Pyramid structure-based node centrality determination method and device, and electronic device

Abstract

The application discloses a kind of based on the method, device and electronic equipment of node centrality determination of pyramid structure, belong to traffic network analysis technical field.Method includes: obtaining traffic network;Extract all base pyramids in traffic network, wherein, with node as root node, the tree-shaped connected subgraph obtained by the base pyramid of node is executed breadth-first search from node, until first time meet when not satisfying layer-by-layer expansion characteristic stop;The base pyramid that node participates is determined as the target pyramid corresponding to node;Determine the centrality score of node based on pyramid participation degree score and / or core proximity score, wherein, the pyramid participation degree score of node is determined based on the number of target pyramid, the core proximity score of node is determined based on the distance between node and the root node of target pyramid.The application embodiment can improve the evaluation accuracy of node centrality, accurately identify the key hub in traffic network.

Description

Technical Field

[0001] This invention belongs to the field of traffic network analysis technology, specifically relating to a method, apparatus, and electronic device for determining node centrality based on a pyramid structure. Background Technology

[0002] Accurately assessing the importance of nodes in transportation networks is crucial for optimizing road network planning, improving operational efficiency, and enhancing system resilience. However, current node importance assessment techniques primarily rely on neutral metrics developed in complex network science. These methods always focus on the node being assessed itself, defining its importance by extracting its local, global, or recursive topological features.

[0003] This logic in existing technologies implicitly treats the network as a completed, static snapshot of the topology. It excels at depicting the status of nodes after network construction but struggles to capture the functional roles nodes play during network generation and expansion. This limitation is particularly pronounced in systems with clear spatial constraints and hierarchical expansion characteristics, such as transportation networks. Take gateway nodes at provincial borders as an example: at the initial planning stages of the road network, they are essential interfaces connecting different regional subnetworks, their significance lying in their structural support role—without which the regional road network cannot connect to the national framework. However, once the road network is built, the locality value of these nodes may be far lower than that of provincial capitals, and the number of shortest paths passing through them may not be outstanding—because the vast majority of shortest paths in the entire network occur between regional cores without frequently traversing these interfaces. Therefore, traditional endogeneity measures in existing technologies systematically underestimate the true value of such nodes.

[0004] It can be seen that most of the centrality measures in the existing technologies follow an endogenous evaluation logic centered on a single node, which cannot effectively identify those nodes with weak local connectivity but which play an irreplaceable basic role in the hierarchical expansion and global connectivity of the entire network. As a result, the evaluation results of node centrality in traffic network analysis are inaccurate and it is difficult to accurately identify key nodes in the traffic network. Summary of the Invention

[0005] The technical problem this invention aims to solve is that the accuracy of node centrality evaluation results in existing technologies is poor, making it difficult to accurately identify key nodes in transportation networks. To address this problem, this invention provides a method, apparatus, and electronic device for determining node centrality based on a pyramid structure.

[0006] The content of this invention includes: In a first aspect, embodiments of the present invention provide a method for determining the node centrality based on a pyramid structure, including: Obtain a transportation network, wherein nodes in the transportation network are used to represent transportation node entities, and edges in the transportation network are used to represent transportation connections between transportation node entities. The transportation node entities include at least one of cities, ports, airports, railway stations, logistics centers, and tourist attractions, and the transportation connections include at least one of highways, railways, waterways, and air routes. Traverse each node in the transportation network and extract all basic pyramids in the transportation network, wherein, based on the node... The root node is the base pyramid, and the slave nodes are the slave nodes. A breadth-first search is initiated, continuing until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered. This layer-by-layer expansion property characterizes the first... The number of nodes contained in the layer is greater than that in the first layer. The characteristics of the number of nodes contained in a layer, nodes For any node in the transportation network, It is a positive integer; For any node in the transportation network, the base pyramid in which the node participates is determined as the target pyramid corresponding to the node; The centrality score of the node is determined based on the pyramid participation score and / or core proximity score, wherein the pyramid participation score of the node is determined based on the number of target pyramids, and the core proximity score of the node is determined based on the distance between the node and the root node of the target pyramid.

[0007] Optionally, nodes Pyramid participation score for: ; in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to represent the number of elements in a set.

[0008] Optionally, nodes Core proximity score for: ; ; in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to characterize nodes exist The structural weights in Used to characterize nodes Reaching the node Minimum number of edges required.

[0009] Optionally, determining the centrality score of the node based on the pyramid participation score and / or core proximity score includes: The centrality score of a node is determined by a weighted sum of the pyramid participation score and the core proximity score.

[0010] Optionally, nodes in the transportation network are extracted. The base pyramid for the root node includes: From node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer; When first encountering a hierarchy Make the first The number of nodes contained in a layer is less than or equal to that of the first layer. When the number of nodes contained in the layer is reached, the breadth-first search is terminated, and the search is performed by node. The root node, containing levels 0 to 10. The tree subgraph formed by all nodes is determined as a subgraph with nodes as its core. The base pyramid for the root node, It is a positive integer.

