A method for identifying the importance of high-order structures in complex networks

Abstract

This invention provides a method for identifying the importance of higher-order structures in complex networks. The specific steps are as follows: Step (1): Calculate the attribute values ​​of higher-order structures in the network, specifically including: Step 1.1 Calculate the size of the higher-order structure. Step 1.2 Calculate the degree deviation of the higher-order structure. Step 1.3 Calculate the circle-to-circle ratio deviation of the higher-order structure. Step (2): Construct an evaluation model for the importance of higher-order structures in the network. Step (3): Use the particle swarm optimization algorithm to solve for the optimized weight coefficients and obtain the importance ranking of higher-order structures in the complex network, specifically including: Step 3.1 Construct and initialize the particle swarm. Step 3.2 Optimize the particle swarm to obtain the optimization results. Step 3.3 Obtain the importance ranking of higher-order structures in the complex network. This invention comprehensively considers the mutual influence between the attributes of nodes in the network and the higher-order structures they form. It uses indicators such as the size of the higher-order structure, the degree deviation, and the circle-to-circle ratio deviation as importance evaluation indicators, breaking through the current limitation of only considering the attributes of nodes themselves. This effectively identifies important higher-order structures in the network and is of great significance for the cascading failure propagation and control of complex networks.

Description

(I) Technical Field

[0001] This invention relates to the field of important node identification technology in network science, and to a method for identifying the importance of high-order structures in complex networks. (II) Background Technology

[0002] In recent years, human group activities and social relationships have been developing in a network-based direction. Different systems in the real world can be abstracted into complex networks, such as social networks, transportation networks, and power networks. Complex network theory abstracts things into nodes and the relationships between things into edges, revealing the laws governing complex systems more clearly. The heterogeneity of nodes significantly affects the structure and function of networks. Identifying influential nodes in a network using quantitative analysis methods has important theoretical significance and application value for preventing and controlling disease outbreaks, promoting or inhibiting information dissemination, and avoiding cascading failures in power grid infrastructure. Therefore, the discovery of important nodes is one of the most critical issues in the fields of network attacks, network flow propagation, and control.

[0003] Current research on the identification of important nodes in complex networks has been gradually improved, including methods such as nearest neighbor-based ranking, path-based ranking, node removal and shrinkage-based ranking, and feature vector-based ranking. Different node importance evaluation methods reflect the importance of nodes from different perspectives, but they neglect the contribution of the higher-order structures formed by nodes to complex networks, failing to accurately identify important higher-order structures in the network. Therefore, proposing a network node importance identification method based on higher-order structures is urgently needed. (III) Summary of the Invention

[0004] This invention proposes a method for identifying the importance of higher-order structures in complex networks, aiming to solve the problem of identifying important higher-order structures in complex networks. This invention comprehensively considers the mutual influence between the attributes of nodes themselves and the higher-order structures they form, using indicators such as the size of the higher-order structures, degree deviation, and cycle-ring ratio deviation as importance evaluation metrics. This overcomes the limitation of current methods that only consider node attributes, and more effectively identifies important higher-order structures in networks. The specific steps are as follows:

[0005] Step (1): Calculate the higher-order structural property values ​​of the network, specifically including:

[0006] Step 1.1 Calculate the size of the higher-order structure.

[0007] Step 1.2 Calculate the degree of deviation of higher-order structure degree.

[0008] Step 1.3 Calculate the degree of deviation of the ring ratio of the higher-order structure.

[0009] Step (2): Construct a network high-order structure importance evaluation model.

[0010] Step (3): The particle swarm optimization algorithm is used to solve for the optimized weight coefficients and obtain the importance ranking of higher-order structures in the complex network, specifically including:

[0011] Step 3.1 Construct and initialize the particle swarm.

[0012] Step 3.2 Particle swarm optimization is performed to obtain the optimization results.

[0013] Step 3.3 Obtain the importance ranking of high-order structures in complex networks. (iv) Description of the attached drawings

[0014] Figure 1 This is a schematic diagram of a method for identifying important network nodes based on a high-order structure according to the present invention. (V) Detailed Implementation

[0015] Exemplary embodiments of the present invention have been described in detail below with reference to the accompanying drawings. The following description includes specific details to aid understanding, but these details should be shown as exemplary only. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the various instances described herein without departing from the scope and spirit of this disclosure. Furthermore, descriptions of well-known functions and structures have been omitted for clarity and brevity.

