A method and apparatus for evaluating the importance of network nodes based on radiation theory.

Abstract

This invention provides a method and apparatus for evaluating the importance of network nodes based on radiation theory. The method includes: obtaining the extinction degree generated by radiation from any node to other nodes in the network to be evaluated based on radiation theory, thus obtaining the extinction influencing factor of the given node; determining the radiation source influencing factor of the given node based on the degree value of the given node in the network to be evaluated; determining the radiative centrality of the given node based on the extinction influencing factor and the radiation source influencing factor; determining the importance of the given node based on the radiative centrality and ranking them to obtain a node importance ranking sequence. This invention applies the light radiative transfer theory from atmospheric physics to the identification of node importance in a network, which can simultaneously consider both local and global information of the network, accurately and effectively evaluate and rank the importance of nodes in the network, and has strong adaptability.

Description

Technical Field

[0001] This invention belongs to the field of network analysis technology, specifically relating to a method and apparatus for evaluating the importance of network nodes based on radiation theory. Background Technology

[0002] The structure of a complex network determines its function. Identifying key nodes facilitates understanding the network's main structural characteristics, enabling more efficient and cost-effective system control. The assessment of node importance is expanding its applications as network science integrates with other disciplines, currently attracting widespread attention in sociology, biology, management, and computer science. With the development of information science and the advent of the big data era, information is characterized by explosive acquisition and rapid dissemination. Redundant information can easily overwhelm decision-makers, making node importance assessment even more fundamental and valuable. The improvement and application of node importance assessment algorithms have remained a research hotspot in the field of complex networks.

[0003] In recent years, scholars have conducted numerous studies on improving centrality metrics based on network topology. These metrics often couple local metrics (node ​​degree or core count) with global metrics (shortest path between nodes), exhibiting a certain paradigm, and their ranking results are significantly influenced by parameter settings and network structure. When considering the dynamic propagation of information in a network, purely static topology metrics are not suitable for examining high-influence nodes. For existing influence diffusion metrics, weighted fusion of multiple metrics achieves complementary advantages and improves the results. Considering that global information is usually only relevant to the static structure of the network, some scholars have introduced economic knowledge to compare node profitability to identify network leaders. Others have drawn on natural science knowledge, using gravity formulas and laws of gravitation to consider key nodes as those with the highest sum of node gravitational values; these metrics have significantly greater physical significance than the previous ones.

[0004] Therefore, the critical node identification problem can be innovated by integrating knowledge from multiple disciplines, thus transforming it from a purely network science problem based solely on mathematics and network topology. Currently, there are no applications of atmospheric physics' theory of light radiation transfer to identify the importance of nodes in networks. Summary of the Invention

[0005] This invention provides a method and apparatus for evaluating the importance of network nodes based on radiation theory, which solves the problem in the prior art that the theory of light radiation transmission in atmospheric physics is not applied to the identification of the importance of nodes in the network in order to accurately and effectively identify the importance of nodes in the network.

[0006] To achieve the above objectives, this invention proposes a method for evaluating the importance of network nodes based on radiation theory, comprising: obtaining the extinction degree generated by radiation from any node to other nodes in the network to be evaluated based on radiation theory, thereby obtaining the extinction influencing factors of the given node; determining the radiation source influencing factors of the given node based on the degree value of the given node in the network to be evaluated; determining the radiation centrality of the given node based on the extinction influencing factors and the radiation source influencing factors; determining the importance of the given node based on the radiation centrality and ranking them to obtain a node importance ranking sequence.

[0007] Optionally, the step of obtaining the extinction degree generated by radiation from any node to other nodes in the network to be evaluated based on radiation theory, and obtaining the extinction influencing factors of any node, includes: obtaining the shortest path from any node i to any other node j based on the network to be evaluated; calculating the attenuation factor and scattering factor of any node i to any other node j based on the shortest path according to radiation theory; calculating the product of the attenuation factor and scattering factor of any node i to any other node j to obtain the extinction degree generated from any node i to any other node j; and summing the extinction degrees generated from any node i to all other nodes j to obtain the extinction influencing factors of any node i.

[0008] Optionally, the calculation of the attenuation factor and scattering factor from any node i to any other node j based on the shortest path according to radiation theory includes: calculating the attenuation factor from any node i to any other node j based on the reduction law of monochromatic radiation, the shortest path, and a preset absorption coefficient; and calculating the product of the scattering effects of the energy at each node along the shortest path by analogy with the scattering law to obtain the scattering factor from any node i to any other node j.

[0009] Optionally, the attenuation law based on monochromatic radiation calculates the attenuation factor from any node i to any other node j according to the shortest path and a preset absorption coefficient, including: if the network to be evaluated is an unweighted network, then the following relationship is applied to calculate the attenuation factor from any node i to any other node j on the shortest path d. ij The attenuation factor on the given surface is used to obtain the attenuation factor from any node i to any other node j: exp(-α·d ij ), where α is the absorption coefficient; if the weights of each edge in the network to be evaluated are considered, the following relationship is applied to perform piecewise weighted summation of the absorption coefficient according to the shortest path to obtain the attenuation factor from any node i to any other node j: Among them, w Λ The shortest path d from node i to node j ij The weights of the Λth edge and the edge.