[0011] Optionally, the weights of edges in the transportation network are used to characterize the expansion cost between transportation node entities, and the expansion cost is determined based on at least one of the construction cost, construction time, and construction difficulty of the transportation connection. The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node To begin performing a breadth-first search, we will start from the node. The cumulative expansion cost to each node is used as the stratification basis, and nodes whose cumulative expansion cost falls within the same preset interval are divided into the same level. For each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

[0012] Optionally, the edges in the traffic network have directionality to characterize feasible directions of traffic flow; The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node Initially, a breadth-first search is performed only along the positive directions of the directed edges. During the breadth-first search process, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

[0013] Secondly, embodiments of the present invention also provide a node centrality determination device based on a pyramid structure, comprising: The acquisition module is used to acquire a transportation network, wherein the nodes in the transportation network are used to represent transportation node entities, and the edges in the transportation network are used to represent transportation connections between transportation node entities. The transportation node entities include at least one of cities, ports, airports, railway stations, logistics centers, and tourist attractions, and the transportation connections include at least one of highways, railways, waterways, and air routes. The extraction module is used to traverse every node in the transportation network and extract all basic pyramids in the transportation network, wherein the pyramids are categorized by node. The root node is the base pyramid, and the slave nodes are the slave nodes. A breadth-first search is initiated, continuing until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered. This layer-by-layer expansion property characterizes the first... The number of nodes contained in the layer is greater than that in the first layer. The characteristics of the number of nodes contained in a layer, nodes For any node in the transportation network, It is a positive integer; The first determining module is used to determine, for any node in the transportation network, the basic pyramid in which the node participates as the target pyramid corresponding to the node; The second determining module is used to determine the centrality score of the node based on the pyramid participation score and / or the core proximity score, wherein the pyramid participation score of the node is determined based on the number of target pyramids, and the core proximity score of the node is determined based on the distance between the node and the root node of the target pyramid.

[0014] Thirdly, embodiments of the present invention provide an electronic device, including: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is configured to read the program in the memory to implement the steps in the method for determining the node centrality based on a pyramid structure as described in the first aspect.

[0015] Fourthly, embodiments of the present invention provide a readable storage medium for storing a program, which, when executed by a processor, implements the steps in the method for determining the node centrality based on a pyramid structure as described in the first aspect.

[0016] The beneficial effects of this invention are as follows: In its embodiments, a pyramid structure is introduced as the basic analysis unit. The frequency of a node's occurrence in all basic pyramids is quantified through pyramid participation scores, characterizing its universal connectivity value as a cornerstone of network expansion. Core proximity scores, utilizing the distance of a node from the root node within its target pyramid, measure its strategic influence on network expansion. Through this approach, an analytical framework centered on multiple roots and exogenous contributions across the entire network is constructed. The evaluation coordinate system is shifted from the node itself to the expansion needs of other nodes in the network, establishing an evaluation system based on exogenous contributions. This provides a novel quantitative tool for the planning, robustness analysis, and security assurance of transportation networks and other complex networks with hierarchical expansion characteristics. It improves the accuracy of node centrality assessment results, enabling reliable identification of key hubs in transportation networks. This, in turn, provides accurate data support for transportation infrastructure planning, emergency evacuation scheduling, multimodal transport optimization, and urban spatial structure analysis. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the node centrality determination method based on a pyramid structure provided in this embodiment of the invention; Figure 2a Example diagram of a traffic network provided for embodiments of the present invention; Figure 2b for Figure 2a The provided example diagram is a basic pyramid diagram of a transportation network; Figure 2c for Figure 2a Example diagram of the target pyramid corresponding to each node in the provided transportation network; Figure 3A schematic diagram of a node centrality determination device based on a pyramid structure provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0018] In the embodiments of this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship. In the embodiments of this application, the term "multiple" refers to two or more, and other quantifiers are similar. The terms "first," "second," etc., in the specification of this application are used to distinguish similar objects and are not used to describe a specific order or sequence. It should be understood that such terms can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first" and "second" are usually of the same class, without limiting the number of objects. For example, the first object can be one or multiple.

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0021] This application provides a method, apparatus, and electronic device for determining node centrality based on a pyramid structure, aiming to construct a novel node centrality evaluation paradigm to systematically compensate for the shortcomings of existing methods in identifying nodes supporting the global structure of a network.

[0022] Please see Figure 1 , Figure 1 This is a flowchart illustrating the method for determining node centrality based on a pyramid structure provided in an embodiment of the present invention. The method specifically includes the following steps: Step 101: Obtain the transportation network. The nodes in the transportation network are used to represent transportation node entities, and the edges in the transportation network are used to represent transportation connections between transportation node entities. The transportation node entities include at least one of cities, ports, airports, railway stations, logistics centers, and tourist attractions. The transportation connections include at least one of highways, railways, waterways, and air routes.

