Multi-agent network layered influence node identification method based on triangular structure recursive compression

Abstract

The invention belongs to the technical field of network science and control, and discloses a multi-agent network hierarchical influence node identification method based on triangular structure recursive compression, which comprises the following steps: firstly, quickly detecting a triangular structure by using an intersection matrix to reduce the triangular counting complexity; evaluating nodes by using CPI comprehensive energy, neighbor change, connectivity and load; a conflict resolution and coverage maximization repulsive force algorithm is designed for a shared node / side triangle and a non-triangular area, so that influence on overlapping is avoided, and distribution is controlled in a balanced manner; top k control nodes are screened through virtual node compression recursion, the number of nodes is further reduced, and network robustness is improved. According to the method, the key nodes with the minimum number and the highest control efficiency can be accurately and efficiently identified, and the method is suitable for dynamic multi-agent networks such as unmanned aerial vehicle clusters and the Internet of Things.

Description

Technical Field

[0001] This invention belongs to the field of network science and control technology, specifically relating to a method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression. Background Technology

[0002] In various forms of multi-agent networks, such as social networks, drone swarms, the Internet of Things (IoT), and the Tactical Internet of Things (TIoT), accurately and efficiently identifying a small number of "influential nodes" (or "key nodes" or "control nodes") that can dominate information dissemination and maintain network structural stability is a core research topic with significant theoretical and practical value. However, existing methods for identifying influential nodes face the following main technical challenges when dealing with complex and dynamic multi-agent networks:

[0003] Limitations of evaluation metrics: Traditional methods, such as degree centrality or betweenness centrality, rely primarily on the static topology of the network for computation. In multi-agent networks, the state of nodes (such as drones) is dynamically changing, including their remaining energy, computational load, and positional stability. These intrinsic, dynamic attributes are crucial to a node's ability to effectively exert its influence, but are often overlooked by traditional static metrics, leading to evaluation results that are out of sync with reality.

[0004] Overlapping Influence and Control Redundancy: Some studies have noted the high cohesion and stability of "triangular structures" formed by three interconnected nodes in a network, and have used this as a basis for node identification. However, these triangular structures are often highly concentrated in the core region of the network, resulting in an overly dense spatial distribution of identified influential nodes with significantly overlapping influence ranges. This "rich man's club" phenomenon causes severe control redundancy—multiple control nodes cover the same area, which contradicts the initial goal of achieving the broadest control with the fewest nodes.

[0005] Lack of ability to handle heterogeneous structures: Real-world networks are typically heterogeneous, containing both tightly connected "communities" composed of triangular structures and sparsely connected "non-triangular regions" or "bridging structures." Existing methods often optimize only for one type of structure, lacking a unified framework that can employ differentiated and adaptive strategies for node selection for these two distinct regions, thus making it difficult to achieve global control coverage.

[0006] The challenge of obtaining the globally optimal set: Most algorithms calculate an influence score for each node and then simply select the top-K nodes with the highest scores as the final result. This approach is essentially an aggregation of local optima and cannot guarantee that the final set of nodes is the globally optimal "minimum control set." Designing a systematic selection mechanism that, from a global perspective, iterates and optimizes to ultimately obtain a node combination that is optimal in both quantity and control efficiency is a major challenge in current technology.

[0007] Therefore, there is an urgent need to develop a novel method for identifying influential nodes. This method should be able to comprehensively evaluate the dynamic attributes of nodes, effectively solve the problem of overlapping influence, and systematically find a minimized set of influential nodes that can efficiently control the entire heterogeneous network through a global optimization strategy. Summary of the Invention

[0008] The purpose of this invention is to provide a hierarchical influence node identification method for multi-agent networks based on triangular structure recursive compression, to overcome the limitations of existing technologies in the selection of key nodes in large-scale multi-agent networks. This method introduces a Control Power Index (CPI) to comprehensively evaluate the potential control capabilities of nodes, and combines this with a robust triangular structure in the network to achieve hierarchical and efficient identification of influence nodes.

