CN115225447B - Complex network key node identification method and system based on voting mechanism - Google Patents

Complex network key node identification method and system based on voting mechanism Download PDF

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CN115225447B
CN115225447B CN202210852784.5A CN202210852784A CN115225447B CN 115225447 B CN115225447 B CN 115225447B CN 202210852784 A CN202210852784 A CN 202210852784A CN 115225447 B CN115225447 B CN 115225447B
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CN115225447A (en
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姜雪松
陈珺
尉秀梅
陈佃迎
柴慧慧
马浩翔
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Qilu University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/30—Decision processes by autonomous network management units using voting and bidding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L43/00—Arrangements for monitoring or testing data switching networks
    • H04L43/08—Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a complex network key node identification method and system based on a voting mechanism, which abstracts an industrial chain into a complex network, integrates a collective influence algorithm, and initializes the voting score and voting capacity of each node in the network; based on the initialized voting capacity, introducing the probability of each node voting on different neighbor nodes to obtain corresponding voting scores, and taking the node with the highest voting score as a key node; the voting capability of the first-order neighbor nodes and the second-order neighbor nodes of the selected nodes is weakened, voting is continued on the unselected nodes, and the steps are repeated until all the key nodes are selected.

Description

Complex network key node identification method and system based on voting mechanism
Technical Field
The disclosure relates to the field of complex network key node identification, in particular to a complex network key node identification method and system based on a voting mechanism.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
With the rapid development of informatization, the social activities of human beings tend to be networked, and complex systems can be abstracted into complex networks. The different nodes have great differences in the functions of the network structure and the functions, and key nodes in various complex networks are excavated, so that the method has important significance in effective utilization.
For example, controlling key nodes in a social network will help prevent the diffusion of rumors; important nodes of the power network are accurately found, and are subjected to important supervision and protection, so that power transmission can be smoothly carried out, and large-area power failure accidents are effectively prevented; identifying and controlling important nodes in the traffic network can effectively solve the problem of traffic jam and the like. The important nodes in the network are controlled, so that the normal operation of the network can be effectively ensured, the huge loss caused by the fault of a certain node in the network can be effectively avoided, and the whole network can be rapidly influenced by taking measures according to the important nodes in the network.
Moreover, in the networking era background, enterprises exist as 'nodes' of complex systems such as an industrial chain, a supply chain or a manufacturing process, and analysis and excavation of key enterprise nodes are extremely important to ensure stable and efficient operation of related complex systems, so that unnecessary losses caused by supply chain breakage can be reduced.
The key nodes mined by the traditional algorithm are likely to be concentrated in a certain same area, and the 'rich club effect' appears, so that the information propagation is not facilitated.
To address the problem of the "rich club effect," Zhang et al propose a volterank algorithm based on a voting mechanism that avoids the "rich club effect" by selecting a spreader across the network from the votes of its neighbors, the selected spreader not participating in the next round of voting and selection, and the voting capabilities of the neighbor nodes of the selected spreader then decaying. Sun et al propose a WVoteRank algorithm that extends from an unlicensed network to a weighted network.
Based on the VoteRank algorithm, kumar et al propose an NCVoteRank algorithm that considers the core value of neighbors in voting and cuts down the voting ability to second-order neighbor nodes in the update phase, making the distribution of the spreader more extensive.
In the information theory, the information amount is a measure of information brought about by a specific event, and the information entropy is a desire for the information amount. Guo et al propose an EnRenew algorithm, which selects a spreader by considering the information entropy of the nodes, updates the information entropy of all the nodes in the local range of the spreader, reserves the local information of the nodes, and is greatly improved on the basis of the original algorithm.
However, the above algorithm does not distinguish the voting capability of different nodes and the voting of each node to different neighbor nodes thereof, ignores partial local information, cannot comprehensively consider the combination of global and local information, and ignores the influence of low-level nodes.
Disclosure of Invention
In order to solve the problems, the disclosure provides a complex network key node identification method and system based on a voting mechanism, which firstly calculates a CI value of a network node by adopting a CI algorithm, initializes the voting capability of the node through the CI value, and fully considers the local information of the node and the influence of low-level nodes. Secondly, a concept of voting probability is introduced, the voting of the network nodes to different neighbor nodes is distinguished through the voting probability, more local information is considered, the importance degree of the nodes is comprehensively evaluated, and finally, the node with larger total votes is obtained.