[0023] Step 102: Traverse every node in the transportation network and extract all basic pyramids in the transportation network, wherein, based on the node... The root node is the base pyramid, and the slave nodes are the slave nodes. A breadth-first search is initiated, continuing until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered. This layer-by-layer expansion property characterizes the first... The number of nodes contained in the layer is greater than that in the first layer. The characteristics of the number of nodes contained in a layer, nodes For any node in the transportation network, It is a positive integer.

[0024] Step 103: For any node in the transportation network, determine the basic pyramid in which the node participates as the target pyramid corresponding to the node.

[0025] Step 104: Determine the centrality score of the node based on the pyramid participation score and / or core proximity score, wherein the pyramid participation score of the node is determined based on the number of target pyramids, and the core proximity score of the node is determined based on the distance between the node and the root node of the target pyramid.

[0026] The node centrality determination method based on a pyramid structure provided in this invention is applied to the transportation field to evaluate the centrality of each node in a transportation network. Nodes in the transportation network represent transportation node entities, including but not limited to cities, ports, airports, railway stations, logistics centers, tourist attractions, or important landmarks. Edges in the transportation network represent transportation connections between transportation node entities, and the transportation connection methods include but are not limited to highways, railways, waterways, and air routes.

[0027] For example, taking a highway network as an example, each node in the transportation network represents a transportation node entity. If the transportation node entity is a specific location such as a port or scenic spot rather than an administrative unit, it is mapped to the county-level administrative unit to which it belongs. The geographical coordinates of each node are taken as the geometric centroid of the boundary of its corresponding administrative unit, calculated based on the official digital map. If two transportation node entities are adjacent to each other on any route in the highway network planning scheme, an edge is established between the corresponding two nodes. In some embodiments, to simplify modeling and focus on intercity connectivity, all urban ring road segments (such as ring roads around a single city) are removed from the edge set.

[0028] It should be understood that, in specific implementation, the traffic network can be modeled as an undirected or directed graph, an unweighted graph or a weighted graph. The weight of the edge can be used to represent actual operating parameters such as travel time, distance, road grade or traffic capacity, and the direction of the edge can be used to represent the direction of traffic connection. For ease of description, the following will first take the traffic network as an example of an undirected and unweighted simple graph.

[0029] Represent the transportation network as an undirected, unweighted simple graph. ,in, For the set of nodes in the transportation network, This represents the total number of nodes in the transportation network, where each node corresponds to an independent transportation node entity within the network. Let the set of edges of the transportation network be . Let be the total number of edges in the transportation network. Representation Nodes With nodes There are undirected connections between them. Among them, nodes... degree Defined as a node The total number of directly adjacent edges of a node. and nodes Shortest path distance between Defined as the minimum number of edges in a path connecting two nodes, i.e., the minimum number of edges between two nodes. Reaching the node The minimum number of edges required if there is no reachable path between two nodes. .node of Rank Neighborhood Defined as a node The shortest path length is exactly The set of nodes, i.e. In particular, That is, a node itself constitutes a 0th-order neighborhood.

[0030] For a set of nodes and edge set The constructed undirected and unweighted simple graph , with nodes A pyramid rooted at a certain point is a tree that satisfies the following conditions: Node set edge set And the expansion rates of adjacent levels satisfy: ; in, , It is a constant. For trees The height. For Any node Pyramid with root node ,like There is no other node in the middle. Pyramid with root node , making Then it is called For a maximal pyramid, for nodes The corresponding maximal pyramid may not be unique; that is, there may be multiple different maximal pyramids, all of which are based on nodes. It is the root node and satisfies the condition of expanding layer by layer, but contains different nodes.

[0031] Based on this, in this embodiment, every node in the transportation network is traversed, and all basic pyramids in the transportation network are extracted, wherein, taking nodes as an example, The root node is the base pyramid, and the slave nodes are the slave nodes. The process begins with a breadth-first search (BFS) that continues until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered.

[0032] In this embodiment, since the base pyramid is determined by the BFS algorithm and an explicit termination condition, the base pyramid is unique (at least its node set and hierarchy are unique). China-Israel node The basic pyramid (BP) for the root node is denoted as . This refers to a set of nodes. The basic pyramid, in which .

[0033] It should be noted that any node There may be multiple Instances, but all instances share the exact same set of nodes. And for any Its hierarchical node set Completely identical. Therefore, for each root node Simply select any one An example can be used to conduct the analysis.