[0009] This invention provides a method for identifying hierarchical influence nodes in multi-agent networks based on triangular recursive compression, comprising the following steps:

[0010] S1. Number the nodes of the network to be analyzed sequentially, and perform triangulation detection only on the forward neighbors with larger sequential numbers based on the intersection matrix to obtain the complete set of triangles;

[0011] S2. Calculate the control index (CPI) for each node in the network to be analyzed;

[0012] S3. Perform conflict resolution control node selection for each triangle detected in step S1;

[0013] If multiple triangles share a node, then the shared node is identified as the unique control node;

[0014] If multiple triangles share an edge, then the node with the largest CPI at both ends of the shared edge is selected as the unique control node.

[0015] If there is a bridging node within the triangle, the probability of the bridging node being selected is reduced, and the node with the largest CPI among the remaining vertices of the triangle is selected as the control node.

[0016] If a triangle has no shared nodes, no shared edges, and no bridging nodes, it is considered a regular triangle. For regular triangles, the node with the largest CPI is directly selected as the control node.

[0017] S4. Perform coverage maximization control node selection on the set of nodes not included in any triangle;

[0018] The coverage capability is obtained by calculating the number of uncovered nodes within two hops of a candidate node. After adding a repulsion penalty, a greedy strategy is used to iteratively select the node with the largest coverage capability and the smallest repulsion until all nodes are covered.

[0019] S5. Compress the control nodes obtained in steps S3 and S4 into virtual nodes along with the set of non-control nodes they directly manage, reconstruct the network topology, and recursively execute steps S1-S4 until the network is compressed to a predetermined level to obtain the target set of control nodes.

[0020] Furthermore, the cross matrix is ​​a node-edge two-dimensional sparse matrix, with rows corresponding to network edges and columns corresponding to network nodes. When an edge connects two nodes, a value of 1 is assigned to the corresponding row and column positions. The intersection operation of the row vectors and column vectors of the cross matrix is ​​used to determine whether a triangle is formed between the node pairs.

[0021] Furthermore, the calculation expression for the control index CPI is as follows:

[0022] CPI(v)=αE norm (v)+βD norm (v)+γNV′ norm (v)+δQ′ norm (v)

[0023] In the formula, CPI(v) represents the comprehensive performance index of node v; E norm (v) represents the normalized energy level of node v; D norm (v) represents the normalized node connectivity of node v; NV′ norm (v) represents the normalized rate of change of the neighbors of node v; Q′ norm (v) represents the normalized communication load of node v; α, β, γ, and δ are the weights of each normalized index, and satisfy α+β+γ+δ=1, which are used to perform differentiated fusion evaluation of node energy, topology, and load characteristics according to different multi-agent network scenarios.

[0024] Furthermore, in step S3, the criteria for determining triangle conflict are as follows:

[0025] The condition for determining a shared node conflict is that different triangles have at least one common vertex.

[0026] Determination conditions for shared edge conflicts: Different triangles have exactly the same two vertices and form a common edge;

[0027] Determination conditions for bridging node conflicts: A certain node is simultaneously a vertex of a triangle and is directly connected to at least one vertex of another triangle.

[0028] Furthermore, the step S4 includes the following sub-steps:

[0029] S4.1 Calculate the node coverage ability;

[0030] When calculating the coverage ability, multiply the number of two-hop neighbors of the candidate node by the reduction factor k, where 0 < k < 1. The calculation expression is as follows:

[0031]

[0032] In the formula, C nt (i) represents the coverage ability of node i, that is, the number of non-triangular nodes that the node can cover; ∣Γ nt (i)∣ represents the number of one-hop non-triangular nodes directly connected to node i; represents the number of two-hop non-triangular neighbor nodes of node i, that is, the number of non-triangular nodes indirectly connected to i through one-hop neighbors;

[0033] S4.2 Calculate the repulsive force received by the node;

[0034] The total repulsive force of the candidate node is the accumulation of the repulsive forces on all selected control nodes. The calculation expression is as follows:

[0035]

[0036] In the formula, R ij represents the repulsive force penalty value of candidate node i received by selected control node j; R i represents the total repulsive force received by candidate node i; V c is the set of selected control nodes, that is, the set composed of all selected control nodes; d ij represents the shortest path length between candidate node i and selected control node j;

[0037] S4.3 Considering the coverage ability and repulsive force comprehensively, iteratively select the node with the maximum coverage ability and the minimum repulsive force by the greedy strategy, that is, select the node with the highest score as the control node;

[0038] Coverage maximization and repulsion mechanism in the non-triangular area:

[0039] S(i) = C nt (i) * (1 - ω·R i )

[0040] In the formula, ω represents the weighting coefficient, which is used to balance the influence of coverage and repulsion, and adjust the weight of coverage efficiency and spatial dispersion; S(i) represents the node's comprehensive score, which is determined by both coverage and repulsion. The larger S(i) is, the more suitable the node is as a control node.

