CN105471637A - Evaluation method and system for importance of node of complex network - Google Patents

Abstract

The invention provides an evaluation method and system for importance of a node of a complex network. The method comprises: K nucleus decomposition is carried out on a given complex network and iteration information and each node Ks value during the decomposition process are kept; according to the iteration information and each node Ks value, a K nucleus iteration factor of each node is calculated; and according to the K nucleus iteration factors of the nodes, importance of a complex network is calculated. According to the invention, the iteration information during the K nucleus decomposition process is fully utilized and the importance of the complex network node can be evaluated accurately in detail. Moreover, the time complexity is low; the large-scale complex network can be evaluated rapidly; and the adaptability is high.

Description

Complex network node importance evaluation method and system

Technical Field

The invention belongs to the technical field of complex network analysis, relates to a complex network node importance evaluation method and system, and particularly relates to a complex network node importance evaluation method and system based on a K-kernel iteration factor.

Background

The importance of accurately measuring the nodes in the complex network has very important significance and effect on the aspects of preventing network attacks, preventing infectious diseases from spreading in crowds, inhibiting the spreading of gossip in the society and the like. The node importance evaluation method can be roughly divided into three categories: a locality approach, a global approach and a random walk based approach. The node degree is a typical locality method. The locality method is generally simple in calculation and low in complexity, but the importance of the nodes in the whole network is hardly reflected by neglecting the global structure information of the network. The larger the network size, the more obvious the drawbacks of the localized approach. Typical global methods include feature vectors, compactness, betweenness, and the like. Although the global method can accurately evaluate the importance of the nodes, the complexity is high due to the need of calculating the information such as the shortest path between the nodes, and the like, and the method is not suitable for large-scale complex networks. Typical random walk methods include PageRank, leader rank, HITS and the like, and these methods also evaluate the importance of complex network nodes from a global perspective, are high in complexity, and are mainly directed to directed networks.

Kitsak et al, in the article "identification of nodes and computing nodes" published in Nature Physics, 2010, noted that node importance depends on its location in the entire network, and proposed a complex network node importance assessment method based on K-kernel decomposition. The method can quickly evaluate the importance of the nodes, has low complexity and can be suitable for large-scale networks. However, the biggest defect of the method is that many nodes are endowed with the same Ks value, and the importance of the nodes cannot be further distinguished.

In recent years, a plurality of scholars expand and improve the K nucleus decomposition method, so that the application range is wider and the accuracy is better. However, up to now, all improvements to the K-kernel decomposition method neglect iterative information generated in the decomposition process, and the information has very important function and significance for node importance evaluation. Assuming that two nodes have the same Ks value, according to Kitsak's theory, the two nodes have the same importance. The importance of a node depends on its location throughout the network. If they are not deleted in the same iteration, indicating that the two nodes are located differently from the network core node, they should have different importance. If the iterative information generated in the K kernel decomposition process is fully utilized, the importance of the nodes with the same Ks value can be further distinguished.

Disclosure of Invention

In view of the above-mentioned disadvantage that the conventional node importance evaluation method based on K-kernel decomposition ignores the iterative information, the present invention aims to provide a method and a system for evaluating the importance of a complex network node, which are used to solve the problems that the conventional node importance evaluation method based on K-kernel decomposition ignores the iterative information and the importance of nodes with the same Ks value cannot be effectively distinguished.

To achieve the above and other related objects, the present invention provides a method for evaluating importance of a complex network node, including:

performing K-kernel decomposition on a given complex network, and storing iteration information in the decomposition process and a Ks value of each node;

calculating a K core iteration factor of each node according to the iteration information and the Ks value of each node;

and calculating the importance of each node according to the K kernel iteration factor.

Preferably, the method for calculating the node K kernel iteration factor includes:wherein,for any node n in a complex network_iK kernel iteration factor of (1); k is a node n in the K kernel decomposition process_i(iv) the assigned Ks value; m is the total number of iterative operations with the value of K in the K kernel decomposition process; in these m iterations, node n_iRemoved at the nth iteration, 1 ≦ n ≦ m.

Preferably, the method for calculating the node importance includes:wherein,for any node n in a complex network_iThe importance of (c);is a node n_iK kernel iteration factor of (1);is a node n_iA value of (d); n is a radical of_iIs a node n_iThe neighbor node set of (2); n is_jIs a node n_iNeighbor node of n_j∈N_i；Is a node n_jK kernel iteration factor of (1);is a node n_jThe value of (a).

