula+Is a distance of
Figure BDA0003073351380000164
Sum node i to negative ideal solution F-Is a distance of
Figure BDA0003073351380000165
Is composed of
Figure BDA0003073351380000166
8) Calculating the comprehensive topological importance metric value T of the ith node by adopting the following formulaiIs composed of
Figure BDA0003073351380000167
VI, identifying key nodes of the complex network according to the comprehensive topological importance metric value of the nodes obtained in the step V; specifically, according to the comprehensive topology importance metric value of the node obtained in the step v, the larger the comprehensive topology importance metric value of the node is, the more critical the node is determined to be to the complex network.
The process of the invention is further illustrated below with reference to a specific example:
fig. 3 is a schematic diagram of a network topology according to an embodiment of the present invention. The attribute values of the nodes in the graph are shown in table 1; the attribute values of degree centrality, clustering coefficient and betweenness are shown in Table 2
Attribute value schematic table for 110 nodes
Figure BDA0003073351380000171
TABLE 2 attribute value schematic table of three indexes
Index set en we γ wk w F+ F-
LD 0.7592 0.3353 0.5158 0.3721 0.3299 0.3299 0
LC 0.9247 0.1049 0.2577 0.1859 0.2065 0.2065 0
GB 0.598 0.5598 0.6126 0.442 0.4637 0.4637 0
The calculation results in table 1 show that the three indexes of node 8 are ranked first, so that the comprehensive topology importance is highest; the three indexes of the No. 4 node are inferior to the No. 8 node, and the clustering coefficient and the betweenness index are higher than the No. 3 node, so that the node is arranged at the second position, and the No. 3 node is arranged at the third position; the positions of the No. 2 node and the No. 6 node are the same, the three indexes are all weaker than the No. 3 node, and the node is arranged at the fourth position; 5. the positions of nodes 7, 9 and 10 are completely the same, and compared with the nodes with the top rank, only the clustering coefficient index is higher, and the degree centrality index and the betweenness centrality index are both 0, so the importance degree is lower; the node 1 has a low importance level because the clustering coefficient and betweenness centrality index are 0 and the degree centrality index is also low.

Claims (8)

1. A complex network key node identification method comprises the following steps:
s1, acquiring node connection relation data of a complex network to be analyzed, and modeling network topology;
s2, calculating local characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a local topology importance index;
s3, calculating global characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a global topology importance index;
s4, calculating a comprehensive topological importance metric value of the node according to the local topological importance index obtained in the step S3 and the global topological importance index obtained in the step S4;
and S5, identifying the key nodes of the complex network according to the comprehensive topological importance metric value of the nodes obtained in the step S4.
2. The method for identifying key nodes of a complex network according to claim 1, wherein the step S1 is to obtain the data of the node connection relationship of the complex network to be analyzed, and model the network topology, specifically, the following steps are adopted for modeling:
A. acquiring node connection relation data of a complex network to be analyzed, and constructing the network into a directionless and unweighted network G (V, E) containing N nodes and M edges according to the number of the nodes and the edges; wherein V is a network node set, and E is an edge set of the network;
B. constructing a network adjacency matrix A ═ a according to the connection relation between nodesij}; wherein a isijIs the element in the ith row and jth column of the network adjacency matrix A, and a if there is a connection between node i and node jij1, otherwise aij＝0。
3. The method for identifying key nodes in a complex network according to claim 2, wherein the step S2 is to calculate local characteristic parameters of the nodes according to the network topology model established in the step S1 to obtain a local topology importance index, specifically, the following steps are adopted to obtain the local topology importance index:
a. calculating the degree centrality index DC of the node i by adopting the following formulai：
Figure FDA0003073351370000021
In the formula DiIs the number of neighbor nodes of the node i and
Figure FDA0003073351370000022
if there is a connection between node i and node j then aij1, otherwise aij0; n is the total number of nodes;
b. calculating the clustering coefficient C of the node i by adopting the following formulai：
Figure FDA0003073351370000023
In the formula PiTo D connected to node iiThe actual number of edges that exist for each node; agglomeration coefficient CiUsed for reflecting the degree of closeness among node neighbors;
c. c, the degree centrality index DC obtained in the step aiAnd the agglomeration coefficient C obtained in step biNormalization is carried out, so that a local topological importance index LD of the node i is obtainediAnd LCi：
Figure FDA0003073351370000024
Figure FDA0003073351370000025
In the formula
Figure FDA0003073351370000026
The minimum value of the centrality index of the medium number in all the nodes is obtained;
Figure FDA0003073351370000027
the maximum value of the centrality index of the medium number in all the nodes is obtained;
Figure FDA0003073351370000028
the maximum value of the clustering coefficients in all the nodes;
Figure FDA0003073351370000029
is the minimum value of the cluster coefficients in all nodes.