In order to achieve the above purpose, the present disclosure adopts the following technical scheme:
in a first aspect, the present disclosure provides a method for identifying key nodes of a complex network based on a voting mechanism, including the steps of:
step 1: abstracting an industrial chain into a complex network, integrating a collective influence algorithm, and initializing voting scores and voting capacities of each node in the network;
step 2: based on the initialized voting capacity, introducing the probability of each node voting on different neighbor nodes to obtain corresponding voting scores, and taking the node with the highest voting score as a key node;
step 3: weakening voting capability of first-order and second-order neighbor nodes of the selected node;
step 4: and (3) voting on the unselected nodes continuously, and repeating the step (2) and the step (3) until all the key nodes are selected.
In a second aspect, the present disclosure provides a complex network key node identification system based on a voting mechanism, comprising:
the initialization module is used for abstracting the industrial chain into a complex network, integrating a collective influence algorithm and initializing the voting score and voting capacity of each node in the network;
the key node identification module is used for introducing the probability of voting of each node to different neighbor nodes based on the initialized voting capacity to obtain corresponding voting scores, and taking the node with the highest voting score as the key node;
the voting capability of the first-order neighbor nodes and the second-order neighbor nodes of the selected nodes is weakened, voting is continued on the unselected nodes, and the steps are repeated until all the key nodes are selected.
A third aspect of the present disclosure provides a computer-readable storage medium.
A computer readable storage medium having stored thereon a program which when executed by a processor performs the steps in a method of complex network key node identification based on voting mechanisms as described in the second aspect of the present disclosure.
A fourth aspect of the present disclosure provides an electronic device.
An electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in the voting mechanism based complex network key node identification method according to the second aspect of the present disclosure when the program is executed.
Compared with the prior art, the beneficial effects of the present disclosure are:
the invention fully considers the local information of the nodes and also considers the influence of the low-level nodes on the network through the voting capability of the CI value initialization nodes.
The invention introduces the concept of voting probability, effectively distinguishes the voting of the nodes to different neighbor nodes thereof through the voting probability P, considers more local information and comprehensively evaluates the importance degree of the nodes.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate and explain the exemplary embodiments of the disclosure and together with the description serve to explain the disclosure, and do not constitute an undue limitation on the disclosure.
Fig. 1 is a schematic diagram of a complex network key node identification method based on a voting mechanism according to an embodiment of the disclosure;
fig. 2 is a schematic diagram of SIR model state transition in an embodiment of the present disclosure;
fig. 3 (a) -3 (F) are experimental results of the variation of the infection amount F (t) with time t according to the embodiment of the present disclosure.
Fig. 4 (a) -4 (F) are diagrams showing the final infection amount F (t) in the case where the ratio ρ of the initial infection node is not fixed in the embodiment of the present disclosure c ) Is a result of the experiment.
FIGS. 5 (a) -5 (F) are graphs showing the final infection amount F (t) in the case where the infection rate μ is not fixed in the embodiment of the present disclosure c ) Is a result of the experiment.
The specific embodiment is as follows:
the disclosure is further described below with reference to the drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments in accordance with the present disclosure. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Example 1
As shown in fig. 1, the present embodiment provides a method and a system for identifying key nodes of a complex network based on a voting mechanism, including the following steps:
step 1: an initialization stage: abstracting an industrial chain into a complex network, integrating a collective influence algorithm, and initializing voting scores and voting capacities of each node in the network;
in step 1, as one or more embodiments, each node V e V is assigned a tuple (S v ，Va v), wherein ,Sv and Vav The voting score and voting capacity of the corresponding node v, respectively.
Initializing the voting score Sv of each node v to 0, and voting energyForce Va v Initialized to 1, i.e. (Sv, va v )＝(0,1)。
Incorporates the CI algorithm, sets the voting capability of each node v, and sets each node v as a binary group (S v ,Va v ) Initialization to (0, log [ CI ] v +1])；
The voting capacity of each node in this embodiment should be different and depending on the degree of importance in the local area, the more important the local node is, the higher the voting capacity is, instead of indifferently set to 1.