The invention also provides a system for evaluating the importance of the complex network node, which comprises the following components:

the K core decomposition module is used for performing K core decomposition on the given complex network and storing iteration information in the decomposition process and the Ks value of each node;

the node K kernel iteration factor calculation module is connected with the K kernel decomposition module and is used for calculating the K kernel iteration factor of each node according to iteration information generated by K kernel decomposition and the Ks value of each node;

and the node importance calculation module is connected with the node K core iteration factor calculation module and calculates the importance of each node according to the K core iteration factor.

Preferably, the calculation function of the node K kernel iteration factor calculation module is:wherein,for any node n in a complex network_iK kernel iteration factor of (1); k is a node n in the K kernel decomposition process_i(iv) the assigned Ks value; m is the total number of iterative operations with the value of K in the K kernel decomposition process; in these m iterations, node n_iRemoved at the nth iteration, 1 ≦ n ≦ m.

Preferably, the calculation function of the node importance calculation module is:wherein,for any node n in a complex network_iThe importance of (c);is a node n_iK kernel iteration factor of (1);is a node n_iA value of (d); n is a radical of_iIs a node n_iThe neighbor node set of (2); n is_jIs a node n_iNeighbor node of n_j∈N_i；Is a node n_jK kernel iteration factor of (1);is a node n_jThe value of (a).

As described above, the method and system for evaluating the importance of a complex network node according to the present invention have the following advantages:

the invention fully utilizes the iteration information in the K kernel decomposition process, and can effectively distinguish the importance of the nodes with the same Ks value. The node K kernel iteration factor is a global index, and the node degree is a local index. The invention has lower time complexity, can quickly and effectively process large-scale complex network data and has strong adaptability.

Drawings

Fig. 1 is a schematic flow chart of a complex network node importance evaluation method according to the present invention.

Fig. 2 is a schematic structural diagram of a complex network node importance evaluation system according to the present invention.

Fig. 3 is a schematic diagram of the topology of a simple example network.

Fig. 4 is a diagram of the complementary cumulative distribution function CCDF of the network shown in fig. 3.

Fig. 5 is a schematic diagram of the complementary cumulative distribution function CCDF of the karateplus network.

Fig. 6 is a diagram illustrating a complementary cumulative distribution function CCDF of the Dolphin network.

FIG. 7 is a diagram of the complementary cumulative distribution function CCDF of the NetScience network.

Fig. 8 is a schematic diagram of a variation of a degree of discrimination index of different node importance evaluation methods when an n parameter of an LFR network generator varies.

Fig. 9 is a schematic diagram of a variation of the discrimination index of the method for evaluating the importance of different nodes when the μ parameter of the LFR network generator varies.

Fig. 10 is a schematic diagram of a variation of the degree of distinction index of different node importance evaluation methods when the k parameter of the LFR network generator varies.

Fig. 11 is a schematic diagram of a change of a discrimination index of a method for evaluating importance of different nodes when a γ parameter of an LFR network generator changes.

Description of the element reference numerals

S1-S3

200 node importance evaluation system

210K nuclear decomposition module

220 node K kernel iteration factor calculation module

230 node importance calculation module

Detailed Description

The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.

Please refer to the attached drawings. It should be noted that the drawings provided in the present embodiment are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.

The present invention will be described in detail with reference to the accompanying drawings.

The invention provides a method for evaluating the importance of a complex network node, which comprises the following steps of:

and S1, performing K-kernel decomposition on the given complex network, and storing iteration information in the decomposition process and the Ks value of each node.

And S2, calculating the K core iteration factor of each node according to the iteration information and the Ks value of each node.

Further, the method for calculating the node K kernel iteration factor comprises the following steps:wherein,for any node n in a complex network_iK kernel iteration factor of (1); k is a node n in the K kernel decomposition process_i(iv) the assigned Ks value; m is the total number of iterative operations with the value of K in the K kernel decomposition process; in these m iterations, node n_iRemoved at the nth iteration, 1 ≦ n ≦ m. Wherein the value refers to the number of nodes that are most adjacent around each node.

And S3, calculating the importance of each node according to the K kernel iteration factor.

Further, the method for calculating the node importance comprises the following steps:wherein,for any node n in a complex network_iThe importance of (c);is a node n_iK kernel iteration factor of (1);is a node n_iA value of (d); n is a radical of_iIs a node n_iThe neighbor node set of (2); n is_jIs a node n_iNeighbor node of n_j∈N_i；Is a node n_jK kernel iteration factor of (1);is a node n_jThe value of (a).