[0034] Optionally, in some embodiments, nodes in the transportation network are extracted. The base pyramid for the root node includes: From node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer; When first encountering a hierarchy Make the first The number of nodes contained in a layer is less than or equal to that of the first layer. When the number of nodes contained in the layer is reached, the breadth-first search is terminated, and the search is performed by node. The root node, containing levels 0 to 10. The tree subgraph formed by all nodes is determined as a subgraph with nodes as its core. The base pyramid for the root node, It is a positive integer.

[0035] In practical implementation, it can be done through... upper node Start by executing the BFS algorithm at each level. Determine whether the condition is met. and in With distance The increase terminates when growth stops, and is identified within linear time. .

[0036] It should be noted that when the traffic network is modeled as an undirected, unweighted simple graph, the breadth-first search is layered by hop count, that is, the visited nodes are divided into layers according to the hop count distance. The specific method is not elaborated here.

[0037] Optionally, in some embodiments, the weights of edges in the traffic network are used to characterize the expansion cost between traffic node entities, the expansion cost being determined based on at least one of the construction cost, construction time, and construction difficulty of the traffic connection; The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node To begin performing a breadth-first search, we will start from the node. The cumulative expansion cost to each node is used as the stratification basis, and nodes whose cumulative expansion cost falls within the same preset interval are divided into the same level. For each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

[0038] It should be understood that the specific values ​​of the preset intervals can be set and adjusted according to the analysis granularity requirements. For example, a smaller interval width can improve the accuracy of layering and capture details of local network expansion; a larger interval width helps to identify macroscopic hierarchical structures and improve computational efficiency. By flexibly configuring the preset intervals, the centrality of nodes can be evaluated at different scales, thus better reflecting the multi-scale operational characteristics of real transportation networks and improving the practicality and interpretability of the centrality index.

[0039] In this embodiment, the expansion cost between traffic node entities is represented by the edge weights, thereby constructing a weighted pyramid. This allows the pyramid participation score and core proximity score to distinguish the differences between expansion via high-level roads and low-level roads, thereby further improving the accuracy of node centrality assessment.

[0040] In some embodiments, with nodes Starting from the node, according to the node Expand nodes in non-decreasing order of the shortest cumulative travel cost to each node, and group nodes with the same shortest cumulative travel cost into the same level.

[0041] Optionally, in some embodiments, the edges in the traffic network have directionality to characterize feasible directions of traffic flow; The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node Initially, a breadth-first search is performed only along the positive directions of the directed edges. During the breadth-first search process, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

[0042] In this embodiment, by modeling the traffic network as a directed graph, the actual propagation direction of traffic flow in the traffic network can be simulated, so that the constructed basic pyramid can truly reflect the reachability and expansion capability starting from the root node, thereby making the calculated node centrality more accurately characterize its influence or hub role in the one-way traffic structure.

[0043] As a hierarchical tree-based network analysis tool, the pyramid structure can capture the inherent growth patterns of complex networks by mining rooted subgraphs widely distributed across the entire network. In this embodiment of the invention, this decomposition method provides a multi-rooted, hierarchical representation of the transportation network. Each basic pyramid can reveal the expansion pattern of the network from local to global perspectives, reconstructing the evaluation logic of node importance from the fundamental perspective of network generation and evolution.

[0044] Based on the extracted basic pyramid, this invention proposes two novel centrality measures for each node in the transportation network to quantify the importance of the node. Specifically, the pyramid participation score and / or core proximity score of each node are calculated.

[0045] The Pyramid Participation Score (PPS) measures a node's universal connectivity value as a common building block for network expansion by quantifying the frequency with which it appears in all possible basic pyramid structures of the transportation network (each rooted at every node in the network). A higher PPS value indicates that the node plays an indispensable connectivity role in the hierarchical expansion of all regions of the network.

[0046] PPS is used to quantify the universality of nodes as basic structural units in a network pyramid, measuring the degree of participation of a node in all basic pyramids rooted at different nodes. Optionally, in some embodiments, for graphs... ,node Pyramid participation score For nodes The cardinality of the set of basic pyramids in which the nodes participate. The corresponding number of target pyramids: ; in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to represent the number of elements in a set.

[0047] The higher the value, the stronger the node. The more different base pyramids a node is contained within, the more extensive its connectivity becomes during the network's hierarchical expansion. It is crucial for establishing and maintaining connectivity between different regional subnetworks, and its failure is highly likely to cause the network to split into multiple disconnected components. Therefore, The higher the value of a node, the higher its centrality score usually is.

[0048] The Core Proximity Score (CPS) measures a node's strategic influence on network expansion by calculating the weighted sum of the inverse levels of its distance from the root node (i.e., the core of influence) across all the basic pyramid structures it participates in. A higher CPS value indicates that the node is more likely to play a role closer to the core, and thus has a stronger control over network coverage and connectivity efficiency.

