Network toughness index multi-dimensional quantitative evaluation method

Abstract

The invention relates to the technical field of network analysis, and further relates to a network toughness index multi-dimensional quantitative evaluation method, which comprises the following steps of: 1, acquiring original topological data of a target network, and constructing a topological base toughness index of the network under the condition of no external impact; 2, calculating a crisis exposure factor; 3, calculating the mediation centrality of each node; calculating a structural hole limit system of each node; combining the mediation centrality and the information redundancy degree to generate an adaptation-recovery index for measuring the self-healing and regeneration capacity of the network; and step 4, carrying out impact resistance correction on the topological base toughness index and the crisis exposure factor, then carrying out index weight amplification according to the adaptation-recovery index, and finally generating a multi-dimensional network toughness comprehensive index in combination with stability correction of network toughness fluctuation. According to the method, network vulnerability identification and toughness strategy optimization based on the structure attribute and the dynamic historical response can be realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of network analysis, and particularly relates to a network resilience index multi-dimensional quantitative evaluation method. BACKGROUND

[0002] In the current complex network research and practical application, network resilience as a multi-dimensional system characteristic has become a hot spot of attention in the cross of many disciplines. Network resilience not only reflects the ability of network to maintain function when resisting external impact, but also involves the ability of rapid recovery and long-term stability after impact. In the prior art, the research on network resilience is mostly focused on the measurement of single dimension or static robustness, and the basic topological indexes such as node degree distribution, average path length and clustering coefficient are usually used as the description means. For example, the connectivity index and the average path length are often used to describe the overall robustness of the network, and it is considered that the high connectivity of nodes or links means that the network structure is more difficult to be segmented when it is subjected to random attack; for another example, the clustering coefficient is used to measure the local clustering effect, and to judge the local absorption and transmission ability of the network when it is subjected to local failure of links or nodes. At the same time, the degree distribution and the degree correlation coefficient of the network are often used to identify the hierarchy and matching mode of the network, and then the stability and anti-impact potential of the network are explained from the aspect of structural characteristics.

[0003] Although the above topological indexes and traditional measurement methods have achieved good application effect in the evaluation of static stability of network structure, they often cannot fully describe the dynamic recovery and adaptation ability of the network when it is subjected to external impact. Because these static topological characteristics lack the information of time dimension, they cannot reflect the real response and adjustment process of the network under continuous external impact. Some researches try to introduce dynamic models, such as simulation based on propagation process, to explore the change of propagation characteristics of the network after impact, so as to reflect the resilience of the network from the side, but due to the lack of actual historical impact data, it is difficult to accurately quantify the influence depth and duration of impact on the actual operation function of the network, so that the evaluation result is often biased towards theoretical deduction rather than real network response. SUMMARY

[0004] The main purpose of the present application is to provide a network resilience index multi-dimensional quantitative evaluation method, which comprehensively considers the topological base resilience, historical crisis impact characteristics, node recovery potential and long-term stability of the network, relies on the continuous fusion of multi-dimensional factors, generates a network resilience comprehensive index which is quantifiable, comparable and dynamically updatable, and can accurately describe the comprehensive ability of complex network in resisting external impact, realizing rapid recovery and maintaining long-term operation stability, so as to help to realize the identification of network vulnerability and optimization of resilience strategy based on structural attributes and dynamic historical response.

[0005] In order to solve the above problems, the technical scheme of the present application is as follows: A network resilience index multi-dimensional quantitative evaluation method, the method comprises: Step 1: Obtain the original topology data of the target network, and construct the topology base resilience index of the network under the condition of no external impact, the greater the value, the healthier the network at the inherent structure level; Step 2: Identify all crisis stages based on historical monitoring records to obtain the total number of crisis stages; for each crisis stage, the percentage of network function decline is calculated as the impact strength; the length of continuous network function decline is calculated as the crisis duration; the time for network function to recover from the lowest point to the baseline before the crisis is calculated as the recovery time; according to the total number of crisis stages, impact strength, crisis duration and recovery time, the crisis exposure factor is calculated; Step 3: Calculate the intermediate centrality of each node to measure the bridge role of the node in the whole network information flow; calculate the structural hole limit system of each node to measure the information redundancy degree controlled by the node; combine the intermediate centrality and information redundancy degree to generate the adaptation-recovery index to measure the self-healing and regeneration ability of the network; Step 4: Correct the topology base resilience index by impact resistance according to the crisis exposure factor, then amplify the index according to the adaptation-recovery index, and finally generate the multi-dimensional network resilience comprehensive index by combining the stability correction of network resilience fluctuation.