In order to consider the influence of low-level nodes more, the embodiment integrates a CI algorithm, and key nodes are searched by considering the CI values of the nodes.
The CI algorithm is integrated, voting capacity of each node v is set, and the set formula is as follows:
wherein ,dv Representing the degree of node v, Γ (v) represents the first-order neighbor set of node v.
CI v Refers to the collective impact strength of a certain determined network.
Wherein CI (Collective Influence, collective impact) presents a large number of previously ignored weakly connected nodes among the best influencers. These nodes are topologically labeled as low-level nodes and can only be discovered through the best collective interactions of all the influencers in the network. Low-level nodes play a major mediating role in the network, although the connection is weak, they may also be strong contributors.
Collective Influence (CI) algorithm definition: ball (v, l) is the set of nodes within the sphere that surrounds node v and belongs to radius (shortest path) l,for the boundary of the sphere, then the collective impact strength obtained by node v at layer i, i.e., the CI value:
wherein ,dv Is the degree of node v; l is a predefined non-negative integer not exceeding the diameter of the finite network, typically taking 3 or 4 in large and medium networks and 2 in small networks.
The CI algorithm comprises the following specific processes:
computing CI of all nodes based on whole network v Value, CI v The node with the greatest value is removed from the network.
Recalculating CI of node included in maximum connected component in network v Value, and continue to write new CI v The node with the largest value is removed from the network and the process is repeated until the largest connected component in the network disappears and the algorithm ends.
The CI algorithm considers interaction of influence nodes and l-layer neighbor nodes, shows the unreachable stability of the algorithm based on topology centrality and the like, and simultaneously reveals strong influence of low-level nodes playing a main broker role on a network, and has immeasurable significance for identification of the low-level influence nodes.
Step 2: voting: based on the initialized voting capability, the probability of voting of each node to different neighbor nodes is introduced to obtain the corresponding voting score.
Wherein the node that gets the most total ticket number is selected as the spreader. In addition, the voting score and voting capacity of the selected node are set to 0, and the next voting process is not participated.
Since the relationship between each node and its different neighbor nodes is typically different, the vote of each node for its different neighbor nodes should also be different.
The voting probability P is introduced to represent the probability of the nodes voting to different neighbor nodes of the nodes, so that the nodes voting to different neighbor nodes of the nodes are distinguished. To consider more local information, the voting probability P of node u to node v is set uv The definition is as follows:
wherein ,dv Representing the degree of node v, Γ (u) represents the first-order neighbor set of node u.
Then, the number of votes by node u for node v is the product of the voting capacity of node u and the voting probability of node u for node v. In the voting phase, the node v obtains the total number of votes S obtained by the node v v Equal to the sum of voting capacities of all first-order neighbor nodes, the formula is:
where Γ (v) represents the first-order neighbor set of node v.
In order to better understand the technical solution, taking an industrial chain as an example, in practical production applications, enterprises exist not only as a single entity, but also as entity enterprises in the industrial chain. The industrial chain is abstracted into a complex network, each enterprise and workshop in the industrial chain network and the relation thereof are mapped into nodes and connecting edges of the complex network, and first-order neighbor nodes of the nodes are enterprise sets with direct relation with the enterprise.
Since the importance level is different for each enterprise and workshop, the voting capacity of each corresponding node should be different, and the more important the local node is, the higher the voting capacity is.
In addition, the relationship between enterprises is also different, so each node should vote differently for its different level neighbor nodes.
The voting probability P is introduced here:
wherein ,dv Representing the degree of enterprise v, i.e., the number of enterprises that have a relationship with enterprise v. Γ (u) represents a set of enterprises that have a relationship with enterprise u. d, d v The larger the enterprise representing the relationship with enterprise v, the more important enterprise v is in the local scope, the larger the voting probability P, and the larger the enterprise v takes the vote of enterprise u. w belongs to the set Γ (u) and represents each enterprise related to enterprise u, d w Representing the degree of enterprise w.Representing the sum of the degrees of all enterprises that have a relationship with enterprise u.