[0010] Optionally, the step of calculating the product of the scattering effects of energy at each node along the shortest path using analogous scattering laws to obtain the scattering factor from any node i to any other node j includes: disregarding the shortest path d. ij Given the starting and ending points, the shortest path d is calculated by analogy with the scattering law. ij The scattering factor from any node i to any other node j is obtained by multiplying the scattering effects of the -1 nodes: in, The shortest path d from node i to any other node j ij The degree of the m-th node passed through, and β is the hyperparameter to be adjusted.

[0011] Optionally, determining the radiative centrality of any node i based on the extinction influence factor and the radiation source influence factor in the network to be evaluated includes: calculating the product of the extinction influence factor and the radiation source influence factor for any node i in the network to be evaluated using the following relationship to obtain the radiative centrality RC of any node i. i :

[0012]

[0013] Among them, SI i For any node i, the radiation source influencing factor, SI i =k i γ γ is the hyperparameter to be adjusted, k i Let EI be the degree value at any node i. i The extinction influencing factors for any node i, where α is the absorption coefficient. The shortest path d from node i to any other node j ij The degree of the m-th node traversed, β is the hyperparameter to be adjusted, and d ij Let be the shortest path from node i to node j.

[0014] Optionally, the network node importance assessment method further includes: calculating the proportion of the number of nodes in the most connected component after removing a node to the total number of nodes according to the importance of each node in the node importance ranking sequence from high to low; plotting a curve with the number of removed nodes as the horizontal axis and the proportion of the number of nodes in the most connected component after removing a node to the total number of nodes as the vertical axis; calculating the area under the curve, and evaluating the quality of the node importance ranking sequence based on the area.

[0015] Based on the same inventive concept, this invention also proposes a network node importance assessment device based on radiation theory, comprising: an extinction influencing factor acquisition unit, used to acquire the extinction degree generated by radiation from any node to other nodes in the network to be assessed based on radiation theory, thereby obtaining the extinction influencing factor of the stated node; a radiation source influencing factor acquisition unit, used to determine the radiation source influencing factor of the stated node based on the degree value of any node in the network to be assessed; and an importance ranking unit, used to determine the radiation centrality of any node based on the extinction influencing factor and the radiation source influencing factor of any node in the network to be assessed, determine the importance of the stated node based on the radiation centrality, and rank them to obtain a node importance ranking sequence.

[0016] Based on the same inventive concept, the present invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the network node importance assessment method based on radiation theory as described above.

[0017] Based on the same inventive concept, the present invention also proposes a computer storage medium storing at least one executable instruction that causes a processor to execute the network node importance assessment method based on radiation theory as described above.

[0018] As can be seen from the above, the beneficial effects of the technical solution provided by the present invention are as follows: The present invention provides a method and apparatus for evaluating the importance of network nodes based on radiation theory. The method includes: obtaining the extinction degree generated by radiation from any node to other nodes in the network to be evaluated based on radiation theory, and obtaining the extinction influencing factors of the any node; determining the radiation source influencing factors of the any node based on the degree value of the any node in the network to be evaluated; determining the radiation centrality of the any node based on the extinction influencing factors and the radiation source influencing factors of the any node in the network to be evaluated; determining the importance of the any node based on the radiation centrality and ranking them to obtain a node importance ranking sequence. This method applies the light radiation transfer theory in atmospheric physics to the identification of node importance in the network, which can simultaneously consider the local and global information of the network, accurately and effectively evaluate and rank the importance of nodes in the network, and has strong adaptability. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the network node importance assessment method based on radiation theory according to an embodiment of the present invention.

[0021] Figure 2 These are example diagrams of four medium-sized real-world networks according to embodiments of the present invention;

[0022] Figure 3 This is a schematic diagram comparing the Kendall correlation coefficients of the network node importance assessment method based on radiation theory in this embodiment of the invention with existing methods.

[0023] Figure 4 This is a schematic diagram comparing the network node importance assessment method based on radiation theory of this invention with the network disintegration efficiency of existing methods.

[0024] Figure 5 This is a schematic diagram of the network node importance assessment device based on radiation theory according to an embodiment of the present invention;

[0025] Figure 6 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0027] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms "first," "second," and similar terms used in the embodiments of this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are only used to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0028] This invention implements a method for evaluating the importance of network nodes based on radiation theory, such as... Figure 1 As shown, network node importance assessment methods based on radiation theory include:

[0029] Step S11: Based on radiation theory, obtain the extinction degree generated by radiation from any node to other nodes in the network to be evaluated, and obtain the extinction influencing factors of any node.

[0030] Radiation is ubiquitous in the real physical environment and is a form of energy transfer, such as acoustic radiation in acoustics, optical radiation in optics, electromagnetic radiation in electricity, and thermal radiation in thermodynamics. These types of radiation share a common characteristic: they continuously release energy outward from the source. During transmission, this energy is generally attenuated by noise or other interference in the medium. When encountering obstacles in different media, the direction and energy value of the transmission can change significantly. To illustrate, imagine throwing a stone into water; the resulting ripples spread outward in concentric circles. When these ripples hit a fallen leaf on the water's surface, their propagation direction no longer spreads radially outward; instead, they reform into a weakened, diffuse wave behind the leaf. There is a correlation between radiation and the importance of network nodes. If a node emits energy that leaves a greater residual energy after traversing the remaining nodes, then that node is likely more important.

