A heterogeneous network adaptive node ranking method fusing seepage switching mechanism

Abstract

The application provides a heterogeneous network adaptive node ranking method fusing seepage switching mechanism, and the method comprises the following steps: constructing a to-be-identified system into a network graph; extracting node multi-scale features to construct a cooperative disassembly index and generate a global node disassembly priority sequence; removing nodes according to the sequence, combining a topological structure difference measure and a dichotomy algorithm to accurately obtain a seepage threshold of network mutation; removing a key node set required for disintegrating network heterogeneity according to the threshold to obtain a residual network; unloading global calculation for the residual network, recalculating node dominance based on local neighborhood feedback to generate a residual reordering sequence; and splicing the key node set and the residual reordering sequence to obtain a final ranking. The seepage threshold is used as a strategy switching mechanism, the resolution failure problem of global indexes in a broken network is overcome, and the key node identification accuracy and network disassembly efficiency are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of node identification technology, specifically to an adaptive node sorting method for heterogeneous networks that incorporates a percolation switching mechanism. Background Technology

[0002] Complex systems, as an emerging interdisciplinary field, utilizes complex network models built upon nodes and edges to provide an effective abstraction and simplification method for characterizing the interactions between individuals within a system. In the structural evolution and dynamic development of complex networks, certain nodes are defined as key nodes due to their crucial supporting role in maintaining information transmission, energy exchange, or system topological stability. Accurately identifying key nodes not only has profound theoretical value but also plays an irreplaceable role in many practical scenarios, such as improving the efficiency of information dissemination in social networks, optimizing resource allocation in transportation networks, and providing scientific guidance for formulating precise intervention strategies in pandemic transmission networks.

[0003] For identifying key nodes in complex networks, several classic methods exist, which can be broadly categorized into two types based on network topological characteristics: one is based on local topological structure, such as degree centrality and eigenvector centrality; the other is based on global topological structure, such as betweenness centrality and proximity centrality. While each method has its advantages, in highly heterogeneous networks, local metrics ignore higher-order topological information, while global metrics are computationally complex and susceptible to path fluctuations in sparse regions, making it difficult to comprehensively characterize node importance. In recent years, researchers have proposed a series of methods that combine local and global information. For example, DomiRank centrality, by introducing adjustable parameters, effectively integrates the local and global topological features of the network, thereby quantifying the dominance of nodes in their respective neighborhoods.

[0004] However, highly heterogeneous networks exhibit significant topological differences across different regions, making it difficult for DomiRank's single adjustable parameter to adapt to the optimal ranking strategy globally. From the perspective of network decomposition dynamics, the heterogeneous characteristics of a network can be gradually dismantled by targeted removal of key nodes, while the critical point of the network's transition to a homogeneous state constitutes a key opportunity for strategy adjustment. Percolation theory, by simulating the node removal process, can accurately characterize the critical behavior of network structure transitioning from massive connectivity to fragmentation. Existing node evaluation methods fail to fully capture this topological evolution information, causing the evaluation dimension based on global connectivity to lose physical meaning after the network crosses the percolation phase transition point (i.e., network structure fragmentation), thus assigning redundant scores to non-important nodes and causing a serious failure in ranking resolution. Summary of the Invention

[0005] To address the resolution degradation problem of single-scale indicators in existing technologies when processing heterogeneous network evolution, this invention proposes an adaptive node ranking method for heterogeneous networks that integrates a percolation switching mechanism. From the dynamic perspective of network topology evolution, it utilizes a percolation threshold as an indicator of policy switching, effectively improving the accuracy of key node identification and the efficiency of network decomposition. The technical solution provided by this invention is as follows:

[0006] An adaptive node ranking method for heterogeneous networks incorporating a percolation switching mechanism includes the following steps:

[0007] S1: Define the complex system to be identified as a system with Each node and Unweighted and undirected network graph with striped edges ;

[0008] S2: Calculate the DomiRank centrality, betweenness centrality, and gateway rank for each node;

[0009] S3: Normalize the DomiRank centrality, betweenness centrality, and gateway ranking of each node, calculate the comprehensive evaluation score for each node, and sort the nodes in descending order according to the scores to generate a global node decomposition priority sequence.

[0010] S4: Remove nodes sequentially according to the global node dismantling priority sequence, introduce a topology difference metric, and use a binary iterative search algorithm to capture the seepage threshold of abrupt changes in network topology within the parameter space of the node removal ratio. ;

[0011] S5: Based on the seepage threshold Determine the set of nodes to be removed to reduce network heterogeneity. These nodes are then removed from the network, resulting in a more homogeneous remaining network. and its corresponding set of remaining nodes ;

[0012] S6: For the remaining network Calculate the set of remaining nodes The DomiRank centrality score of each node is calculated, and the nodes are rearranged in descending order of their DomiRank centrality scores.