Then, the number of votes by enterprise u for enterprise v is the product of the voting capacity of enterprise u and the voting probability of enterprise u for enterprise v.
In the voting phase, the total number of votes obtained by enterprise v is:
where Γ (v) represents the set of enterprises that have a relationship with enterprise v.
Step 3: updating: to make the spreader more widely distributed, voting capabilities of first and second order neighbor nodes of a selected node are impaired to varying degrees:
wherein ,d is the average of all nodes and k is the distance between the selected node and its neighbor nodes (i.e., k=1, 2).
Step 4: iteration stage: repeating steps 2 and 3 until n spreaders are selected, wherein n is a constant.
For example, n=5, if one wants the most critical 5 businesses of a certain industry chain network. And (3) selecting one key enterprise through the step 1 and the step 2, updating through the step 3, and repeating the step 2 and the step 3, wherein each time the step 2 is performed, one key enterprise is selected, and 5 key enterprises are selected.
The detailed procedure of the present embodiment of the CIVoteRank is shown in algorithm 1.
The CI value and the voting probability P reflect local information of the network to a certain extent, and compared with the VoteRank algorithm, the CIVoteRank algorithm introduces more local information than the method of directly setting the voting capacity to 1. Meanwhile, the CI algorithm considers the influence of the low-level nodes, and the importance degree of the nodes is more comprehensively evaluated.
In order to verify the effectiveness of the present invention, a specific experimental procedure is as follows:
1. data set: 6 real networks with different sizes and structures are selected, and the description of topology information is shown in the following table. Wherein N is the number of network nodes, M is the number of network edges, and d max For the maximum degree of the network,<d>is the average degree of the network.
Table 1 description of network topology information
Network system N M d max <d>
Jazz network 198 2742 100 27.69
CE network 453 2025 237 8.94
Email network 1133 5451 71 9.62
Hamster network 2426 16631 273 13.71
Router network 5022 6258 106 2.49
Condmat network 23133 93497 281 8.08
2. Propagation model and performance index:
the propagation capabilities of the identified nodes are modeled using SIR models. SIR models are the most common epidemic propagation models. Nodes in the SIR model are divided into three states: susceptibility (S), infected (I), and recovered (R). Initially, the initial spreader is in state I and the other nodes are in state S. In each time step, each infected node randomly infects its susceptible neighbor with a probability α, the state of the infected neighbor changing from S to I. At the same time, the infected node moves from state I to state R with probability beta, and the node reaching state R gets immunity and cannot be infected again until reaching a stable state. The infection rate is defined herein as μ, expressed asFig. 2 is a schematic diagram of each state transition in the SIR model.
In the SIR model, the propagation capability of a node can be determined by the time-dependent infection amount F (t) and the final infection amount F (t) c ) To evaluate. At any time t, the infection amount F (t) is the sum of the number of infected nodes and the number of restored nodes in the network divided by the total number of nodes in the network, i.e.:
the larger F (t) indicates that at time t, the more nodes are infected by the initially infected node.
Final infection amount F (t) c ) Indicating that the sum of the number of restored nodes in the network divided by the total number of nodes in the network, when steady state is reached, is:
F(t c ) The larger the tableThe larger the scale affected when steady state is reached. Because of the randomness in the model, the model needs to be independently operated for multiple times, and the final result is averaged over the simulation times.
3. Analysis of experimental results:
to evaluate the performance of the different methods extensively, the invention was analyzed experimentally for centrality, K-shell, H-index, voteRank and EnRenew.
According to the SIR model, in the case where the infection rate μ=1.5 and the ratio ρ of the initial infection node=0.03, the results of 100 independent runs were averaged, and experimental results of the resulting infection amount F (t) over time t are shown in fig. 3 (a) -3 (F). The aim of the experiment was to compare the speed of infection of different methods with a fixed number of initial infection nodes. At the same propagation time t, the larger the F (t), the larger the scale of infection in the network, and the faster the propagation speed. From the results of fig. 3 (a) -3 (f), it can be seen that, with the same number of initially infected nodes, civolterank can infect more nodes on most networks than other methods. The CIVoteRank is significantly better than other methods in terms of the amount of infection at the steady stage on Email networks, hamter networks and Condmat networks. But the performance of this approach on Jazz networks is not ideal because the network is small and dense in size, and a node with higher selectivity is used as the initial infection node, such as a centrality approach, which can produce better results. In addition, the overall infection by K-shells is almost worst, especially in medium-to-large networks, because the nodes identified by K-shells tend to be more concentrated in the same area, and the nodes selected by CIVoteRank are more widely distributed. From the propagation speed point of view, the same number of nodes are infected on most networks, and the CIVoteRank takes less time than other methods, which indicates that the node selected by the CIVoteRank has a stronger propagation capability.