[0031] The intensity of light radiation is mainly affected by two factors: the strength of the light source and the energy changes along the propagation path. Taking atmospheric radiation as an example, the Earth's atmosphere contains various particles, including aerosols of various shapes and sizes, as well as cloud droplets and ice crystals. The process by which light travels from the sun to the Earth's outer atmosphere and continues to radiate towards the ground involves an extinction process before it can be utilized by terrestrial organisms. This process includes absorption, scattering, and reflection by the medium. Simplifying, the extinction process generally consists of scattering and absorption.

[0032] In step S11, optionally, the shortest path from any node i to any other node j is obtained based on the network to be evaluated; the attenuation factor and scattering factor of any node i to any other node j are calculated based on the shortest path according to radiation theory; the product of the attenuation factor and scattering factor of any node i to any other node j is calculated to obtain the extinction degree produced by any node i to any other node j; the extinction degree produced by any node i to each other node j is summed to obtain the extinction influencing factors of any node i.

[0033] When only the reduction in radiation caused by absorption is considered, the reduction law of monochromatic radiation is as follows:

[0034]

[0035] The visible light radiation energy I is lost exponentially over a distance of 0 to s1, where k is the absorption coefficient and ρ is the optical quality along each integration path.

[0036] In this embodiment of the invention, based on the attenuation law of monochromatic radiation, the attenuation factor from any node i to any other node j is calculated according to the shortest path and a preset absorption coefficient. Specifically, if the network to be evaluated is an unweighted network, the following relationship is applied to calculate the attenuation factor from any node i to any other node j along the shortest path d. ij The attenuation factor on the given surface is used to obtain the attenuation factor from any node i to any other node j: exp(-α·d ij ), where α is the absorption coefficient. That is, since it is an unweighted network, d can be obtained by directly adding the edges of the shortest path. ij If the weights of each edge in the network to be evaluated are considered, the following relationship is applied to perform a piecewise weighted summation of the absorption coefficients based on the shortest path to obtain the attenuation factor from any node i to any other node j: Among them, w Λ The shortest path d from node i to node j ij The weights of the Λth edge and the α-th edge are given. A larger weight results in lower loss on the shortest path. Embodiments of this invention can adjust the information loss of the shortest path by changing the value of α.

[0037] Light scattering is a complex process. When the diameter of the scattering particles is much smaller than the wavelength of the incident light, typically less than 1 / 10 of the wavelength, Rayleigh scattering occurs. The intensity is inversely proportional to the fourth power of the wavelength, resulting in the lowest scattering efficiency, with scattering almost evenly distributed forward and backward. When the particle size increases to a level comparable to the wavelength, Mie scattering occurs. The intensity is inversely proportional to the square of the wavelength, and the scattering intensity weakens as the particle size increases, while forward scattering continuously strengthens with increasing particle diameter.

[0038] In this embodiment of the invention, the scattering factor from any node i to any other node j is obtained by calculating the product of the scattering effects at each node along the shortest path using the analogy scattering law. Specifically, the shortest path d is disregarded. ij Given the starting and ending points, the shortest path d is calculated by analogy with the scattering law. ij The scattering factor from any node i to any other node j is obtained by multiplying the scattering effects of the -1 nodes: in, The shortest path d from node i to any other node j ij Let β be the degree of the m-th node traversed, and let β be the hyperparameter to be adjusted. In different physical contexts, such as the spread of rumors or infectious diseases, the information at a node may be primarily gain (β > 0), primarily dissipation (β < 0), or remain unchanged (β = 0). Therefore, β can be adjusted to change the degree.

[0039] The extinction degree produced by any node i in the network to be evaluated to any other node j is the product of the attenuation factor and the scattering factor of any node i to any other node j. By traversing all connectable nodes j (j≠i) of node i and summing the global extinction degrees, the extinction influencing factors of any node i are obtained:

[0040]

[0041] Among them, EI i For any node i, the extinction factor is the attenuation factor used here, which is the attenuation factor of the unweighted network exp(-α·d). ij If each edge in the network to be evaluated has a weight, then the corresponding decay factor is used.

[0042] Step S12: Determine the radiation source influencing factors of any node based on the degree value of any node in the network to be evaluated.

[0043] In this embodiment of the invention, if it is necessary to consider the radiation source intensity of different nodes, a light source intensity term can be defined. Analogously, for network nodes, this corresponds to whether or not local information of the node is considered. The degree value at node i is defined as k. i Therefore, the factors influencing the radiation source at any node i are obtained: γ is the hyperparameter to be tuned, where γ = 0 or γ > 0. γ = 0 indicates that local information is not considered. γ > 0 indicates that local information is considered. Generally, the larger the degree value at a node, the stronger the radiation source. For example, a more influential online celebrity possesses more dissemination resources.