[0049] The core proximity score quantifies a node's strategic influence by assessing its distance from the root node within the base pyramid it participates in (i.e., the target pyramid to which the node corresponds). The closer a node is to the root node of the target pyramid, the greater its influence on that root node. Optionally, in some embodiments, for graphs... and the given root node ,node In the base pyramid The structural weights in the code are defined as follows: ; in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to characterize nodes Reaching the node The minimum number of edges required. In this way, nodes that are closer to the root node in a leap are assigned a higher contribution weight.

[0050] Furthermore, nodes Core proximity score , is defined as the sum of its structural weights in all corresponding target pyramids: ; The higher the value, the stronger the node. In the numerous basic pyramids, these nodes are always located near the root node. These nodes are the network core with strong influence, capable of reaching and affecting most areas of the network through a short path; their failure will severely reduce the overall operational efficiency of the network. Therefore, The higher the value of a node, the higher its centrality score usually is.

[0051] In some embodiments, the pyramid engagement score or core proximity score is determined as the centrality score of a node. In other embodiments, the sum of the pyramid engagement score and the core proximity score is determined as the centrality score of a node. In still other embodiments, the centrality score of a node is determined based on a weighted sum of the pyramid engagement score and the core proximity score.

[0052] Please see Figures 2a-2c To intuitively demonstrate the definitions and calculation processes of PPS and CPS, the following uses... Figure 2a Using the traffic network shown as an example, the calculation process of PPS and CPS will be explained.

[0053] First, extract Figure 2a In the network shown, each node serves as the root node and corresponds to a basic pyramid. This yields all the basic pyramids in the network; please refer to [link / reference] for details. Figure 2b For example, node 3 corresponds to... It is a pyramid with a height of 2, containing 9 nodes; and node 4 corresponds to The height is 1. The basic pyramids corresponding to the root nodes 2, 7, 8, and 9 are all pyramids with a height of 0, because the degree of these nodes is 1, and the hierarchical expansion process will terminate immediately.

[0054] Please see Figure 2c For any node , Measure node How many different base pyramids are included, i.e., nodes The number of corresponding target pyramids reflects the universal connectivity value of that node. Then quantization node The overall proximity of a node to the root node (RN) of each target pyramid it participates in reflects its universal influence. Taking node 4 as an example, its layer number (LN) in each target pyramid is determined. Specifically, the node's level in each target pyramid is... , , All are located on the first floor. Currently at level 0, it participates in 4 different base pyramids; therefore, the target pyramid corresponding to node 4 is... , , , ,therefore The CPS calculation process for node 4 is as follows: .

[0055] In this embodiment, a backpropagation (BP) algorithm is constructed with all nodes in the transportation network as the root structure, achieving a fundamental transformation of the evaluation coordinate system from "the node itself" to "all other nodes in the network." A node-based... The BP for the root node is essentially a BP for the network slave nodes. Logical simulation of the process of expanding outward along the shortest path.

[0056] By assigning each node the identity of a root node and simulating its expansion process, the transportation network is deconstructed into multiple interconnected hierarchical subgraphs. Based on this deconstruction, PPS quantifies a node's universality as a common cornerstone for network expansion by counting how many different root nodes' graphs it appears in. A higher value means that more areas of the network must pass through that node as it extends outwards, thus indicating the node's greater universality in supporting network connectivity. CPS, on the other hand, measures a node's distance from the core during these expansion processes through hierarchical weighting. Closer distances indicate a node's tendency to play a strategic role near hubs, and a stronger ability to control network coverage and connectivity efficiency. Through the settings of PPS and CPS, the value of a node is no longer defined solely by its topological characteristics, but rather by the breadth and strategic depth of its participation in all levels of network expansion.

[0057] For ease of understanding, the following explanation uses different types of transportation networks as examples. In some embodiments, the transportation network is a comprehensive highway network. The spatial distribution of high PPS (Power, Power, and Scaling) areas in the comprehensive highway network is highly consistent with that of high CPS (Concentration, Power, and Scaling) areas, both centered on the intersection of the Guanzhong Plain and the Central Plains urban agglomeration, forming a core cluster area. This area is the concentrated location of comprehensive transportation hubs in the entire backbone highway network after the integration of expressways and ordinary national highways.

[0058] In other embodiments, the transportation network is a general national highway network, whose topology exhibits stronger spatial homogeneity, and its hierarchical expansion pattern is more consistent with the geographical pattern of traditional land transportation systems. In the general national highway network scenario, PPS quantifies the breadth of node participation in the basic pyramid structure rooted at each administrative unit. The value of this indicator directly reflects the universal importance of a node as a cross-regional and cross-level connectivity hub during the expansion of the national highway network. The higher the value, the more crucial it is as a core connectivity node that needs to be universally included when the root nodes of different regions carry out hierarchical expansion of the road network, and the stronger its supporting role in the overall connectivity of the national highway network. From a spatial differentiation perspective, the PPS of the general national highway network exhibits a gradient hierarchical structure around the trunk line direction, rather than a simple concentric circle distribution, while the CPS core agglomeration pattern presents a cross-shaped configuration dominated by north-south corridors. The spatial differentiation characteristics of PPS and CPS directly reflect the hub hierarchy, structural core, and cross-regional connectivity logic of the general national highway network.