[0006] Further, the original topology data includes: the degree of each node, the local clustering coefficient, the number of independent paths and the average shortest path length to all other nodes.

[0007] Further, step 1 specifically includes: at the node scale, multiply the node degree and the local clustering coefficient to represent the connectivity-aggregation coupling effect, directly take the number of independent paths as the diversity factor, and take the inverse of the average shortest path length to represent the transmission efficiency; at the network overall scale, sum and average the above three types of node factors respectively, then amplify the connectivity-aggregation coupling effect and the transmission efficiency twice, and take the sum of the results and the diversity factor as the logarithmic conversion to obtain the topology base resilience index under the condition of no external impact.

[0008] Further, in step 2, multiply the impact strength and the duration of each crisis stage, and then sum them up, and divide the result by the total cumulative value of the sum of the impact strength and the recovery time to obtain the crisis exposure factor; the greater the value of the crisis exposure factor, the more fragile the network in the impact stage.

[0009] Further, step 3 specifically includes: setting an evaluation time window and locking a reference topology snapshot, in which each node is assigned a time weight; under the same reference topology snapshot, calculating the normalized betweenness centrality of all nodes; synchronously calculating the structural hole limitation of all nodes, and performing inverse Sigmoid compression on the structural hole limitation to make the structural hole advantage present a numerical saturation upper limit, avoiding the imbalance of evaluation results caused by absolute monopoly nodes; dividing the normalized betweenness centrality by the structural hole limitation of each node to obtain the bridge-hole coupling rate, then weighting and accumulating the bridge-hole coupling rate with the time weight as a multiplier, and taking the square root of the accumulated result to form the recovery potential index of the node level; assigning the same weight or weighting according to the node weight to the recovery potential index of each node in the network, calculating the weighted arithmetic mean, and using it to depict the average recovery potential level of the whole network; then, based on the same weight system, calculating the squared difference of each node's recovery potential index and the weighted average value of the network and summing them up to obtain the weighted squared deviation of the distribution, which reflects the uniformity of the distribution of recovery potential among different nodes; finally, combining the weighted arithmetic mean and the weighted squared deviation in a harmonic weighting manner to form a comprehensive measurement index that can reflect the average strength and distribution balance of the recovery potential among network nodes, and obtaining the adaptation-recovery index.

[0010] Further, the time weight is obtained by inversely scaling the standard deviation of the intermediate centrality sequence of the node in the last period, which emphasizes the dominant role of structural stable nodes in the recovery process; the normalized betweenness centrality is obtained by three transformations of quartile de-extremum, 0-1 linear stretching and power law reduction, which ensures that the bridge effect can maintain the distribution difference and not be hidden by extreme values.

[0011] Further, step 3 further comprises: in parallel, traversing all possible two-by-two combinations between nodes, counting the number of independent parallel paths between each pair of nodes, and calculating the ratio of the number of independent parallel paths between each pair of nodes to the maximum number of parallel paths between two nodes in theory, to quantify the link diversity of the network; at the same time, calculating the modularity coefficient of the Louvain community partition result of the network, and converting it into an attenuation factor using inverse translation, to reflect the positive contribution of partition isolation to diffusion suppression; multiplying the primary recovery coefficient by the link diversity ratio, and then adding the attenuation factor in an additive manner to obtain the comprehensive recovery potential without scale compression; if the comprehensive recovery potential exceeds the theoretical upper limit of resilience, mapping and compressing it using a hyperbolic tangent function to ensure consistency of the index interval; to offset the index comparability deviation caused by the difference in network size, introduce the node number logarithm term as the denominator adjustment, so that a larger network with more dispersed structure will not be overestimated in recovery potential due to the large number of nodes, to obtain the size-standardized result; based on the size-standardized result, perform numerical normalization processing to finally output the adaptation-recovery index, which is continuous and monotonic between 0 and the theoretical maximum value, and positively correlated with the bridge-cave synergy degree, link diversity and partition isolation.