[0044] Step S13: Determine the radiative centrality of any node in the network to be evaluated based on the extinction influencing factors and the radiation source influencing factors, determine the importance of any node based on the radiative centrality and sort them to obtain a node importance ranking sequence.

[0045] In this embodiment of the invention, the radiation value resulting from the combined effect of SI and EI at node i is defined as the radiative centrality RC of node i. Optionally, the radiative centrality RC of any node i in the network to be evaluated is obtained by calculating the product of the extinction influence factor and the radiation source influence factor using the following formula. i :

[0046]

[0047] Among them, SI i For any node i, the radiation source influencing factor, SI i =k i γ γ is the hyperparameter to be adjusted, ki Let EI be the degree value at any node i. i The extinction influencing factors for any node i, where α is the absorption coefficient. The shortest path d from node i to any other node j ij The degree of the m-th node traversed, β is the hyperparameter to be adjusted, and d ij EI is the shortest path from node i to node j. i The attenuation factor can be adopted from the attenuation factor of the unweighted network, exp(-α·d), depending on the different networks being evaluated. ij (or each edge has a weight corresponding to the decay factor of the network to be evaluated)

[0048] It can be seen that the radiative centrality RC of any node i i There are three hyperparameters α, β, and γ. Different values ​​of these three hyperparameters represent different physical meanings, therefore, the radiative centrality RC i Fine-tuning can be performed based on the properties of different networks to achieve RC radiation centrality. i It possesses a degree of flexibility and is not applied uniformly to networks with significant differences. Furthermore, because it employs a summation method, the radiative centrality RC... i The same applies to disconnected graphs. Simply extract the nodes of each connected subgraph in sequence. The summation will only give the sum of the radiation values ​​of the subgraph in which the node is located. The smaller the size of the subgraph in which the node is located, the greater the likelihood that it is of low importance.

[0049] The following compares the effectiveness of eight existing baseline metrics with the radiation centrality (RC) proposed in this invention for different networks (small-to-medium-sized simulated networks and real networks). The eight baseline metrics include: degree centrality (DC), proximity centrality (CC), betweenness centrality (BC), information centrality (IC), eigenvector centrality (EC), PageRank value (PR), gravity centrality (GC), and natural connectivity (NC).

[0050] In this embodiment of the invention, the standard susceptible-infective-recovered or removed (SIR) model is used to evaluate the actual propagation impact of nodes. A selected node in the network is sequentially designated as an I node, and the other nodes as S nodes. At each time step, each I node can infect its neighboring S nodes with an infection probability β0, transforming them into I nodes. Then, at the next time step, the original I node recovers from the disease with probability μ, becoming an R node with immunity. The subsequently infected I nodes continue to infect their S nodes. The SIR process is repeated until no new I nodes are generated, representing a steady state. The number of R nodes is calculated to reflect the true impact range of the initially selected nodes. In this embodiment, μ is uniformly set to 1.0 because the μ value only affects the time step for reaching a steady state, and β0∈[0,1] is taken to be slightly larger than the propagation threshold β. th The value of β th If β is 0.309, then β0 is set to 0.31 to meet the conditions for the spread of infectious diseases. In this embodiment of the invention, the influence of each node is first calculated using different metrics, sorted in descending order, and then each ranked node is regarded as a seed node. The number of infected nodes is obtained by substituting the node into the SIR model. The more critical the node, the more infected nodes there are. To ensure the reliability of the results, all nodes must undergo at least 1000 independent experiments and then the average value is taken. The Kendall correlation coefficient between the ranking results of different indicators and the SIR (infectious disease) ranking results is calculated to evaluate the effectiveness of different indicators.

[0051] Kendall correlation coefficient is used to express the degree of matching between two sequences S1 and S2:

[0052]

[0053] Where τ(S1,S2) is the Kendall correlation coefficient between two sequences S1 and S2, and N is the total number of combinations in sequences S1 and S2. c and N d These represent the number of consistent and inconsistent pairs, respectively. Similar to the Pearson correlation coefficient used to compare quantitative variables, the larger the absolute value of the Kendall correlation coefficient, the closer the Kendall correlation coefficient is to 1 or -1, indicating a stronger correlation; the closer the Kendall correlation coefficient is to 0, the weaker the correlation. The closer the ranking result obtained here is to +1, the more effective the algorithm is. It is evident that compared to the other eight types of algorithms, RC's ranking results are more reliable in the example network.

[0054] The embodiments of this invention verify the applicability and effectiveness of radiation centrality by applying eight basic key node identification algorithms, such as DC and BC, to network models generated through simulation and real complex networks existing in the real world, along with the RC algorithm proposed in the embodiments of this invention.