The protection scope of the present invention is not limited to the execution sequence of the steps of the complex network node importance evaluation method based on the K-kernel iteration factor, and all the node importance evaluation methods after any form of deformation according to the principle of the present invention are included in the protection scope of the present invention.

The invention also provides a complex network node importance evaluation system which can realize the complex network node importance evaluation method, but the realization device of the complex network node importance evaluation method comprises but is not limited to the complex network node importance evaluation system.

As shown in fig. 2, the complex network node importance evaluation system 200 includes: the system comprises a K core decomposition module 210, a node K core iteration factor calculation module 220 and a node importance calculation module 230.

The K-kernel decomposition module 210 performs K-kernel decomposition on the input complex network, and stores iteration information in the decomposition process and Ks values of each node.

The node K-core iteration factor calculation module 220 is connected to the K-core decomposition module 210, and calculates a K-core iteration factor of each node according to iteration information generated by K-core decomposition and the Ks value of each node. Further, the calculation function of the node K kernel iteration factor calculation module is as follows:

${\mathrm{\δ}}_{n_i}=k\·(1+\frac{n}{m})$

wherein,for any node n in a complex network_iK kernel iteration factor of (1); k is a node n in the K kernel decomposition process_i(iv) the assigned Ks value; m is the total number of iterative operations with the value of K in the K kernel decomposition process; in these m iterations, node n_iRemoved at the nth iteration, 1 ≦ n ≦ m.

The node importance calculating module 230 is connected to the node K-core iteration factor calculating module 220, and calculates the importance of each node according to the K-core iteration factor of the node. Further, the calculation function of the node importance calculation module is as follows:

${\mathrm{IC}}_{n_i}={\mathrm{\δ}}_{n_i}\·d_{n_i}+\underset{n_j\∈N_i}{\Σ}{\mathrm{\δ}}_{n_j}\·d_{n_j}$

wherein,for any node n in a complex network_iThe importance of (c);is a node n_iK kernel iteration factor of (1);is a node n_iA value of (d); n is a radical of_iIs a node n_iThe neighbor node set of (2); n is_jIs a node n_iNeighbor node of n_j∈N_i；Is a node n_jK kernel iteration factor of (1);is a node n_jThe value of (a).

In view of the defect that iteration information is ignored in the node importance evaluation technology based on K-kernel decomposition, the invention provides a method and a system for evaluating the importance of complex network nodes, which are used for solving the problems that iteration information is ignored in the existing node importance evaluation method based on K-kernel decomposition, the importance of nodes with the same Ks value cannot be effectively distinguished, and the like. The invention fully utilizes the iteration information in the K kernel decomposition process, and can effectively distinguish the importance of the nodes with the same Ks value. The node K kernel iteration factor is a global index, and the node degree is a local index. The invention has lower time complexity, can quickly and effectively process large-scale complex network data and has strong adaptability.

The present invention will be described in further detail with reference to the following examples and the accompanying drawings.

Example one

In this embodiment, a simple example network is taken as an example, and the importance evaluation method of the complex network node provided by the present invention is used for evaluating the importance of the network node. The topology of an exemplary network is shown in fig. 3, which contains 17 nodes. In this embodiment, the node importance evaluation of the exemplary network shown in fig. 3 by using the complex network node importance evaluation method specifically includes the following steps:

1) and performing K-core decomposition on the given example network, and storing iteration information in the decomposition process and the Ks value of each node. The K-core decomposition information for the example network is shown in table 1.

Table 1: k-core decomposition information for example networks

Degree of value	Iteration numbering	Removing nodes	Node Ks value
				1	1	1,2,3,5,9,14,17	1
1	2	4,16	1
				2	1	6	2
2	2	7,8,15	2
				3	1	10,11,12,13	3

2) And calculating the K core iteration factor of each node according to the iteration information generated by the K core decomposition and the Ks value of each node. According to the K-core iteration factor calculation method of the present invention, the calculated K-core iteration factors of the exemplary network nodes are shown in table 2.

Table 2: k-kernel iteration factor for an example network node

Node numbering	K kernel iteration factor	Node numbering	K kernel iteration factor
				1	1.5	10	6.0
2	1.5	11	6.0
				3	1.5	12	6.0
4	2.0	13	6.0
				5	1.5	14	1.5
6	3.0	15	4.0
				7	4.0	16	2.0
8	4.0	17	1.5
				9	1.5

3) And calculating the importance of each node according to the K kernel iteration factor of the node. The importance of the exemplary network nodes calculated according to the node importance calculation method of the present invention is shown in table 3.