[0016] The terms and words used in the following description and claims are not limited to their literal meaning, but are intended only for the clear and consistent understanding of the inventors in carrying out the invention. Therefore, it will be clear to those skilled in the art that the following description of various exemplary embodiments of the invention is provided for illustrative purposes only and is not intended to limit the invention as defined by the appended claims and their equivalents.

[0017] Step (1): Calculate the higher-order structural property values ​​of the network. Specifically, this includes:

[0018] Step 1.1: The size of higher-order structures in a network can be represented by the number of nodes in the structure. The set of nodes for the s-th higher-order structure in the network. Where len s Let be the size of the s-th higher-order structure of the network.

[0019] Step 1.2: The degree deviation of higher-order structures can be reflected by the degree deviation between the degree of each node in the higher-order structure and the average degree of the network. The calculation is as follows:

[0020]

[0021] Where η1 is the weighting coefficient for the deviation of higher-order structure degree, η1∈[0,1]; k i It is the degree of the i-th node in the higher-order structure. <k>σ represents the average degree of the network. i It is a Boolean variable, if k i < <k>Then σ i =1, otherwise σ i =0; It represents the maximum negative deviation of the node degree in the network; It represents the maximum positive deviation of the node degree in the network.

[0022] Step 1.3: The deviation of the loop ratio in a higher-order structure can be reflected by the deviation between the loop ratio of each node in the higher-order structure and the average loop ratio of the network. The calculation is as follows:

[0023]

[0024] Where η2 is the weighting coefficient for the degree of deviation of the higher-order structure loop, η2∈[0,1]; r i It is the ring ratio of the i-th node in the higher-order structure. <r>The average circle ratio of the network; It is a Boolean variable, if r i < <r>,but otherwise It represents the maximum negative deviation of the ring ratio of nodes in the network; It represents the maximum positive deviation of the node ring ratio in the network.

[0025] Example 1: Taking Ryanair's network as an example, the network has 383 nodes, 1202 edges, a maximum node degree of 85, an average network degree of 6.5, and an average cycle ratio of 24.1226. s The value can be a positive integer greater than or equal to 3, and the attribute values ​​of each higher-order structure can be calculated according to formulas (1) and (2). and

[0026] Step (2): Construct a network high-order structure importance evaluation model.

[0027] In the operation of a network, nodes do not exist independently; their cooperation with surrounding nodes is crucial for the network's proper functioning. Therefore, this invention comprehensively considers the mutual influence of the nodes' own attributes and the higher-order structures they form within the network, using indicators such as the size of the higher-order structure, degree deviation, and cycle-to-ring ratio deviation as importance evaluation metrics, calculated as follows:

[0028]

[0029] Among them, I s Let be the importance of the s-th higher-order structure in the network.

[0030] Example 2, continued from Example 1.

[0031] Taking the Ryanair network as an example, considering indicators such as the size of higher-order structures, the degree of deviation of higher-order structures, and the degree of deviation of higher-order structure loops, the attribute values ​​of each higher-order structure in the network are calculated according to formulas (1) and (2). Subsequently, under the initial randomization conditions of η1 and η2, the importance index of the higher-order structures of the network is initially obtained through formula (3).

[0032] Step (3): Use the particle swarm optimization algorithm to solve for the optimized weight coefficients and obtain the importance ranking of high-order structures in complex networks.

[0033] To obtain the optimal network higher-order structure importance evaluation model, the weight coefficients η1 and η2 in formulas (1) and (2) need to be optimized. Specifically, this includes:

[0034] Step 3.1: Construct and initialize the particle swarm. Construct a particle swarm containing Num particles and initialize the initial state of each particle. and speed

[0035] Each particle represents a weight allocation in an importance evaluation model. Step 3.2: Particle swarm optimization to obtain the optimization result. Based on a typical particle swarm optimization algorithm, using the maximum size of the connected sub-cluster after node failure as the objective value, and the particle weight coefficients η1 and η2 as variables, optimization is performed within a specified number of iterations. Iterative experiments are conducted to obtain the optimization result.