[0055] First, a random network is generated through simulation. The three classic network models are the ER network, the Watts-Strogatz network (WS), and the scale-free network (Barabasi-Albert network, BA), all with 200 nodes. The ER network is generated according to a fixed number of nodes and a fixed probability of edge connections, involving the parameter PER, which represents the probability of an edge connecting any two distinct nodes. Setting PER = 0.01, the constructed network is a disconnected graph (therefore, the IC index cannot be used to rank this network). The ER network is often used as a reference, considered the lowest-order zero model. The WS network model involves two parameters, KWS and PWS. KWS indicates that each node in the network is only connected to its KWS nearest neighbors, and PWS represents the reconnection probability of all links in the network. Setting KWS = 4 and PWS = 0.001, the WS model simulates networks with small-world and clustering characteristics. The BA network model involves a parameter m, representing the number of links added to existing nodes by a newly added node. That is, each new node adds m new links, which are preferentially added to existing nodes; here, m = 4. The BA model is a simulation of a network with a power-law degree distribution based on preferred connections. The structural parameters of the three simulated networks obtained are shown in Table 1.

[0056] Table 1 Basic structural parameters of the simulation network

[0057]

[0058] In the table, N and M represent the number of nodes and edges in the network, respectively. <k>Km and C represent the average degree and maximum degree, respectively; CC is the average clustering coefficient; r is the network's matching coefficient; H represents degree heterogeneity; and β... th This is the threshold for network propagation referenced in the SIR model.

[0059] The isomatch coefficient r reveals the degree correlation of a network (i.e., the Pearson correlation coefficient), that is, the tendency for nodes with similar degree values ​​to connect to each other:

[0060]

[0061] Wherein, cov(k) i k j ) represents sequence k i and sequence k j The covariance, Var(k) i k j ) represents sequence k i and sequence k j The variance of the network. If, overall, nodes with higher degree tend to be connected to nodes with higher degree, then the network is said to be positively correlated in degree, or the network is homogamous (r > 0); if, overall, nodes with higher degree tend to be connected to nodes with lower degree, then the network is said to be negatively correlated in degree, or the network is heterogamous (r < 0).

[0062] Degree heterogeneity H is used to describe the degree heterogeneity of a network's degree distribution. It can be defined in various ways. Here, H is defined as shown in the following formula. The defined H always satisfies H≥1. The higher the degree heterogeneity, the larger the value of H.

[0063]

[0064] in, <k>For average degree, <k 2 > represents the second-order average degree.

[0065] Propagation threshold β th It is closely related to the connectivity structure of the network, and its definition is shown in the following formula:

[0066]

[0067] In the SIR model, the prevalence rate is zero when the infection rate is below a threshold, and finite when it is above this threshold.

[0068] Most complex networks in the real world possess scale-free characteristics. Compared to other models, the BA network is more representative of the general characteristics of real-world networks. Comparing the three simulated networks in Table 1, it can be found that the BA network is more prone to large-degree nodes, exhibits stronger heterogeneity and degree heterogeneity, and has a lower contagion threshold, making contagion more likely to occur, compared to the ER and WS networks.

[0069] The network repository is an interactive network database that stores thousands of real-world network data sets. Due to limitations in computing power, this embodiment of the invention selects... Figure 2 The four medium-sized real-world networks shown are (a) Wiki-Vote, a social network for voting to elect administrators on Wikipedia; (b) Dolphins, a social network for long-beaked dolphins; and (c) and (d) Infect-hyper and Infect-dublin, two different types of infectious disease transmission networks.

[0070] Table 2 shows the basic structural parameters of the four real networks selected.

[0071]

[0072] Table 2 calculates the basic structural parameters of the four selected networks. N and M are the number of nodes and edges of the network, respectively. It can be seen that the Dolphins network is the smallest, while the other three networks are of moderate size. <k>The largest is Infect-hyper. Taking the Infect-hyper network as an example, let's compare the structural properties of various networks, combined with... Figure 2 (c) It can also be observed that the connections between its nodes are more compact, and the average clustering coefficient CC also shows the strongest compactness. The network propagation threshold β th The lowest value indicates that the spread of infectious diseases is more likely to occur, the degree of heterogeneity H is the lowest, and the isomatch coefficient r is negative.

[0073] Because the hyperparameters determined by different network structures may not be consistent, the RC index needs to determine the values ​​of three hyperparameters. The specific steps are as follows: (1) Apply the SIR model to the constructed ER, WS, and BA networks to perform propagation simulation and obtain the node importance ranking results of each network, which are used as a reference; (2) Take the values ​​of each hyperparameter of the RC index in equal arithmetic order, where α∈[0,2), β∈[-1,1), and γ∈[0,1). Since the scale of the constructed simulation network is small, γ, which is related to local effects, is not taken as a large value. The three hyperparameters each take 10 values ​​in the interval, resulting in a total of 10 values. 3 There are 10 candidate RC indicators, thus yielding 10 3 (3) Sort the importance sequence of the group nodes; (4) Calculate the Kendall correlation coefficient τ between the group undetermined sequence and the SIR sorted sequence; (5) Find the α, β, and γ corresponding to the maximum Kendall correlation coefficient τ value.