[0041] In each iteration, the node with the largest S(i) is selected as the next control node. At the same time, the uncovered set of its neighborhood and the repulsion of other candidate nodes are updated so that the final selected control node can cover as many non-triangular nodes as possible, while maintaining sufficient spatial dispersion and reducing redundancy and overlap.

[0042] Furthermore, in step S5, when a control node and the set of non-control nodes it manages are compressed into a virtual node, the condition for the connection between the two virtual nodes is that at least one pair of nodes in the original node set corresponding to each of the two virtual nodes are directly connected in the original network.

[0043]

[0044] In the formula, E′ represents the edge set in the compressed virtual network, that is, the set of connections between virtual nodes; E represents the edge set in the original network, that is, the direct connection between the original nodes; v, c′ represent two virtual nodes obtained after compression; (v, c′) ∈ E′ indicates that there is a connection edge between virtual node v and virtual node c′ in the virtual network; H(c) is the set of original nodes corresponding to virtual node c′, that is, the set consisting of a control node and the non-control nodes it manages; u is an original node belonging to the set H(c); (v, u) ∈ E indicates that there is a direct connection between node v and node u in the original network.

[0045] Furthermore, in step S5, the preset termination condition is one of the following two:

[0046] The network at this level no longer contains any triangular structures;

[0047] Or the number of virtual nodes in the current layer of the network is less than or equal to a preset Top-K value.

[0048] Beneficial effects:

[0049] This invention discloses a hierarchical influence node identification method for multi-agent networks based on triangular structure recursive compression. First, it utilizes an intersection matrix to quickly detect triangular structures, reducing the complexity of triangular counting. Then, it uses CPI (Constant Influence Scale) to comprehensively evaluate nodes based on energy, neighbor changes, connectivity, and load. For shared node / edge triangles and non-triangular regions, it designs conflict resolution and coverage maximization repulsion algorithms to avoid overlapping influences and balance control distribution. Finally, it recursively selects the Topk control nodes through virtual node compression, further reducing the number of nodes and improving network robustness. This invention can accurately and efficiently identify the fewest critical nodes with the highest control efficiency, and is applicable to dynamic multi-agent networks such as UAV swarms and the Internet of Things.

[0050] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0051] Figure 1 This is a decision flowchart for preliminary screening of control nodes in an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram illustrating how a multi-agent system is abstractly mapped to a network topology model in an embodiment of the present invention;

[0053] Figure 3 These are schematic diagrams illustrating two typical triangular structure configurations used in embodiments of the present invention to explain the conflict resolution mechanism, wherein... Figure 3 (a) is a triangle structure with shared nodes. Figure 3 (b) is a triangular structure for bridging nodes;

[0054] Figure 4 This is a schematic diagram of the network hierarchical recursive compression process in an embodiment of the present invention. Detailed Implementation

[0055] To make the technical solutions, advantages, and objectives of the present invention clearer, 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, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of this application.

[0056] This invention provides a hierarchical influence node identification method for multi-agent networks based on triangular structure recursive compression. Its core lies in using a systematic, hierarchical, iterative process to select the optimal set of influence nodes from a complex network. The method specifically includes the following steps:

[0057] S1. Number the nodes of the network to be analyzed sequentially, and perform triangulation detection only on the forward neighbors with larger sequential numbers based on the intersection matrix to obtain the complete set of triangles;

[0058] The first step is to perform network modeling of the research subjects. (Refer to...) Figure 2 A multi-agent system consisting of multiple agents and their communication links is abstracted as a network graph G = (V, E) composed of nodes and edges. In the graph, agents Agent 1 to Agent 30 are mapped one-to-one to nodes 1 to 30.