[0059] Taking the above specific embodiments as examples, the method provided by the embodiments of the present invention can systematically identify three types of structural nodes in the transportation network that are seriously underestimated by traditional measures.

[0060] The first type of structural node is geographically located near provincial administrative boundaries, serving as an essential "interface" for connecting road networks in adjacent provinces. While existing technologies like Betweenness Centrality (BN) can theoretically identify these nodes, their calculation logic is based on statistics of all shortest path pairs across the entire network. Therefore, it naturally favors nodes located at the geometric center of the network or in traffic convergence areas. Since inter-provincial gateway nodes are often located on the edge of local networks, their proportion of global shortest paths is far less than that of core hubs. Thus, BN cannot accurately measure the centrality of these nodes.

[0061] The PPS and CPS provided by this invention can accurately identify such nodes because its evaluation logic is no longer limited to the global shortest path traffic perspective, but switches to the access perspective of the local expansion process. The essential function of inter-provincial gateway nodes is that they are the only or very few connection points when the road networks of two adjacent provinces (or regions) expand into each other. When a BP expansion is performed with a node in one province as the root node, the expansion path will almost inevitably pass through that gateway to reach nodes in the other province. Therefore, these nodes appear repeatedly in a large number of cross-regional BPs, thus obtaining high PPS values ​​and improving the accuracy of the centrality evaluation results for these nodes.

[0062] The second type of structural nodes are located at the intersections of east-west and north-south national trunk highways, forming the backbone of the road network. However, these nodes generally have low administrative levels, and their own traffic demand is far less than that of provincial capitals, resulting in less prominent local degree values. The degree centrality method in existing technologies fails to identify these nodes because it only counts the number of direct connections, without considering the quality or direction of those connections. A node connecting four ordinary highways has the same degree value as a node connecting four national trunk highways. While betweenness centrality can partially capture the bridging function of intersections, its calculation depends on the specific shortest path distribution. If cross-regional traffic flows in both north-south and east-west directions do not all need to transfer at this node (some can detour via other parallel routes), its betweenness ranking will drop significantly.

[0063] In this embodiment, PPS and CPS fundamentally change the evaluation reference system by enumerating the backpropagation (BP) of all root nodes. Nodes located at the intersection of trunk lines have unique value because they are simultaneously essential intersections for expansion in multiple directions. When expanding southeastward from a Northwest node, these trunk line intersections are crucial springboards for traversing geographical units; similarly, when expanding northwestward from an East China node, they are unavoidable pathways. In other words, their existence is superimposed from expansion processes in multiple directions and regions, resulting in a significant weighting effect in the cumulative calculation of PPS / CPS. From a structural perspective, PPS / CPS can accurately reveal the skeletal supporting role of these nodes as intersections of network latitude and longitude lines, improving the accuracy of the centrality evaluation results for such nodes.

[0064] The third type of structural nodes are typically located in the transitional and connecting zones of regional road networks. They are neither provincial capital economic centers nor national trunk line hubs, but rather gradient hubs connecting heterogeneous geographical units such as high-density core areas and low-density peripheral areas, and plains and mountains. Traditional global indicators (such as proximity centrality and betweenness centrality) naturally tend to assign high scores to nodes located at the geometric center of the network or connecting core areas when uniformly ranking all network nodes. Because gradient nodes are located in a relatively isolated area, their global topological statistics (average shortest path distance, shortest path percentage) are far inferior to those of core hubs, and therefore cannot reflect their true supporting value in cross-regional road network connections.

[0065] In this embodiment, the ability of PPS / CPS to identify such nodes stems from its source-specific evaluation and overall accumulation calculation mechanism. A gradient node may seem insignificant from a global perspective, but its importance becomes apparent when the evaluation perspective shifts to the low-density area it connects to. This mechanism essentially quantifies the connecting value of gradient nodes in ensuring full road network coverage and supporting regional collaboration. They provide gradient channels for edge areas to access the core network, serving as an indispensable transitional support for achieving balanced network coverage.

[0066] The three types of structural nodes mentioned above correspond to three structural functions in transportation network expansion: inter-regional interface function (inter-provincial gateway), backbone maintenance function (trunk line intersection), and gradient connection function (transition node). The PPS and CPS provided in this embodiment of the invention can improve the accuracy of the centrality evaluation results for these types of nodes by simulating multi-level expansion of the entire network.