[0074] Using the SIR model's network propagation method to evaluate algorithm performance is not optimistic for certain network structures. Besides the RC metric, the reliability of the node importance ranking results for the other eight reference metrics is also low on ER and WS networks. Figure 3 The bar chart plots the Kendall correlation coefficients between the ranking results of each indicator on the three types of networks and the SIR ranking results. The upper part of the chart supplements the significance p-values ​​of the correlation significance test, and marks the thresholds for highly significant (p<0.01) and significant (p<0.05). Here, the three hyperparameters of RC are the optimal hyperparameter combinations calculated above for each model. It can be seen that for the BA network, the correlation between each indicator and the SIR ranking results is relatively high, and all of them passed the significance test, with the correlation coefficient of RC being slightly higher than other ranking methods. However, the correlation of the WS network is generally low (around τ=0.1), and the results do not meet the requirement of being highly significant. The results are neither reliable (failed the significance test) nor usable (low correlation), so this type of network is not suitable for comparison with SIR. The ER network is not connected, so the ranking results of the IC indicator cannot be obtained. Only CC, EC, PR, GC, and RC passed the significance test, and RC had the highest correlation, but it was only 0.28, which is not strong. Based on the above discussion, the following two conclusions can be drawn: (1) The evaluation effect of the algorithm evaluation standard based on the network propagation method is affected by the network structure. For example, it is more applicable to the BA network, and the results all passed the significance test; (2) By comparing the τ values ​​that passed the significance test, it can be found that the RC index has a higher τ value in different networks, which proves the performance advantage of the RC index over the reference index.

[0075] Using correlation coefficients to determine ranking results is not applicable to all networks. Therefore, this embodiment of the invention also adopts a second approach—network collapse efficiency—to judge the effectiveness of node importance ranking from the perspective of network structure. Specifically, the number of nodes in the largest connected component can be calculated to determine the structural characteristics of the network after an attack. To verify the effectiveness of the identified key nodes, nodes can be removed from the network in descending order of importance. The largest connected subgraph among the remaining nodes is calculated, and the proportion of nodes contained in it is used as an evaluation index of network robustness. Preferably, based on the node importance ranking sequence, the proportion of nodes in the largest connected component after node removal is calculated from high to low importance. A curve is plotted with the number of removed nodes as the x-axis and the proportion of nodes in the largest connected component after node removal as the y-axis. The area under the curve is calculated, and the effectiveness of the node importance ranking sequence is evaluated based on the area.

[0076] Theoretically, the more accurate the node importance ranking, the higher the efficiency of network disintegration in that order, and the more fragile the network. To make the comparison results general, it is assumed here that the propagated energy will be attenuated by scattering at the network nodes, and the local influence of the light source also has a high impact. The attenuation coefficient on the network path is referenced with the optimal hyperparameters of the BA network, and (α, β, γ) = (0.2, -0.5, 1), resulting in the final expression of RC used in the embodiments of this invention:

[0077]

[0078] On seven types of networks, including three simulated networks (Figures a-c) and four real networks (Figures d-g), Figure 4 This visually illustrates the change in the size of the largest connected component of the network after nodes are removed sequentially in descending order of importance. The horizontal axis represents the number of nodes removed, and the vertical axis represents the proportion of nodes in the largest connected component to the total number of nodes. The nine different curves in each subgraph represent different disintegration results from the nine proposed algorithm rankings. ER represents a disconnected graph, and IC has no ranking result; nodes are removed sequentially according to their index. The more important the node removed first, the higher the network disintegration efficiency, and the smaller the area under the curve. Figure 4 The thick black curve represents the network disintegration simulation results of the RC sorting algorithm. It can be seen that, except for the Infect-Dublin network where its network disintegration efficiency is relatively inferior to other algorithms, its network disintegration efficiency is at a medium-to-high level in the other six networks. The Infect-hyper network is somewhat special because its strongly coupled network structure makes any disintegration order disadvantageous in the early stages of disintegration.

[0079] To accurately compare the network breakdown efficiency of each algorithm, based on Figure 4 The results were calculated for the area under the curve, as shown in Table 3. During the calculation, the number of nodes removed on the horizontal axis was divided by the total number of nodes and normalized to the removal ratio, with a value range of [0,1]. The normalized area under the curve SR ∈ [0,0.5] was obtained from this. Comparing the area under the curves of the nine types of algorithms, the results of SR values ​​less than RC were marked with an underline. It can be found that: (1) The SR of the Infect-hyper network is slightly less than 0.5, and the network disintegration efficiency is very poor; (2) The RC index has a significant advantage. Among all the listed networks, it ranks among the top four of the nine types of algorithms. Except for the fourth place in the BA and Infect-dublin networks, it ranks among the top three in other networks. In WS, its efficiency is significantly better than other networks, ranking first; (3) The algorithms with network disintegration efficiency better than RC are mainly DC, BC, and PR. In summary, the quality of the proposed RC index is at the middle to upper level among the reference indices. This shows that the network node importance evaluation method based on radiation theory in the embodiments of the present invention can accurately and effectively evaluate and rank the importance of nodes in the network, and has strong adaptability.

[0080] Table 3. Area under the simulation curves for network disintegration of simulated and real networks.