[0059] The cross matrix is ​​a two-dimensional sparse matrix of nodes and edges. Rows correspond to network edges and columns correspond to network nodes. When an edge connects two nodes, a value of 1 is assigned to the corresponding row and column positions. The intersection operation of the row vectors and column vectors of the cross matrix is ​​used to determine whether a pair of nodes forms a triangle.

[0060] The goal of the intersection matrix triangle discovery algorithm described in S1 is to efficiently and without repetition enumerate all triangles (i,j,k) in an undirected simple graph G=(V,E). The core idea is to number each node sequentially, only look for neighbors "forward," ensuring each triangle is calculated only once; use the intersection matrix M (rows = edges, columns = nodes) to quickly retrieve edges associated with a given node, and then obtain its adjacency vector through simple matrix-vector multiplication and subtraction; the triangle can be located by finding the intersection of two forward neighbors. Specifically:

[0061] The n nodes in the graph are numbered sequentially as 1, 2, ..., n. For each node i, the forward neighbor set is defined as:

[0062] N forward (i)={j|N i [j]=2,j>i}

[0063] By retaining only the neighbors with larger numbers, we can ensure that each triangle is discovered exactly once by the unique smallest numbered node iii, thus avoiding redundant calculations.

[0064] M is an edge-node incidence matrix, where each row corresponds to an edge e in the graph. k ={v p ,v q}; the column corresponds to each node. If edge e k Connect node v pWith v q Then set M(e) in the matrix. k ,v i ) = 1, M(e k ,v j = 1. All other elements are 0. Since each edge involves only 2 nodes, M is extremely sparse and suitable for storage using a sparse structure.

[0065] Extract all rows related to node i from M to obtain submatrix M. conn(i) M conn(i) Transpose the vector and multiply it on the left by a column vector of all 1s (length equal to the number of rows) to obtain vector N. i =M conn(i) T • If Ni(j), it means that node j and i are at the two endpoints of the same edge, that is, j is a neighbor of i (which may be a forward or non-forward neighbor). Retain the neighbors with numbers greater than i to obtain the true forward neighbor set N. forward (i)={j| i ()=2,>i}.

[0066] For each forward neighbor j of i, repeatedly calculate the set N of forward neighbors of j. forward (j). Calculate the intersection and determine the triangle accordingly:

[0067] triangles = {(i,j,k) | k∈N} forward (i)∩N forward (j)}

[0068] S2. Calculate the control index (CPI) for each node in the network to be analyzed;

[0069] CPI is a comprehensive indicator designed to fully assess the control potential of a node. The higher the CPI value, the greater the node's potential as a control node. The four CPI indicators are weighted by adjustable parameters α, β, γ, and δ, with α+β+γ+δ=1. This is used to perform differentiated fusion evaluation of node energy, topology, and load characteristics according to different multi-agent network scenarios.

[0070] CPI(v)=αE norm (v)+βD norm (v)+γNV′ norm (v)+δQ′ norm (v)

[0071] In the formula, CPI(v) represents the comprehensive performance index of node v; E norm (v) represents the normalized energy level of node v; D norm (v) represents the normalized node connectivity of node v; NV′ norm (v) represents the normalized rate of change of the neighbors of node v; Q′norm (v) represents the normalized communication load of node v; α, β, γ, and δ are the weights of each normalized index, and satisfy α+β+γ+δ=1, which are used to perform differentiated fusion evaluation of node energy, topology, and load characteristics according to different multi-agent network scenarios.

[0072] To ensure the comparability of indicators with different dimensions, this formula employs two normalization strategies for positive and negative indicators respectively:

[0073]

[0074] This applies to E(v) and D(v). The larger the original value, the closer the normalized result is to 1. For inverse indices, reciprocal normalization is used.