Table 3: importance of an example network node

Node numbering	Importance of	Node numbering	Importance of
				1	9.3333	10	127.3333
2	6.3333	11	102.0000
				3	6.3333	12	114.0000
4	15.6667	13	114.0000
				5	9.3333	14	37.3333
6	27.6667	15	63.3333
				7	68.0000	16	16.6667
8	61.3333	17	4.6667
				9	13.3333

As can be seen from table 3, almost all example network nodes are given different importance. The importance evaluation method of the complex network node can well distinguish the importance of the example network node, thereby proving the effectiveness of the invention.

Example two

In the embodiment, an example network, a real network and a manual network are taken as examples, and the complex network node importance assessment method provided by the invention is used for node importance assessment of the network and compared with other typical node importance assessment methods. Typical methods of selection include: node degree method (abbreviated as d), traditional K-kernel decomposition (abbreviated as KS), mixedness decomposition (abbreviated as MDD), minimum K-kernel method (abbreviated as min-KS), shortest distance method (abbreviated as KS-K), and extended neighbor kernel method (abbreviated as C) of neighbor kernel_nc+). The method is abbreviated as KS-IF. In order to better evaluate the performance of various importance evaluation methods, a discrimination index M is introduced here. The discrimination index is defined as follows:

$M\left(R\right)={\left(1-\frac{\underset{r\∈R}{\Σ}{n}_r(n_r-1)}{n(n-1)}\right)}^2$

wherein R is a rank vector of network node importance, n is the total rank number of the vector R, n is_rIs the number of nodes in the r-th level. If all the nodes are in the same importance level, the value of the discrimination index M is 0, and the corresponding evaluation method cannot distinguish the importance of each node. If each importance level only contains 1 node, and the value of the discrimination index M is 1, the corresponding evaluation method can effectively discriminate the importance of each node and has the strongest discrimination capability.

First, the example network shown in fig. 3 is selected, the importance of the example network nodes is evaluated by the 7 methods, the nodes are sorted according to the importance, and the sorting result is shown in table 4. Each column of Table 4 corresponds to a method of importance assessment, with nodes of the same level having the same importance and "others" representing all nodes remaining. As can be seen from table 4, the method (KS-IF) of the present invention can accurately and finely distinguish the importance of the network nodes, and the number of nodes per importance level is at most 2, compared to the other 6 typical methods.

Table 4: ranking results of example network node importance

In order to further explain the performance of the method, 8 real networks with different scales are selected, and the discrimination indexes M of the 7 importance evaluation methods are analyzed and compared. These 8 real networks include: karateclub network, Dolphin network, Jazz network, NetScience network, E-mail network, Blogs network, PGP network, and Enron network. Table 5 shows the ability of the 7 importance assessment methods to differentiate the importance of the 8 real network nodes. It can be seen that: the method (KS-IF) of the invention allows to obtain maximum division values of the zones for the 8 real networks. Compared with other 6 node importance evaluation methods, the method provided by the invention can more carefully and accurately identify the importance of the real network node.

Table 5: capability of different importance evaluation methods for distinguishing importance of real network nodes

To further illustrate the performance of the method of the present invention, the results of Table 5 are shown using the complementary cumulative distribution function CCDF. Fig. 4 to 7 show CCDF of 4 networks, i.e., an example network, karateplus network, Dolphin network, and NetScience network, respectively. According to the principle of CCDF, if the number of nodes in the same importance level is larger, the CCDF will decrease faster, otherwise, the CCDF will decrease slowly along the diagonal. As can be seen from fig. 4 to 7, the CCDF of the method (KS-IF) of the present invention decreases slowly along the diagonal, which shows that the method of the present invention can distinguish the difference in importance between the network nodes well.

In order to further illustrate the performance of the method of the present invention, an artificial complex network is generated by means of an LFR network generator, and the method of the present invention is evaluated using the artificial complex network. The LFR network generator has 4 important parameters, which are node size n (numberrofnodes), average node degree k (averagegreeeofnodes), community structure mixture parameter μ (mixtureof communique) and power-law distribution γ (power-law distribution). The change of the 4 parameters will affect the topology of the artificially complex network. Fig. 8 to 11 show the change of the discrimination index M of different node importance evaluation methods when 1 parameter is kept changed for the 4 parameters and the remaining 3 parameters are not changed. It can be seen that: the method (KS-IF) of the invention allows to obtain maximum segmentation index values for said artificially complex network. Compared with other 3 node importance evaluation methods, the method provided by the invention can more carefully and accurately identify the node importance of the artificial complex network.