[0012] Further, the process of numerical normalization based on the size-standardized result comprises: taking the size-standardized result as a reference, performing Box-Cox transformation on it and multiplying it by a constant to perform numerical stretching, and finally output the adaptation-recovery index.

[0013] Further, step 4 specifically comprises: taking the value of the topology base resilience index divided by the crisis exposure factor plus one as the structure-impact correction term; setting the exponential weight of the structure-impact correction term as the ratio of the adaptation-recovery index to the adaptation-recovery index plus one, to reflect the amplification effect of recovery capacity on overall resilience, to obtain the correction adjustment result; selecting the latest year as the time window, calculating the standard deviation of all topology base resilience indexes in the time window to represent the long-term fluctuation range of the base resilience; taking the negative topology base resilience index standard deviation value of the natural exponential function as the stability correction term; multiplying the correction adjustment result by the stability correction term to obtain the multi-dimensional network resilience comprehensive index; the larger the value of the network resilience comprehensive index, the stronger the network resilience.

[0014] The network resilience index multidimensional quantitative evaluation method has the following beneficial effects: the network resilience multidimension can be comprehensively quantified, and the limitations of traditional single topology or propagation model are compensated. The method fully considers the local structure properties of nodes such as connectivity, clustering coefficient, number of independent paths and global transmission efficiency, and introduces time sequence information such as impact strength, duration and recovery duration based on historical crisis events, which effectively offsets the inherent structure strength of the network and external impact history. By introducing time-weighted bridge-hole coupling rate and structure hole limit system correction, the bridge effect and redundancy information control ability at the node level are further integrated, and the redundancy path and community isolation effect are measured by the link diversity ratio and the modularization coefficient, so as to realize the three-dimensional characterization of the adaptation-recovery ability. Through the fusion of the index weight amplification mechanism and the stability correction term, it is ensured that the comprehensive resilience index can sensitively capture the recovery potential and long-term fluctuation characteristics, and the numerical value is monotonous and continuous, and the comparability is strong, which is suitable for dynamic tracking. In summary, the method not only improves the response recognition accuracy of the network in the face of external impact, but also provides operable index support in resilience strategy optimization, and provides a strong theoretical basis and practical tool for multi-level and full-cycle resilience enhancement management of complex networks. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 A network resilience index multidimensional quantitative evaluation method provided for an embodiment of the application is shown in the method flowchart. Figure 2 A relationship scatter plot of the intermediate centrality and the structure hole limit system in the embodiment of the application. Figure 3 A node degree and local clustering coefficient distribution graph in the embodiment of the application. DETAILED DESCRIPTION

[0016] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should be within the scope of protection of the present application.

[0017] Embodiment 1: Reference Figure 1 A network resilience index multidimensional quantitative evaluation method, the method comprising: Step 1: Obtain the original topology data of the target network, and construct the topology base resilience index of the network under the condition of no external impact. The greater the value, the healthier the network at the inherent structure level. Step 2: Identify all crisis stages based on historical monitoring records, and obtain the total number of crisis stages; for each crisis stage, count the percentage of network function decline as the impact intensity; count the length of continuous network function decline as the crisis duration; count the time taken for network function to recover from the lowest point to the pre-crisis baseline as the recovery duration; calculate the crisis exposure factor according to the total number of crisis stages, impact intensity, crisis duration, and recovery duration; Step 3: Calculate the intermediary centrality of each node to measure the node's role as a bridge in the network's information flow; calculate the structural hole limitation system of each node to measure the degree of information redundancy controlled by the node; combine the intermediary centrality and information redundancy to generate the adaptation-recovery index that measures the network's self-healing and regenerative capacity; Step 4: Perform impact resistance correction by combining the topological base resilience index with the crisis exposure factor, then perform index weight amplification based on the adaptation-recovery index, and finally combine the stability correction of network resilience fluctuations to generate the multi-dimensional network resilience comprehensive index.