[0081]

[0082] The differences in the ranking results of the indicators are examined based on the monotonicity coefficients shown in the following formula:

[0083]

[0084] Where N is the size of the network, N c M(X) represents the number of nodes with the same index value c. If M(X) = 1, it indicates that the sorting method is completely monotonic, and each node is classified into a different index value; M(X) = 0 indicates that all nodes are at the same level. The calculation results are shown in Table 4. It can be seen that RC is completely monotonic in most networks, which is better than classic algorithms such as DC, CC, BC, and GC, and comparable to EC and PR in terms of monotonicity.

[0085] Table 4 shows the monotonicity coefficients of the node importance ranking obtained by each algorithm.

[0086]

[0087] This invention proposes a novel algorithm for identifying node importance using interdisciplinary knowledge: a network node importance assessment method based on radiation theory. It employs a novel approach by applying the light radiation transmission theory from atmospheric physics to the identification of high-influence nodes in a network. This radiation centrality RC index can simultaneously consider both local and global information of the network, and the proposed node importance index has practical physical meaning. This radiation theory-based network node importance assessment method is also applicable to disconnected graphs and is computationally convenient. By comparing the node importance ranking of RC with eight classic indices in small-to-medium-sized simulated and real networks, the superiority of the proposed RC index is demonstrated in both correlation calculations with network propagation rankings and applications to network disintegration efficiency optimization. Furthermore, the ranking results obtained from RC exhibit good monotonicity, accurately and effectively assessing and ranking the importance of nodes in the network, facilitating the effective discovery of important nodes, and demonstrating strong adaptability.

[0088] In summary, the network node importance assessment method based on radiation theory in this invention obtains the extinction degree generated by radiation from any node to other nodes in the network to be assessed based on radiation theory, thus obtaining the extinction influencing factors of any node; determines the radiation source influencing factors of any node based on the degree value of any node in the network to be assessed; determines the radiative centrality of any node based on the extinction influencing factors and the radiation source influencing factors of any node in the network to be assessed; and determines the importance of any node based on the radiative centrality and sorts them to obtain a node importance ranking sequence. By applying the light radiation transfer theory in atmospheric physics to the identification of node importance in the network, it can simultaneously consider the local and global information of the network, accurately and effectively assess and rank the importance of nodes in the network, and has strong adaptability.

[0089] The foregoing has described specific embodiments of the present invention. In some cases, the actions or steps described in the embodiments of the present invention may be performed in a different order than that shown in the embodiments and the desired results may still be achieved. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0090] This invention also provides a network node importance assessment device based on radiation theory, such as... Figure 5 As shown, the network node importance assessment device based on radiation theory includes: an extinction influence factor acquisition unit, a radiation source influence factor acquisition unit, and an importance ranking unit. Among them,

[0091] The extinction influencing factor acquisition unit is used to obtain the degree of extinction generated by radiation from any node to other nodes in the network to be evaluated based on radiation theory, and to obtain the extinction influencing factors of any node.

[0092] The radiation source influencing factor acquisition unit is used to determine the radiation source influencing factors of any node based on the degree value of any node in the network to be evaluated.

[0093] The importance ranking unit is used to determine the radiative centrality of any node in the network to be evaluated based on the extinction influencing factors and the radiation source influencing factors, determine the importance of any node based on the radiative centrality, and rank them to obtain a node importance ranking sequence.

[0094] For ease of description, the above apparatus is described by dividing it into various functional units. Of course, in implementing the embodiments of the present invention, the functions of each unit can be implemented in one or more software and / or hardware.

[0095] The apparatus of the above embodiments is applied to the corresponding methods in the foregoing embodiments and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0096] Based on the same inventive concept, embodiments of the present invention also provide an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any of the above embodiments.

[0097] This invention provides a non-volatile computer storage medium storing at least one executable instruction that can execute the method described in any of the above embodiments.

[0098] Figure 6 This embodiment illustrates a more specific hardware structure of an electronic device, which may include a processor 601, a memory 602, an input / output interface 603, a communication interface 604, and a bus 605. The processor 601, memory 602, input / output interface 603, and communication interface 604 are interconnected internally via the bus 605.

[0099] The processor 601 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention.

[0100] The memory 602 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 602 can store the operating system and other application programs. When the technical solution provided by the method embodiment of the present invention is implemented by software or firmware, the relevant program code is stored in the memory 602 and is called and executed by the processor 601.

[0101] Input / output interface 603 is used to connect input / output modules to realize information input and output. Input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touch screens, microphones, various sensors, etc., and output devices may include displays, speakers, vibrators, indicator lights, etc.

[0102] The communication interface 604 is used to connect a communication module (not shown in the figure) to enable communication between this device and other devices. The communication module can communicate via wired means (e.g., USB, Ethernet cable) or wireless means (e.g., mobile network, Wi-Fi, Bluetooth).

[0103] Bus 605 includes a pathway for transmitting information between various components of the device (e.g., processor 601, memory 602, input / output interface 603, and communication interface 604).

[0104] It should be noted that although the above-described device only shows the processor 601, memory 602, input / output interface 603, communication interface 604, and bus 605, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of the present invention, and not necessarily all the components shown in the figures.

[0105] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this disclosure (including the claims) is limited to these examples; within the framework of this disclosure, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of the present invention as described above, which are not provided in detail for the sake of brevity.