[0075]

[0076] S3. Perform conflict resolution control node selection for each triangle detected in step S1;

[0077] This step, on the underlying network that completes the CPI calculation, initially filters out a batch of control nodes through a sophisticated decision-making process. This decision-making process is as follows: Figure 1 As shown. Type detection is performed on each substructure of the input network; if the unit to be processed forms a triangle, the process proceeds to the triangle processing branch; otherwise, it proceeds to the non-triangle processing branch. If it is a triangle, it is further determined whether the triangle is a "shared node triangle". (Refer to...) Figure 3 (a) Node 3 serves as the common vertex of both the left triangle (1,2,3) and the right triangle (3,4,5), forming a typical shared node structure. In this case, the decision process enters the "Yes" branch, directly selecting the shared node (node ​​3) as the control node. This strategy allows one node to control multiple closely connected areas, greatly improving control efficiency. If "No," the process continues to determine if it is a "shared-edge triangle." A shared-edge triangle is two triangles sharing a common edge. In this case, the decision process enters the "Yes" branch, selecting the node with the largest CPI value at both ends of the shared edge as the control node to avoid redundancy of two control nodes on one edge. If it is also not a shared-edge triangle, the process continues to determine if a "bridging node" exists within the triangle. (Refer to...) Figure 3(b), Node 3 is the vertex of triangle (1, 2, 3) and is adjacent to vertex 4 of another triangle (4, 5, 6). At this time, both node 3 and 4 are regarded as "bridging nodes". To ensure the robustness of the network (to avoid critical bridges from being attacked), the present invention will reduce the selection priority of bridging nodes. Therefore, the decision-making process enters the "yes" branch. Among the three vertices forming this triangle, the bridging nodes are excluded, and among the remaining non-bridging nodes, "select the node with the largest CPI value among the non-bridging nodes" as the control node. If a triangle is neither a shared node nor a shared edge and does not contain bridging nodes, it is determined as a regular triangle. The decision-making process enters the final "no" branch and directly "select the point with the largest CPI value in the triangle" as the control node.

[0078] S4. Perform the selection of the coverage maximization control node for the node set not included in any triangle;

[0079] Calculate the number of uncovered nodes within two hops of the candidate node to obtain the coverage ability, and iteratively select the node with the largest coverage ability and the smallest repulsive force with the greedy strategy after adding the repulsive force penalty until all nodes are covered;

[0080] S4.1 Calculate the node coverage ability;

[0081] When calculating the coverage ability, multiply the number of two-hop neighbors of the candidate node by the reduction factor k, where 0 < k < 1, and the calculation expression is as follows:

[0082]

[0083] In the formula, C nt (i) represents the coverage ability of node i, that is, the number of non-triangle nodes that the node can cover; ∣Γ nt (i)∣ represents the number of one-hop non-triangle nodes directly connected to node i; represents the number of two-hop non-triangle neighbor nodes of node i, that is, the number of non-triangle nodes indirectly connected to i through one-hop neighbors;

[0084] S4.2 Calculate the repulsive force received by the node;

[0085] The total repulsive force of the candidate node is the accumulation of the repulsive force penalties for all selected control nodes, and the calculation expression is as follows:

[0086]

[0087] In the formula, R ij represents the repulsive force penalty value received by candidate node i from selected control node j; R i represents the total repulsive force received by candidate node i; V c is the set of selected control nodes, that is, the set composed of all selected control nodes; dij This represents the shortest path length between candidate node i and the selected control node j;

[0088] S4.3 Taking into account both coverage and repulsion, a greedy strategy is used to iteratively select the node with the largest coverage and the smallest repulsion, that is, to select the node with the highest score as the control node.

[0089] Coverage maximization and exclusion mechanisms within non-triangular regions:

[0090] S(i)=C nt (i)*(1-ω·R i )

[0091] In the formula, ω represents the weighting coefficient, which is used to balance the influence of coverage and repulsion, and adjust the weight of coverage efficiency and spatial dispersion; S(i) represents the node's comprehensive score, which is determined by both coverage and repulsion. The larger S(i) is, the more suitable the node is as a control node.

[0092] In each iteration, the node with the largest S(i) is selected as the next control node. At the same time, the uncovered set of its neighborhood and the repulsion of other candidate nodes are updated so that the final selected control node can cover as many non-triangular nodes as possible, while maintaining sufficient spatial dispersion and reducing redundancy and overlap.

[0093] S5. Compress the control nodes obtained in steps S3 and S4 into virtual nodes along with the set of non-control nodes they directly manage, reconstruct the network topology, and recursively execute steps S1-S4 until the network is compressed to a predetermined level to obtain the target set of control nodes.