[0067] The method provided in this invention can improve the accuracy of node centrality evaluation results, accurately identify truly influential hub nodes (such as key transfer stations and logistics distribution centers), thereby avoiding resource misallocation due to centrality misjudgments. It can also accurately assess the connectivity of transportation nodes such as ports, railway stations, and freight hubs within the integrated transportation network. This method not only enhances the physical interpretability of centrality indicators but also further supports downstream applications such as intelligent navigation, logistics resource allocation, and network resilience assessment, expanding the practical value of node centrality analysis in intelligent transportation systems.

[0068] like Figure 3 As shown, this embodiment of the invention also provides a node centrality determination device 300 based on a pyramid structure, comprising: The acquisition module 301 is used to acquire a traffic network, wherein the nodes in the traffic network are used to represent traffic node entities, and the edges in the traffic network are used to represent traffic connections between traffic node entities. The traffic node entities include at least one of cities, ports, airports, railway stations, logistics centers, and tourist attractions, and the traffic connections include at least one of highways, railways, waterways, and air routes. Extraction module 302 is used to traverse every node in the transportation network and extract all basic pyramids in the transportation network, wherein, based on the node... The root node is the base pyramid, and the slave nodes are the slave nodes. A breadth-first search is initiated, continuing until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered. This layer-by-layer expansion property characterizes the first... The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in the layer, nodes For any node in the transportation network, It is a positive integer; The first determining module 303 is used to determine, for any node in the transportation network, the basic pyramid in which the node participates as the target pyramid corresponding to the node; The second determining module 304 is used to determine the centrality score of the node based on the pyramid participation score and / or the core proximity score, wherein the pyramid participation score of the node is determined based on the number of target pyramids, and the core proximity score of the node is determined based on the distance between the node and the root node of the target pyramid.

[0069] Optionally, nodes Pyramid participation score for: ; in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to represent the number of elements in a set.

[0070] Optionally, nodes Core proximity score for: ; ; in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to characterize nodes exist The structural weights in Used to characterize nodes Reaching the node Minimum number of edges required.

[0071] Optionally, the second determining module 304 is specifically used for: The centrality score of a node is determined by a weighted sum of the pyramid participation score and the core proximity score.

[0072] Optionally, nodes in the transportation network are extracted. The base pyramid for the root node includes: From node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer; When first encountering a hierarchy Make the first The number of nodes contained in a layer is less than or equal to that of the first layer. When the number of nodes contained in the layer is reached, the breadth-first search is terminated, and the search is performed by node. The root node, containing levels 0 to 10. The tree subgraph formed by all nodes is determined as a subgraph with nodes as its core. The base pyramid for the root node, It is a positive integer.

[0073] Optionally, the weights of edges in the transportation network are used to characterize the expansion cost between transportation node entities, and the expansion cost is determined based on at least one of the construction cost, construction time, and construction difficulty of the transportation connection. The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node To begin performing a breadth-first search, we will start from the node. The cumulative expansion cost to each node is used as the stratification basis, and nodes whose cumulative expansion cost falls within the same preset interval are divided into the same level. For each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

[0074] Optionally, the edges in the traffic network have directionality to characterize feasible directions of traffic flow; The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node Initially, a breadth-first search is performed only along the positive directions of the directed edges. During the breadth-first search process, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

[0075] The node centrality determination device 300 based on the pyramid structure provided in this application embodiment can execute the above method embodiment, and its implementation principle and technical effect are similar, so it will not be described again here.

[0076] It should be noted that the division of units in the embodiments of this application is illustrative and only represents one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units.

[0077] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0078] like Figure 4 As shown, this application embodiment provides an electronic device 400, including: a memory 402, a processor 401, and a program stored in the memory 402 and executable on the processor 401; the processor 401 is used to read the program in the memory 402 to implement the steps in the node centrality determination method based on the pyramid structure as described above.

[0079] This application also provides a readable storage medium storing a program. When the program is executed by a processor, it implements the various processes of the above-described method for determining the node centrality based on a pyramid structure and achieves the same technical effect. To avoid repetition, it will not be described again here. The readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to magnetic storage (such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MOs), etc.), optical storage (such as compact disks (CDs), digital video discs (DVDs), Blu-ray discs (BDs), high-definition versatile discs (HVDs), etc.), and semiconductor storage (such as read-only memory (ROMs), erasable programmable read-only memory (EPROMs), electrically erasable programmable read-only memory (EEPROMs), non-volatile memory (NAND flash), solid-state drives (SSDs)).

[0080] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0081] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, 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 is stored in a storage medium (such as ROM / RAM, disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0082] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other modifications under the guidance of this application without departing from its spirit, and all of these modifications are within the scope of protection of this application.