[0018] Specifically, in the structure layer, the method abstracts any actual network as a topological object composed of nodes and edges, considering that the connectivity between nodes, local cluster degree, information transmission distance, and parallel path number together determine the normal function level that the network can maintain without disturbance; at this level, the method aggregates the global connectivity strength, clustering tightness, transmission efficiency, and redundancy path richness of the network, and merges them into the topological base resilience index, thereby mapping the inherent structure of the network to a single value that represents the "buffer space" provided by the system.

[0019] Secondly, in the impact layer, the method introduces the concept of exposure in risk science, considering the historically observed external crises as one trial after another, and by counting the impact intensity, duration, recovery duration, and total number of crisis stages, it converts the entire process of each function decline and recovery into a quantifiable time risk trajectory, and then aggregates these trajectories into a crisis exposure factor, which reveals the composite risk load faced by the network at different time periods and its cumulative vulnerability; the essence of this factor is a joint characterization of impact frequency, magnitude, and recovery rate, which compresses the impact history in time into a comparable scale in space.

[0020] Then in the adaptation layer, the method follows the importance of "bridge node", "information control node" and "redundant path" in organizational behavior for quick recovery, respectively measures the information hub efficiency represented by the intermediary centrality, the resource monopoly degree represented by the structural hole limit system, the redundant flow richness represented by the link diversity ratio and the community isolation intensity represented by the modularization coefficient, and maps them to the adaptation-recovery index through nonlinear coupling to express whether the network can self-organize to form alternative paths after the function is damaged and the regeneration potential of blocking the chain failure to a certain extent; In this layer, the bridge performance of the node and the information redundancy are regarded as the micro driving force, and the multi-path and the partition isolation are regarded as the macro safety valve, both of which are converted into single body dimension after the scale is unified.

[0021] Finally in the integration layer, the method considers that the contributions of the structure layer, the impact layer and the adaptation layer are not linearly added, but there is a significant amplification or offset effect, so it proposes three-step fusion logic of impact resistance correction, exponential weight amplification and stability correction: the impact resistance correction deducts the crisis exposure factor by the topological base resilience index, so that the inherent buffer and external load are hedged in the same framework; The exponential weight amplification implements power amplification on the correction result in the interval of zero to one by the adaptation-recovery index, emphasizing the multiplier effect of self-healing potential on overall resilience; The stability correction then introduces the structural base fluctuation amplitude of the sliding window, maps the reverse weight of long-term volatility to the exponential space, and suppresses the score of the network with short-term peak but long-term instability.

[0022] The multi-dimensional network resilience comprehensive index generated by the product of the three holds the four main lines of "innate strength", "historical load", "acquired recovery" and "long-term stability" at the same time, and realizes the quantitative expression of the whole life cycle resilience of complex networks with a single scale. The core innovation of this principle is: on the one hand, it extends the traditional static robustness based on connectivity or average path length to dynamic resilience considering the timing of the impact and the reconstruction of the function; on the other hand, it overcomes the defects of simple global indicators or simple local indicators by introducing the multi-scale coupling of community isolation and information hub; at the same time, the modular architecture is adopted in the calculation framework, which makes the topological base resilience index, the crisis exposure factor, the adaptation-recovery index and the comprehensive index independent of each other and can exchange input and output, which not only ensures the flexibility of the method in practice, but also ensures the comparability and accumulation of the index system. In specific implementation, the system first records the node relationship and the function index marked with time stamp in the data storage layer through the graph database or sparse matrix; in the calculation layer, it sequentially calls the structure extraction service, the historical impact analysis service, the self-healing potential evaluation service and the index fusion service, and uses a unified data interface to transfer intermediate results between services; in the display layer, the system projects the multi-dimensional network resilience comprehensive index and each sub-index to the interactive time sequence panel and structure heat map, helping users observe the resilience evolution from the time and structure dimensions; in the application layer, the index can drive risk warning, vulnerability positioning and resource scheduling decisions, and can be linked with the simulation platform to test the improvement effect of intervention strategies on comprehensive resilience. In summary, the principle framework of this method takes the topology of complex networks as the host, integrates the timing exposure concept of the impact chain, combines the multi-scale self-healing mechanism of nodes-paths-communities, and then converts it into a single index through multi-factor coupling, finally completes the quantitative evaluation of the network resilience panorama.