[0036] Step 3.3: Obtain the importance ranking of higher-order structures in the complex network. Based on the optimized weight coefficients η1 and η2 obtained in Step 3.2, recalculate the importance of higher-order structures in the complex network according to formulas (1)-(3), and sort them in descending order to obtain the important higher-order structures in the network.

[0037] Example 3, continued from Example 2.

[0038] Taking Ryanair's network as an example, let Num = 1000, and initialize the initial state of each particle. and speed Clearly, each particle represents a weight allocation in an importance evaluation model. Under the random node removal mode, the maximum size of the network's connected sub-clusters after failure is evaluated based on the weight allocation of each particle. The velocity and position of the particle swarm are updated according to a typical particle swarm optimization algorithm, allowing the particles to optimize within the solution space to find the optimal result, which represents the optimization results of the weight coefficients η1 and η2. Subsequently, the optimized weight coefficients η1 and η2 are substituted back into step 2, and the importance of higher-order structures in the complex network is recalculated according to formulas (1)-(3). These are then sorted in descending order to obtain the important higher-order structures in the network.

[0039] This invention comprehensively considers the mutual influence between the attributes of nodes in the network and the higher-order structures they form. It uses indicators such as the size of the higher-order structure, the degree of deviation, and the degree of deviation of the circle-to-circle ratio as importance evaluation indicators, breaking through the current limitation of only considering the attributes of the nodes themselves. It effectively identifies important higher-order structures in the network and is of great significance for the propagation and control of cascading failures in complex networks.

[0040] The examples described above illustrate in detail the implementation of various parts of the present invention. The specific implementation of the present invention is not limited thereto. For those skilled in the art, all obvious changes made to the method without departing from the spirit and scope of the claims are within the protection scope of the present invention.< / r> < / r> < / k> < / k>

Claims

1. A method for identifying the importance of high-order structures in complex networks, comprising the following steps: Step 1: Calculate the higher-order structural attribute values ​​of the network based on its topology. These structural attribute values ​​include: Size of higher-order structures Degree of deviation from higher-order structure Degree of deviation from the higher-order structure circle ; Obtain the number of nodes in each higher-order structure in the network, and construct a node set for each higher-order structure based on the number of nodes in the higher-order structure. ; in, The number of nodes in the s-th higher-order structure; The size of the higher-order structure; The degree of deviation of the higher-order structure The calculation is as follows; (1)； in, It is a weighting coefficient for the degree of deviation of higher-order structure. ; It is the degree of the i-th node in the higher-order structure. The average degree of the network; It is a Boolean variable, if ,but ,otherwise ; It represents the maximum negative deviation of the node degree in the network; It represents the maximum positive deviation of the node degree in the network; The degree of deviation of the higher-order structural circle The calculation is as follows: (2)； in, It is a weighting coefficient for the degree of deviation of the higher-order structure loop. ; It is the ring ratio of the i-th node in the higher-order structure. The average circle ratio of the network; It is a Boolean variable, if ,but ,otherwise ; It represents the maximum negative deviation of the ring ratio of nodes in the network; It represents the maximum positive deviation of the node ring ratio in the network; Step 2: Construct a network high-order structure importance evaluation model, including the following steps: Based on the size of higher-order structures Degree of deviation from higher-order structure Degree of deviation from the higher-order structure circle Calculate the initial importance of each higher-order structure in the network. ; ； Step 3: Solve for the optimized weight coefficients using the particle swarm optimization algorithm. and The steps include: ...and obtaining the importance ranking of higher-order structures in complex networks. Step 3.1: Node set based on higher-order structure Construct and initialize the particle swarm; The initial state of each particle. and speed Each particle represents a weighting coefficient allocation method for an importance evaluation model; Step 3.2: Using the maximum size of the connected sub-cluster after node failure as the target value, and the particle weight coefficients... and Using these variables, iterative experiments are conducted within a specified number of iterations to obtain the weighting coefficients. and Optimization results; Step 3.3: Based on the optimized weight coefficients and Recalculate the initial importance of higher-order structures in complex networks. The recalculated initial importance The higher-order structures in the network are sorted from largest to smallest to obtain the important higher-order structures in the network.

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