[0013] S7: Remove node set The node sequence and the set of remaining nodes after rearrangement The node sequences are concatenated in chronological order to generate the final complete node importance sorting sequence.

[0014] Preferably, the DomiRank centrality of nodes in S2 The analytical formula is:

[0015]

[0016] In the formula, To adjust the competition intensity parameter between local and global topology information weights, It is an adjacency matrix. It is the identity matrix. It is a vector of all 1s. The dominance threshold.

[0017] Preferably, the comprehensive evaluation score in S3 The formula is:

[0018]

[0019] in, , and These are the preset linear weighting coefficients. For the normalized DomiRank centrality of nodes, For the normalized node betweenness centrality, This is the normalized ranking of node gateways.

[0020] Preferably, the calculation formula for the topological difference measure in S4 is as follows:

[0021]

[0022] in, Representing a network diagram With network diagram Topological differences between them and Representing network diagrams respectively With network diagram The global average distance distribution and A measure of the non-uniformity of node distance distribution. and Representing network diagrams respectively Network diagram and its supplementary image Central distribution Indicates the Jensen-Shannon divergence. , and These are the weighting coefficients.

[0023] Preferably, the seepage threshold is obtained using the binary iterative search algorithm in S4. The specific calculation logic is as follows:

[0024] S41: Define the initial search interval within the parameter space of the node removal ratio. And preset the tolerance threshold ε;

[0025] S42: Calculate the midpoint of the current search interval. ;

[0026] S43: According to the global node decomposition priority sequence, the proportion removed from the network is... High-priority nodes obtain the corresponding current network state. ;

[0027] S44: Calculate the boundary network state using the formula for the topological difference metric. With the current network status The first topological difference value between them and the current network status With another boundary network state The second topological difference value between them ;

[0028] S45: Compare the difference value of the first topology structure with the difference value of the second topology structure. If... Then update the lower bound. Otherwise, update the upper bound. ;

[0029] S46: Determine the length of the updated search interval If the value is less than the preset tolerance threshold ε, stop the iteration and use the median of the current interval as the seepage threshold. Otherwise, return to execute S42.

[0030] Preferably, in S5, the seepage threshold is utilized. Calculate the minimum number of nodes to be removed, and extract the corresponding number of nodes from the global node decomposition priority sequence from top to bottom to form the set of nodes to be removed. ,satisfy Remove the set of nodes from the original network. Includes the nodes and all their edges.

[0031] Compared with existing technologies, the beneficial effects achieved by this invention are as follows: This invention deeply couples node ranking with the network disassembly process, accurately locating key backbone nodes that maintain network heterogeneity by constructing multi-scale collaborative disassembly indices. Simultaneously, it innovatively introduces a topology difference measure and a bisection method to accurately capture the seepage threshold of network collapse, using this threshold as an adaptive switching mechanism to drive the ranking strategy to smoothly transition from global structural disassembly to local dominance evaluation after the network crosses a phase transition point. This dynamic strategy switching based on topology evolution effectively eliminates redundant interference from macroscopic indices in fragmented networks, making the algorithm significantly superior to traditional single centrality measures in terms of network disassembly efficiency, connectivity disruption capability, and propagation process suppression, greatly enhancing the effectiveness and robustness of key node identification in complex non-uniform systems. Attached Figure Description

[0032] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0033] Figure 1 This is a schematic diagram illustrating the evolution of the node sorting method framework of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] To make the above-mentioned objectives, features and effects of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1: An adaptive node sorting method for heterogeneous networks incorporating a percolation switching mechanism. The overall process is divided into two stages: global structure decomposition and local homogeneous rearrangement. Figure 1 As shown, it includes the following steps:

[0037] S1: Define the complex system to be identified as a system with Each node and Unweighted and undirected network graph with striped edges ;

[0038] S2: Calculate the DomiRank centrality (local dominance), betweenness centrality (global transmission efficiency), and gateway ranking (cross-community gateway effect) of each node in the network.

[0039] S3: Based on the normalized micro, macro and meso multi-scale features, construct a collaborative decomposition index, calculate the comprehensive evaluation score of each node in the global structure decomposition stage, and perform preliminary sorting of nodes in descending order according to the scores to generate a global node decomposition priority sequence.

[0040] S4: Remove nodes sequentially according to the global node dismantling priority sequence, introduce a topology difference metric D-measure, and use a binary iterative search algorithm to capture the seepage threshold of network topology abrupt changes within the parameter space of the node removal ratio. ;

[0041] S5: Based on the seepage threshold Determine the minimum set of nodes to be removed required to reduce network heterogeneity. Its scale meets These nodes are then removed from the network, resulting in a more homogeneous remaining network. and its corresponding set of remaining nodes ;

[0042] S6: For the remaining network that has entered the homogenization state Dynamically switch to a single-dimensional index based on local dominance assessment and recalculate the set of remaining nodes. The DomiRank centrality score of each node is calculated and adaptively rearranged in descending order of the scores.