[0094] Hierarchical recursive compression and iterative optimization. (Refer to...) Figure 4 This diagram visually illustrates the core idea of ​​hierarchical recursive compression of networks. On the left side of the diagram, a lower-level network that has completed step S2 is shown. Solid black nodes represent selected control nodes, and hollow white nodes represent managed non-control nodes. This step treats each black control node and its surrounding white non-control nodes (enclosed by gray curves) as a whole, logically "compressing" them into a completely new virtual node. As shown on the right side of the diagram, all these virtual nodes together constitute a smaller, more topologically simpler upper-level network. Whether two virtual nodes are connected depends on whether at least one pair of nodes in their respective original node sets are directly connected in the original network. On this newly constructed upper-level network, the complete process of S1 and S2 is repeated—that is, calculating new CPI values ​​for the virtual nodes (which can inherit or aggregate the original CPI) and then applying them again. Figure 1 The decision-making process shown selects a higher-level control node set C1.

[0095] The compression and selection process iterates continuously (C1→C2→...), with the network hierarchy continuously increasing and the importance of nodes also increasing. The iteration process terminates when a preset termination condition is met (e.g., the number of virtual nodes in the current layer of the network is less than or equal to a preset K value, or the network no longer contains a triangular structure). Ultimately, the set of control nodes C* selected in the top-level network is the globally optimized, minimum-number set of globally influential nodes ultimately identified by this invention.

[0096] In step S5, when a control node and the set of non-control nodes it manages are compressed into a virtual node, the condition for the connection between the two virtual nodes is that at least one pair of nodes in the original node set corresponding to each of the two virtual nodes are directly connected in the original network.

[0097]

[0098] In the formula, E′ represents the edge set in the compressed virtual network, that is, the set of connections between virtual nodes; E represents the edge set in the original network, that is, the direct connection between the original nodes; v, c′ represent two virtual nodes obtained after compression; (v, c′) ∈ E′ indicates that there is a connection edge between virtual node v and virtual node c′ in the virtual network; H(c) is the set of original nodes corresponding to virtual node c′, that is, the set consisting of a control node and the non-control nodes it manages; u is an original node belonging to the set H(c); (v, u) ∈ E indicates that there is a direct connection between node v and node u in the original network.

[0099] In step S5, the preset termination condition is one of the following two: the network at the current level no longer contains any triangular structure; or the number of virtual nodes in the network at the current level is less than or equal to a preset Top-K value.

[0100] The hierarchical influence node identification method for multi-agent networks based on triangular structure recursive compression provided by this invention can reduce the number of control nodes and computational overhead while ensuring coverage and network robustness, and has good engineering feasibility.

[0101] It is hereby declared that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression, characterized in that, It includes the following steps: S1. Number the nodes of the network to be analyzed in order, and only perform triangular structure detection on the forward neighbors with larger sequential numbers based on the intersection matrix to obtain the set of all triangles; S2. Calculate the control power index CPI of each node in the network to be analyzed; S3. Perform conflict resolution control node selection for each triangle detected in step S1; If multiple triangles have shared nodes, the shared nodes are identified as the only control nodes; If multiple triangles have shared edges, select the node with the largest CPI at both ends of the shared edge as the only control node; If there are bridging nodes in a triangle, reduce the probability of the bridging node being selected and select the node with the largest CPI among the remaining vertices of the triangle as the control node; If a triangle has no shared nodes, no shared edges, and no bridging nodes, it is determined as a regular triangle, and the node with the largest CPI is directly selected as the control node for the regular triangle; S4. Perform coverage maximization control node selection on the set of nodes not included in any triangle; Calculate the number of uncovered nodes within two hops of the candidate node to obtain the coverage ability, and iteratively select the node with the largest coverage ability and the smallest repulsive force in a greedy strategy after adding repulsive force penalties until all nodes are covered; S5. Compress the control nodes obtained in steps S3 and S4 with the set of non-control nodes directly managed by them into virtual nodes, reconstruct the network topology, and recursively execute steps S1 - S4 until the network is compressed to a predetermined level to obtain the target control node set.