At the ratio ρ of different initial infected nodes, the results of 100 independent runs were averaged, and the final infection amount F (t c ) The experimental results of (a) are shown in fig. 4, in which the infection rate μ=1.5. The aim of the experiment is to compare the final affected of different methods in case the number of initial infected nodes is not fixedScale of the process. The more nodes initially infected, the greater the size that is ultimately affected. From the results of fig. 4 (a) -4 (f), it can be seen that, with the same ρ value, CIVoteRank can always infect more nodes on most networks than other methods. When the p value is smaller, the results of all methods differ less, but when there are more nodes initially infected, the CIVoteRank can affect more nodes. Particularly, in large-scale complex networks such as Router networks and Condmat networks, the result of CIVoteRank is obviously better than that of a centrality method and an EnRenew method, which shows that the invention is correct to consider the influence of low-degree nodes rather than the improvement of nodes with higher pure selectivity.
At different infection rates μ, the results of 100 independent runs were averaged to obtain the final infection amount F (t c ) The experimental results of (a) and (f) are shown in fig. 5 (a) to 5 (f), wherein the ratio ρ=0.03 of the initial infected node. The different infection rates μ have a greater impact on the infection process, the greater the infection rate μ, the greater the final affected scale. When the infection rate μ is small, the results of all algorithms are poor. It can be seen from fig. 5 (a) -5 (f) that, at the same infection rate μ, the civolterank can reach the maximum infection scale on most networks, especially on the Hamster network and the Condmat network, and the finally affected scale of the civolterank is far larger than that of other algorithms. In addition, all methods do not produce good results due to the high sparsity of Router networks. Overall results indicate that civolterank has a stronger generalization ability than other methods.
Example two
The embodiment provides a complex network key node identification system based on a voting mechanism, which comprises the following steps:
the initialization module is used for abstracting the industrial chain into a complex network, integrating a collective influence algorithm and initializing the voting score and voting capacity of each node in the network;
the key node identification module is used for introducing the probability of voting of each node to different neighbor nodes based on the initialized voting capacity to obtain corresponding voting scores, and taking the node with the highest voting score as the key node;
the voting capability of the first-order neighbor nodes and the second-order neighbor nodes of the selected nodes is weakened, voting is continued on the unselected nodes, and the steps are repeated until all the key nodes are selected.
The method comprises the steps of integrating a collective influence algorithm, setting the voting score and the voting capacity of each node in a complex network in the initialization of the voting score and the voting capacity of each node in the network, wherein the formula for setting the voting capacity of each node in the complex network is as follows:
wherein ,CIv The collective impact strength obtained for node v, d v Representing the degree of node v, d u Representing the degree of node u, Γ (v) represents the first-order neighbor set of node v.
Based on the initialized voting capability, the step of introducing the probability of each node voting on different neighbor nodes to obtain the corresponding voting score comprises the following steps:
obtaining the voting probability of the node u to the node v according to the degree of the node v and the degree of the first-order neighbor set of the node u;
and obtaining a voting score corresponding to the node v based on the sum of products of the initialized voting capacity of the node u and the voting probability of the node u to the node v.
Example III
The embodiment of the present disclosure provides a computer readable storage medium having a program stored thereon, which when executed by a processor, implements the steps in the voting mechanism-based complex network key node identification method according to the first embodiment.
Example IV
An embodiment of the present disclosure provides an electronic device, including a memory, a processor, and a program stored on the memory and executable on the processor, where the processor implements steps in the voting mechanism-based complex network key node identification method according to the first embodiment when the processor executes the program.