[0043] S7: Remove node set The node sequence and the set of remaining nodes after rearrangement The node sequences are concatenated in chronological order to generate the final complete node importance sorting sequence.

[0044] It should be explained that in step S1, in practical application scenarios, complex systems can be social networks, communication infrastructure networks, or epidemic propagation networks, etc. The node set V is used to represent discrete entities in the system, and the edge set E is used to represent the interactions or physical connections between entities. By abstracting complex systems into unweighted undirected graphs, a standardized data structure foundation is provided for subsequent topological feature extraction and network decomposition.

[0045] In step S2, since heterogeneous networks are essentially the result of multi-scale structural interweaving, single-scale indicators all have their own representational blind spots in non-uniform topological environments. This embodiment extracts features from three dimensions to eliminate topological blind spots: at the microscale, the DomiRank centrality of each node in the network graph is calculated to quantify the neighborhood competition and local dominance of nodes in a resource-constrained environment. Its steady-state analytical formula is:

[0046]

[0047] In the formula, To adjust the competition intensity parameter between local and global topology information weights, It is an adjacency matrix. It is the identity matrix. It is a vector of all 1s. The dominance threshold is used; at a macroscopic scale, the betweenness centrality of each node is calculated. This characterizes its global transmission performance and cross-regional bridging function across the entire network; at the mesoscale, it calculates the gateway ranking of each node. This characterizes its cross-community gateway effect.

[0048] In step S3, to eliminate the interference of different units on the evaluation results, the obtained DomiRank centrality, betweenness centrality, and gateway ranking are first processed using the Min-Max normalization method. Then, preset linear weight coefficients are used... , and The fusion is performed, and the collaborative decomposition of computing node v is evaluated to obtain a comprehensive score:

[0049]

[0050] By summarizing the scores of all nodes and sorting them in descending order, the obtained global node decomposition priority sequence accurately identifies the key skeleton nodes that maintain the current macroscopic heterogeneous topology of the network.

[0051] In step S4, the core is to capture the critical point of phase transition in the network topology during the decomposition process. The calculation system of the introduced topology difference metric D-measure is defined as follows:

[0052]

[0053] in, Representing a network diagram With network diagram Topological differences between them and Representing network diagrams respectively With network diagram The global average distance distribution and A measure of the non-uniformity of node distance distribution. and Representing network diagrams respectively Network diagram and its supplementary image Central distribution Indicates the Jensen-Shannon divergence. , and These are the weighting coefficients.

[0054] Obtain the seepage threshold The specific calculation logic of the binary iterative search algorithm is as follows: define an initial search interval within the parameter space of the node removal ratio. And preset the tolerance threshold ε; at each iteration, calculate the midpoint of the interval. According to the global node dismantling priority sequence generated by S3, the proportion removed from the network is: High-priority nodes obtain the corresponding current network state. The boundary network state is calculated using the above formulas. Compared with the current state Topological differences and the current status With another boundary state Topological differences ;like This indicates that the current removal ratio has not yet triggered a sudden collapse of the network's macroscopic structure, and the lower bound has been updated. Conversely, if the network has crossed the phase transition point, the upper bound should be updated. Continue this iterative comparison process until the interval length is reached. At this point, the median value of the current search interval is taken as the seepage threshold. .

[0055] In step S5, the precisely captured seepage threshold is utilized. Calculate the size of the core nodes to be removed, and extract the corresponding number of backbone nodes from the global node decomposition priority sequence from top to bottom to form the set of nodes to be removed. Remove from the original network. This includes the nodes and all their edges. This operation essentially strips away the heterogeneous skeleton of the network, completely disintegrating the original giant connected components and obtaining a homogeneous residual network composed of multiple weakly connected or isolated subgraphs. .

[0056] In step S6, after crossing the seepage threshold and entering the residual stage, the network structure is severely fragmented. If global path metrics such as betweenness centrality are continued to be used, a large number of nodes will receive zero values ​​or redundant equivalent scores due to missing paths, causing the evaluation resolution to fail. Therefore, this embodiment adaptively unloads the global operator at this stage, in the remaining network... Within the connected component, for the set of nodes Each node in Using the formula:

[0057]

[0058] The DomiRank centrality value is recalculated based solely on the local features of the residual topology. The remaining nodes are then summarized in descending order based on the recalculated scores to obtain the residual rearrangement sequence.