2. The method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression according to claim 1, characterized in that: The cross matrix is a node-edge two-dimensional sparse matrix, where the rows correspond to network edges and the columns correspond to network nodes. When an edge connects two nodes, a value of 1 is assigned at the corresponding row and column positions. Whether a triangle is formed between node pairs is judged by the intersection operation of the row vector and column vector of the cross matrix.

3. The method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression according to claim 2, characterized in that, The calculation expression of the control power index CPI is as follows: CPI(v)=αE norm (v)+βD norm (v)+γNV′ norm (v)+δQ′ norm (v) In the formula, CPI(v) represents the comprehensive performance index of node v; E norm (v) represents the normalized energy level of node v; D norm (v) represents the normalized node connectivity of node v; NV′ norm (v) represents the normalized rate of change of the neighbors of node v; Q′ norm (v) represents the normalized communication load of node v; α, β, γ, and δ are the weights of each normalized index, and satisfy α+β+γ+δ=1, which are used to perform differentiated fusion evaluation of node energy, topology, and load characteristics according to different multi-agent network scenarios.

4. The method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression according to claim 3, characterized in that, In step S3, the determination criteria for triangle conflicts are as follows: Determination condition for shared node conflicts: Different triangles have at least one same vertex; Determination condition for shared edge conflicts: Different triangles have exactly the same two vertices and form a common edge; Determination condition for bridging node conflicts: A certain node is simultaneously a vertex of a triangle and is directly connected to at least one vertex of another triangle.

5. The method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression according to claim 4, characterized in that, Step S4 includes the following sub-steps: S4.1 Calculate the node coverage ability; When calculating the coverage ability, multiply the number of two-hop neighbors of the candidate node by a reduction factor k, where 0 < k < 1, and the calculation expression is as follows: In the formula, C nt (i) represents the coverage capability of node i, that is, the number of non-triangular nodes that the node can cover; |Γ nt (i)∣ represents the number of one-hop non-triangular node nodes directly connected to node i; This represents the number of two-hop non-triangular neighbor nodes of node i, that is, the number of non-triangular node nodes indirectly connected to i through a one-hop neighbor; S4.2 Calculate the repulsive force received by the node; The total repulsive force of the candidate node is the accumulation of the repulsive forces of all selected control nodes, and the calculation expression is as follows: In the formula, R ij R represents the repulsion penalty value that candidate node i receives from the selected control node j; i V represents the total repulsive force experienced by candidate node i; c d represents the set of selected control nodes, that is, the set of all control nodes that have been selected; ij This represents the shortest path length between candidate node i and the selected control node j; S4.3 Considering the coverage ability and repulsive force comprehensively, iteratively select the node with the largest coverage ability and the smallest repulsive force in a greedy strategy, that is, select the node with the highest score as the control node; ​ S(i)=C nt (i)*(1-ω·R i ) ​ In each iteration, the node with the largest S(i) is selected as the next control node. At the same time, the uncovered set of its neighborhood and the repulsion of other candidate nodes are updated so that the final selected control node can cover as many non-triangular nodes as possible, while maintaining sufficient spatial dispersion and reducing redundancy and overlap.

6. The method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression according to claim 5, characterized in that: In step S5, when a control node and the set of non-control nodes it manages are compressed into a virtual node, the condition for the connection between the two virtual nodes is that at least one pair of nodes in the original node set corresponding to each of the two virtual nodes are directly connected in the original network. In the formula, E′ represents the edge set in the compressed virtual network, that is, the set of connections between virtual nodes; E represents the edge set in the original network, that is, the direct connection between the original nodes; v, c′ represent two virtual nodes obtained after compression; (v, c′) ∈ E′ indicates that there is a connecting edge between virtual node v and virtual node c′ in the virtual network; H(c) is the set of original nodes corresponding to virtual node c′, that is, the set consisting of a control node and the non-control nodes it manages; u is an original node belonging to the set H(c); (v, u) ∈ E indicates that there is a direct connection between node v and node u in the original network.

7. The method for identifying hierarchical influence nodes in multi-agent networks based on triangular structure recursive compression according to claim 6, characterized in that, In step S5, the preset termination condition is one of the following two: The network at this level no longer contains any triangular structures; Or the number of virtual nodes in the current layer of the network is less than or equal to a preset Top-K value.

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