Claims

1. A method for determining node centrality based on a pyramid structure, characterized in that, include: Obtain a transportation network, wherein nodes in the transportation network are used to represent transportation node entities, and edges in the transportation network are used to represent transportation connections between transportation node entities. The transportation node entities include at least one of cities, ports, airports, railway stations, logistics centers, and tourist attractions, and the transportation connections include at least one of highways, railways, waterways, and air routes. Traverse each node in the transportation network and extract all basic pyramids in the transportation network, wherein, based on the node... The root node is the base pyramid, and the slave nodes are the slave nodes. A breadth-first search is initiated, continuing until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered. This layer-by-layer expansion property characterizes the first... The number of nodes contained in the layer is greater than that in the first layer. The characteristics of the number of nodes contained in a layer, nodes For any node in the transportation network, It is a positive integer; For any node in the transportation network, the base pyramid in which the node participates is determined as the target pyramid corresponding to the node; The centrality score of the node is determined based on the pyramid participation score and / or core proximity score, wherein the pyramid participation score of the node is determined based on the number of target pyramids, and the core proximity score of the node is determined based on the distance between the node and the root node of the target pyramid.

2. The method for determining node centrality based on a pyramid structure according to claim 1, characterized in that, node Pyramid participation score for: ； in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to represent the number of elements in a set.

3. The method for determining node centrality based on a pyramid structure according to claim 1, characterized in that, node Core proximity score for: ； ； in, Used to characterize nodes The base pyramid for the root node, Used for characterization The set of nodes, Used to characterize nodes exist The structural weights in Used to characterize nodes Reaching the node Minimum number of edges required.

4. The method for determining node centrality based on a pyramid structure according to claim 1, characterized in that, The determination of the centrality score of the node based on the pyramid participation score and / or core proximity score includes: The centrality score of a node is determined by a weighted sum of the pyramid participation score and the core proximity score.

5. The method for determining node centrality based on a pyramid structure according to claim 1, characterized in that, Extracting nodes from the traffic network The base pyramid for the root node includes: From node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer; When first encountering a hierarchy Make the first The number of nodes contained in a layer is less than or equal to that of the first layer. When the number of nodes contained in the layer is reached, the breadth-first search is terminated, and the search is performed by node. The root node, containing levels 0 to 10. The tree subgraph formed by all nodes is determined as a subgraph with nodes as its core. The base pyramid for the root node, It is a positive integer.

6. The method for determining node centrality based on a pyramid structure according to claim 5, characterized in that, The weights of edges in the transportation network are used to characterize the expansion cost between transportation node entities. The expansion cost is determined based on at least one of the construction cost, construction time, and construction difficulty of the transportation connection. The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node To begin performing a breadth-first search, we will start from the node. The cumulative expansion cost to each node is used as the stratification basis, and nodes whose cumulative expansion cost falls within the same preset interval are divided into the same level. For each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

7. The method for determining node centrality based on a pyramid structure according to claim 5, characterized in that, The edges in the traffic network are directional, used to characterize the feasible directions of traffic flow; The slave node Begin performing a breadth-first search, during which, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer includes: From node Initially, a breadth-first search is performed only along the positive directions of the directed edges. During the breadth-first search process, for each level... Determine whether the condition is satisfied. The number of nodes contained in the layer is greater than that in the first layer. The number of nodes contained in a layer.

8. A node centrality determination device based on a pyramid structure, characterized in that, include: The acquisition module is used to acquire a transportation network, wherein the nodes in the transportation network are used to represent transportation node entities, and the edges in the transportation network are used to represent transportation connections between transportation node entities. The transportation node entities include at least one of cities, ports, airports, railway stations, logistics centers, and tourist attractions, and the transportation connections include at least one of highways, railways, waterways, and air routes. The extraction module is used to traverse every node in the transportation network and extract all basic pyramids in the transportation network, wherein the pyramids are categorized by node. The root node is the base pyramid, and the slave nodes are the slave nodes. A breadth-first search is initiated, continuing until the first instance of a tree-like connected subgraph that does not satisfy the layer-by-layer expansion property is encountered. This layer-by-layer expansion property characterizes the first... The number of nodes contained in the layer is greater than that in the first layer. The characteristics of the number of nodes contained in a layer, nodes For any node in the transportation network, It is a positive integer; The first determining module is used to determine, for any node in the transportation network, the basic pyramid in which the node participates as the target pyramid corresponding to the node; The second determining module is used to determine the centrality score of the node based on the pyramid participation score and / or the core proximity score, wherein the pyramid participation score of the node is determined based on the number of target pyramids, and the core proximity score of the node is determined based on the distance between the node and the root node of the target pyramid.

9. An electronic device, comprising: A memory, a processor, and a program stored in the memory and executable on the processor; characterized in that the processor is configured to read the program from the memory to implement the steps in the method for determining the node centrality of a pyramid structure as described in any one of claims 1 to 7.

10. A readable storage medium for storing a program, characterized in that, When the program is executed by the processor, it implements the steps in the method for determining the node centrality of a pyramid structure as described in any one of claims 1 to 7.

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