[0059] In step S7, the set of nodes that can most efficiently dismantle the global structure will be selected. The sequence, as a high-priority sorting segment, is associated with the set of nodes reflecting local residual dominance. Perform sequential concatenation. The output sequence is the final ranking list of the importance of key network nodes, covering the entire lifecycle of topology awareness and policy adaptive switching.

[0060] Example 2: The computer-readable storage medium of this example stores a computer program that, when executed by a processor, implements the steps in the heterogeneous network adaptive node sorting method with a fused percolation switching mechanism in Example 1.

[0061] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0062] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0063] Example 3: The computer device of this example includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the heterogeneous network adaptive node sorting method with fused percolation switching mechanism of Example 1.

[0064] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0065] Those skilled in the art will clearly understand that each implementation can be achieved using software plus the necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A heterogeneous network adaptive node ranking method incorporating a percolation switching mechanism, characterized in that, Includes the following steps: S1: Define the complex system to be identified as a system with Each node and Unweighted and undirected network graph with striped edges ; S2: Calculate the DomiRank centrality, betweenness centrality, and gateway rank for each node; S3: Normalize the DomiRank centrality, betweenness centrality, and gateway ranking of each node, calculate the comprehensive evaluation score for each node, and sort the nodes in descending order according to the scores to generate a global node decomposition priority sequence. S4: Remove nodes sequentially according to the global node dismantling priority sequence, introduce a topology difference metric, and use a binary iterative search algorithm to capture the seepage threshold of abrupt changes in network topology within the parameter space of the node removal ratio. ; S5: Based on the seepage threshold Determine the set of nodes to be removed to reduce network heterogeneity. These nodes are then removed from the network, resulting in a more homogeneous remaining network. and its corresponding set of remaining nodes ; S6: For the remaining network Calculate the set of remaining nodes The DomiRank centrality score of each node is calculated, and the nodes are rearranged in descending order of their DomiRank centrality scores. S7: Remove node set The node sequence and the set of remaining nodes after rearrangement The node sequences are concatenated in chronological order to generate the final complete node importance sorting sequence.

2. The method for adaptive node ranking in heterogeneous networks with a fusion percolation switching mechanism according to claim 1, characterized in that, DomiRank centrality of nodes in S2 The analytical formula is: ； In the formula, To adjust the competition intensity parameter between local and global topology information weights, It is an adjacency matrix. It is the identity matrix. It is a vector of all 1s. The dominance threshold.

3. The method for adaptive node ranking in heterogeneous networks with a fusion percolation switching mechanism according to claim 2, characterized in that, S3 Comprehensive Evaluation Score The formula is: ； in, , and These are the preset linear weighting coefficients. For the normalized DomiRank centrality of nodes, For the normalized node betweenness centrality, This is the normalized ranking of node gateways.

4. The method for adaptive node ranking in heterogeneous networks with a fusion percolation switching mechanism according to claim 3, characterized in that, The formula for calculating the topological difference measure in S4 is as follows: ； in, Representing a network diagram With network diagram Topological differences between them and Representing network diagrams respectively With network diagram The global average distance distribution and A measure of the non-uniformity of node distance distribution. and Representing network diagrams respectively Network diagram and its supplementary image Central distribution Indicates the Jensen-Shannon divergence. , and These are the weighting coefficients.

5. The heterogeneous network adaptive node sorting method with integrated percolation switching mechanism according to claim 4, characterized in that, The seepage threshold is obtained using the binary iterative search algorithm in S4. The specific calculation logic is as follows: S41: Define the initial search interval within the parameter space of the node removal ratio. And preset the tolerance threshold ε; S42: Calculate the midpoint of the current search interval. ; S43: According to the global node decomposition priority sequence, the proportion removed from the network is... High-priority nodes obtain the corresponding current network state. ; S44: Calculate the boundary network state using the formula for the topological difference metric. With the current network status The first topological difference value between them and the current network status With another boundary network state The second topological difference value between ; S45: Compare the difference value of the first topology structure with the difference value of the second topology structure. If... Then update the lower bound. Otherwise, update the upper bound. ; S46: Determine the length of the updated search interval If the value is less than the preset tolerance threshold ε, stop the iteration and use the median of the current interval as the seepage threshold. Otherwise, return to execute S42.

6. The method for adaptive node ranking in heterogeneous networks with a fusion percolation switching mechanism according to claim 1, characterized in that, S5 utilizes the seepage threshold Calculate the minimum number of nodes to be removed, and extract the corresponding number of nodes from the global node decomposition priority sequence from top to bottom to form the set of nodes to be removed. ,satisfy Remove the set of nodes from the original network. Includes the nodes and all their edges.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the heterogeneous network adaptive node sorting method with a fused percolation switching mechanism as described in any one of claims 1-6.

8. A computer device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the heterogeneous network adaptive node sorting method with fusion percolation switching mechanism as described in any one of claims 1-6.

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