[0106] The embodiments of this invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this invention should be included within the scope of protection of this disclosure.< / k> < / k> < / k>

Claims

1. A method for evaluating the importance of network nodes based on radiation theory, characterized in that, The network node importance assessment method includes: The extinction degree generated by radiation from any node to other nodes in the network to be evaluated is obtained based on radiation theory, and the extinction influencing factors of any node are obtained, including: obtaining the shortest path from any node i to any other node j based on the network to be evaluated; calculating the attenuation factor and scattering factor of any node i to any other node j based on the shortest path according to radiation theory; calculating the product of the attenuation factor and scattering factor of any node i to any other node j to obtain the extinction degree generated from any node i to any other node j; summing the extinction degrees generated from any node i to all other nodes j to obtain the extinction influencing factors of any node i. The radiation source influencing factors of any node are determined based on the degree value of any node in the network to be evaluated. The radiative centrality of any node in the network to be evaluated is determined based on the extinction influencing factors and the radiation source influencing factors. The importance of any node is then determined and ranked based on the radiative centrality, resulting in a node importance ranking sequence.

2. The network node importance assessment method as described in claim 1, characterized in that, The calculation of the attenuation factor and scattering factor from any node i to any other node j based on radiation theory and the shortest path includes: Based on the reduction law of monochromatic radiation, the attenuation factor from any node i to any other node j is calculated according to the shortest path and the preset absorption coefficient. The scattering factor from any node i to any other node j is obtained by calculating the product of the scattering effects of the energy at each node along the shortest path using the analogy scattering law.

3. The network node importance assessment method as described in claim 2, characterized in that, The attenuation law based on monochromatic radiation calculates the attenuation factor from any node i to any other node j according to the shortest path and a preset absorption coefficient, including: If the network to be evaluated is an unweighted network, then the following relationship is applied to calculate the shortest path from any node i to any other node j. The attenuation factor on the given surface is used to obtain the attenuation factor from any node i to any other node j: ,in, The absorption coefficient; If the weights of each edge in the network to be evaluated are considered, the following relationship is applied to perform a piecewise weighted summation of the absorption coefficients based on the shortest path to obtain the attenuation factor from any node i to any other node j: ,in, The shortest path from node i to node j and the The weight of the edge.

4. The network node importance assessment method as described in claim 2, characterized in that, The step of calculating the product of the scattering effects of energy at each node along the shortest path using analogous scattering laws to obtain the scattering factor from any node i to any other node j includes: The shortest path is not considered. Given the starting and ending points, the shortest path is calculated by analogy with the scattering law. The product of the scattering effects of each node is used to obtain the scattering factor from any node i to any other node j: ,in, The shortest path from node i to any other node j The degree of the m-th node passed through. These are the over-parameters to be adjusted.

5. The network node importance assessment method as described in claim 1, characterized in that, The step of determining the radiative centrality of any node based on the extinction influence factors and the radiation source influence factors of any node in the network to be evaluated includes: The product of the extinction influence factor and the radiation source influence factor for any node i in the network to be evaluated is calculated using the following formula to obtain the radiative centrality of any node i. : in, The radiation source influencing factors for any node i. , The hyperparameter to be adjusted. Let be the degree value at any node i. The extinction influencing factors for any node i. The absorption coefficient is... The shortest path from node i to any other node j The degree of the m-th node passed through. The hyperparameter to be adjusted. Let be the shortest path from node i to node j.

6. The network node importance assessment method as described in claim 1, characterized in that, The network node importance assessment access method also includes: Based on the importance of each node in the node importance sorting sequence, calculate the proportion of the number of nodes in the most connected component to the total number of nodes after removing a node, in descending order of the importance of each node; Plot a curve with the number of nodes removed as the x-axis and the ratio of the number of nodes in the most connected component after node removal to the total number of nodes as the y-axis. Calculate the area under the curve and evaluate the quality of the node importance ranking sequence based on the area.

7. A network node importance assessment device based on radiation theory, characterized in that, The network node importance assessment includes: The extinction influencing factor acquisition unit is used to obtain the extinction degree generated by radiation from any node to other nodes in the network to be evaluated based on radiation theory, and to obtain the extinction influencing factor of the given node. This includes: obtaining the shortest path from any node i to any other node j based on the network to be evaluated; calculating the attenuation factor and scattering factor of any node i to any other node j based on the shortest path according to radiation theory; calculating the product of the attenuation factor and scattering factor of any node i to any other node j to obtain the extinction degree generated from any node i to any other node j; and summing the extinction degrees generated from any node i to all other nodes j to obtain the extinction influencing factor of any node i. The radiation source influencing factor acquisition unit is used to determine the radiation source influencing factors of any node based on the degree value of any node in the network to be evaluated. The importance ranking unit is used to determine the radiative centrality of any node in the network to be evaluated based on the extinction influencing factors and the radiation source influencing factors, determine the importance of any node based on the radiative centrality, and rank them to obtain a node importance ranking sequence.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the network node importance assessment method based on radiation theory as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the network node importance assessment method based on radiation theory as described in any one of claims 1 to 6.

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