By combining the specific contents of the invention and the first embodiment and the second embodiment, the invention carries out K-core decomposition on a given complex network, and stores iteration information in the decomposition process and a Ks value of each node; calculating a K core iteration factor of each node according to the iteration information and the Ks value of each node; and calculating the importance of the complex network node according to the K core iteration factor of the node.

The invention fully utilizes the iteration information in the K kernel decomposition process, and can effectively distinguish the importance of the nodes with the same Ks value. The invention considers global index and local index at the same time, and carries out comprehensive and objective evaluation on the importance of the node based on the K kernel iteration factor and degree information of the node. The invention has lower time complexity, can quickly and effectively process large-scale complex network data and has strong adaptability.

In conclusion, the present invention effectively overcomes various disadvantages of the prior art and has high industrial utilization value.

The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.

Claims (6)

1. A method for evaluating the importance of a complex network node is characterized by comprising the following steps:

performing K-kernel decomposition on a given complex network, and storing iteration information in the decomposition process and a Ks value of each node;

calculating a K core iteration factor of each node according to the iteration information and the Ks value of each node;

and calculating the importance of each node according to the K kernel iteration factor.

2. The method for evaluating the importance of the complex network node according to claim 1, wherein the method for calculating the iteration factor of the node K core comprises:

${\mathrm{\δ}}_{n_i}=k\·(1+\frac{n}{m})$

wherein,for any node n in a complex network_iK kernel iteration factor of (1); k is a node n in the K kernel decomposition process_i(iv) the assigned Ks value; m is the total number of iterative operations with the value of K in the K kernel decomposition process; in these m iterations, node n_iRemoved at the nth iteration, 1 ≦ n ≦ m.

3. The method according to claim 1, wherein the method for calculating the node importance comprises:

${\mathrm{IC}}_{n_i}={\mathrm{\δ}}_{n_i}\·d_{n_i}+\underset{n_j\∈N_i}{\Σ}{\mathrm{\δ}}_{n_j}\·d_{n_j}$

wherein,for any node n in a complex network_iThe importance of (c);is a node n_iK kernel iteration factor of (1);is a node n_iA value of (d); n is a radical of_iIs a node n_iThe neighbor node set of (2); n is_jIs a node n_iNeighbor node of n_j∈N_i；Is a node n_jK kernel iteration factor of (1);is a node n_jThe value of (a).

4. A complex network node importance evaluation system, the complex network node importance evaluation system comprising:

the K core decomposition module is used for performing K core decomposition on the given complex network and storing iteration information in the decomposition process and the Ks value of each node;

the node K kernel iteration factor calculation module is connected with the K kernel decomposition module and used for calculating the K kernel iteration factor of each node according to the iteration information generated in the K kernel decomposition process and the Ks value of each node;

and the node importance calculation module is connected with the node K core iteration factor calculation module and calculates the importance of each node according to the K core iteration factor.

5. The complex network node importance evaluation system of claim 4, wherein the computation function of the node K kernel iterative factor computation module is:

${\mathrm{\δ}}_{n_i}=k\·(1+\frac{n}{m})$

wherein,for any node n in a complex network_iK kernel iteration factor of (1); k is a node n in the K kernel decomposition process_i(iv) the assigned Ks value; m is the total number of iterative operations with the value of K in the K kernel decomposition process; in these m iterations, node n_iRemoved at the nth iteration, 1 ≦ n ≦ m.

6. The complex network node importance evaluation system of claim 4, wherein the computing function of the node importance calculation module is:

${\mathrm{IC}}_{n_i}={\mathrm{\δ}}_{n_i}\·d_{n_i}+\underset{n_j\∈N_i}{\Σ}{\mathrm{\δ}}_{n_j}\·d_{n_j}$

wherein,for any node n in a complex network_iThe importance of (c);is a node n_iK kernel iteration factor of (1);is a node n_iA value of (d); n is a radical of_iIs a node n_iThe neighbor node set of (2); n is_jIs a node n_iNeighbor node of n_j∈N_i；Is a node n_jK kernel iteration factor of (1);is a node n_jThe value of (a).