The foregoing is merely a preferred embodiment of the present disclosure, and is not intended to limit the present disclosure, so that various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
While the specific embodiments of the present disclosure have been described above with reference to the drawings, it should be understood that the present disclosure is not limited to the embodiments, and that various modifications and changes can be made by one skilled in the art without inventive effort on the basis of the technical solutions of the present disclosure while remaining within the scope of the present disclosure.

Claims (5)

1. The complex network key node identification method based on the voting mechanism is characterized by comprising the following steps:
step 1: abstracting an industrial chain into a complex network, integrating a collective influence algorithm, and initializing voting scores and voting capacities of each node in the network;
step 2: based on the initialized voting capacity, introducing the probability of each node voting on different neighbor nodes to obtain corresponding voting scores, and taking the node with the highest voting score as a key node;
step 3: weakening voting capacity of first-order and second-order neighbor nodes of the selected key node;
step 4: voting is continued on the unselected nodes, and the step 2 and the step 3 are repeated until all key nodes are selected;
the collective influence algorithm is integrated, in the process of initializing the voting score and the voting capacity of each node in the network, the voting capacity of each node in the complex network is set, and the voting capacity of each node in the complex network is set according to the following formula:
wherein ,CIv The collective impact strength obtained for node v, d v Representing the degree of node v, d u Representing the degree of node u, Γ (v) represents the first-order neighbor set of node v;
computing CI of all nodes based on whole network v Value, CI v The node with the highest value is removed from the network, and CI of the node contained in the maximum connected component in the network is recalculated v Value, and continue to write new CI v The node with the largest value is removed from the network, and the process is repeated until the largest connected component in the network disappears;
based on the initialized voting capability, the step of introducing the probability of each node voting on different neighbor nodes to obtain the corresponding voting score comprises the following steps:
obtaining the voting probability of the node u to the node v according to the degree of the node v and the degree of the first-order neighbor set of the node u;
and obtaining a voting score corresponding to the node v based on the sum of products of the initialized voting capacity of the node u and the voting probability of the node u to the node v.
2. The method for identifying key nodes of a complex network based on voting mechanism as claimed in claim 1, wherein the voting capability of the first-order and second-order neighbor nodes of the weakened selected key node is:
wherein ,d is the average of all nodes, and k is the distance between the selected node and its neighbor nodes.
3. The complex network key node identification system based on the voting mechanism is characterized by comprising the following components:
the initialization module is used for abstracting the industrial chain into a complex network, integrating a collective influence algorithm and initializing the voting score and voting capacity of each node in the network;
the key node identification module is used for introducing the probability of voting of each node to different neighbor nodes based on the initialized voting capacity to obtain corresponding voting scores, and taking the node with the highest voting score as the key node; weakening voting capability of first-order and second-order neighbor nodes of the selected node, continuously voting on unselected nodes, and repeating the steps until all key nodes are selected;
the collective influence algorithm is integrated, in the process of initializing the voting score and the voting capacity of each node in the network, the voting capacity of each node in the complex network is set, and the voting capacity of each node in the complex network is set according to the following formula:
wherein ,CIv The collective impact strength obtained for node v, d v Representing the degree of node v, d u Representing the degree of node u, Γ (v) represents the first-order neighbor set of node v;
computing CI of all nodes based on whole network v Value, CI v The node with the highest value is removed from the network, and CI of the node contained in the maximum connected component in the network is recalculated v Value, and continue to write new CI v The node with the largest value is removed from the network, and the process is repeated until the largest connected component in the network disappears;
based on the initialized voting capability, the step of introducing the probability of each node voting on different neighbor nodes to obtain the corresponding voting score comprises the following steps:
obtaining the voting probability of the node u to the node v according to the degree of the node v and the degree of the first-order neighbor set of the node u;
and obtaining a voting score corresponding to the node v based on the sum of products of the initialized voting capacity of the node u and the voting probability of the node u to the node v.
4. A computer readable storage medium having stored thereon a program, which when executed by a processor performs the steps in the voting mechanism based complex network key node identification method according to any one of claims 1-2.
5. An electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, wherein the processor implements the steps in the voting mechanism-based complex network key node identification method of any one of claims 1-2 when the program is executed by the processor.
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