4. The method for identifying key nodes in a complex network according to claim 3, wherein the step S3 is to calculate global feature parameters of the nodes according to the network topology model established in the step S1 to obtain a global topology importance index, specifically, the following steps are adopted to calculate the global topology importance index:
(1) calculating the betweenness B of the node i by adopting the following formulai：
Figure FDA0003073351370000031
In the formula sigmast(i) Is the number of shortest paths from node s to node t through node i; sigmastIs the number of pieces of shortest path from node s to node t;
(2) for the betweenness B obtained in the step (1)iNormalization is carried out, so that a global topological importance index GB of the node i is obtainedi：
Figure FDA0003073351370000032
In the formula
Figure FDA0003073351370000033
The minimum value of the intermediary number for all nodes;
Figure FDA0003073351370000034
the maximum number of intermediaries for all nodes.
5. The method for identifying key nodes of a complex network according to claim 4, wherein the step S4 is performed to calculate a comprehensive topology importance metric of the nodes according to the local topology importance index obtained in the step S3 and the global topology importance index obtained in the step S4, specifically, the step S4 is performed to calculate the comprehensive topology importance metric of the nodes by using the following steps:
1) the information entropy weight we of the jth index is calculated by adopting the following formulaj：
Figure FDA0003073351370000035
Wherein m is the total number of indexes; en is a radical ofjIs the entropy of the jth index and
Figure FDA0003073351370000036
n is the total number of nodes, pijIs the specific gravity of the ith node under the jth index
Figure FDA0003073351370000037
rijAn index value of a j index of the ith node;
2) calculating the integral Kendel correlation coefficient gamma of the jth index and other indexes by adopting the following formulaj：
Figure FDA0003073351370000041
Wherein m is the total number of indexes; tau isjtThe Kendel correlation coefficient of the j index and the t index is obtained;
3) calculating the Kendel coefficient weight wk of the j index by adopting the following formulajIs composed of
Figure FDA0003073351370000042
4) Calculating the objective weight w of the jth index by the following formulajIs composed of
Figure FDA0003073351370000043
5) The weighted node index matrix S is calculated by the following formula
Figure FDA0003073351370000044
6) Calculating a positive ideal solution F by adopting the following formula according to the weighting node index matrix S obtained in the step 5)+Negative ideal solution F-Is composed of
Figure FDA0003073351370000045
7) The ith node is calculated to the positive ideal solution F by the following formula+Is a distance of
Figure FDA0003073351370000046
Sum node i to negative ideal solution F-Is a distance of
Figure FDA0003073351370000047
Is composed of
Figure FDA0003073351370000048
8) Calculating the comprehensive topological importance metric value T of the ith node by adopting the following formulaiIs composed of
Figure FDA0003073351370000049
6. The method according to claim 5, wherein the Kendell correlation coefficient in step 2) is calculated by:
for two node importance indicators, each having N elements, X ═ X (X) is set1,x2,...,xn) And Y ═ Y1,y2,...,yn) (ii) a When x isi＞xjAnd y isi＞yjOr, xi＜xjAnd y isi＜yjWhen, identify (x)i,yi) And (x)j,yj) This is a correlation for the data, otherwise (x) is assertedi,yi) And (x)j,yj) This is irrelevant to the data; thus, the Kendel correlation coefficient τ of the two node importance indicatorsXYThe calculation formula of (A) is as follows:
Figure FDA0003073351370000051
in the formula NcThe number of the related data pairs; n is a radical ofdNumber of unrelated data pairs; the same elements in X and Y form a small set, s1The number of elements belonging to X in the small set; s2The number of elements belonging to Y in the small set; n is0Is an intermediate number and
Figure FDA0003073351370000052
7. the method for identifying key nodes of a complex network as claimed in claim 6, wherein the key nodes of the complex network are identified according to the comprehensive topology importance metric of the nodes obtained in step S4 in step S5, and specifically, the key nodes are determined to be more critical to the complex network according to the comprehensive topology importance metric of the nodes obtained in step S4, the larger the comprehensive topology importance metric of the nodes is.
8. A power grid key node identification method comprising the complex network key node identification method as claimed in any one of claims 1 to 7, the method is characterized by comprising the following steps:
i, determining a power grid to be analyzed;
and II, taking the power grid to be analyzed determined in the step I as a complex network to be analyzed, and identifying key nodes of the power grid to be analyzed by adopting the steps S1-5 of any one of claims 1-7.
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