[0023] Further, the original topology data includes: the degree of each node, the local clustering coefficient, the number of independent paths, and the average shortest path length to all other nodes.

[0024] The original topology data is defined as a set of basic structure quantities that can completely characterize the local connection characteristics and global transmission characteristics of nodes, specifically including four contents: first, the degree of each node, which is used to quantify the number of direct connections possessed by the node and reflects the basic connectivity potential of the node in the network; second, the local clustering coefficient of each node, which is used to measure the probability of forming a closed triangle among the neighbors of the node and reveal the tightness of the cluster around the node; third, the number of independent paths, which is used to count the number of non-intersecting conflict-free paths that can exist between node pairs and reflect the overall redundant path reserve of the network; fourth, the average shortest path length to all other nodes, which is used to describe the radiation radius and information transmission efficiency of the node on a global scale.

[0025] Reference Figure 2The figure shows the relationship distribution between the network node betweenness centrality and the structural hole limitation system. The horizontal coordinate represents the normalized betweenness centrality, the value range is 0 to 1.6, and the vertical coordinate represents the structural hole limitation system, the value range is 0 to 0.8. Each black solid dot in the figure represents a node in the network, a total of 20 node samples. Through the analysis of these node data, it can be found that there is a negative correlation between the normalized betweenness centrality and the structural hole limitation system, that is, the higher the betweenness centrality of the node, the lower the structural hole limitation system, which indicates that the key node playing a bridge role in the network information flow usually has stronger information control ability and lower structural constraint. The dashed line in the figure represents the trend fitting line of the data points, which extends from the lower left corner to the upper right corner, further verifying the negative correlation between the two. This relationship distribution provides an important data basis for the subsequent calculation of the bridge-hole coupling rate, which is obtained by dividing the normalized betweenness centrality by the structural hole limitation system node by node, and is used to measure the potential contribution ability of the node in the network recovery process.

[0026] Referring to Figure 3 The figure shows the distribution relationship between the network node degree and the local clustering coefficient. The horizontal coordinate represents the node degree, the value range is 0 to 16, and the vertical coordinate represents the local clustering coefficient, the value range is 0 to 0.8. Each black solid dot in the figure represents a node in the network, a total of 16 node samples. From the scatter distribution, it can be observed that there is a negative correlation trend between the node degree and the local clustering coefficient, that is, the node with higher node degree has relatively lower local clustering coefficient, which conforms to the typical characteristics in the complex network theory. The annotation box in the lower right corner of the figure clearly explains the calculation method of the connectivity-aggregation coupling effect, that is, multiplying the node degree and the local clustering coefficient. This coupling effect is an important part of constructing the topological base resilience index, and represents the synergistic effect of network connectivity and aggregation at the node scale. At the overall scale of the network, through the summation and averaging processing of the connectivity-aggregation coupling effects of all nodes, combined with the transmission efficiency and diversity factor, after twice amplification and logarithmic conversion, the topological base resilience index under the condition of no external impact is finally formed, which reflects the health degree of the network at the inherent structure level.

[0027] Further, step 1 specifically includes: at the node scale, multiplying the node degree and the local clustering coefficient to represent the connectivity-aggregation coupling effect, directly taking the number of independent paths as the diversity factor, and taking the reciprocal of the average shortest path length to represent the transmission efficiency; at the overall scale of the network, the summation and averaging of the above three types of node factors are performed, and then the connectivity-aggregation coupling effect and the transmission efficiency are amplified twice, and the results are logarithmically converted with the sum of the diversity factor to obtain the topological base resilience index under the condition of no external impact.

[0028] The method multiplies each node degree and the local clustering coefficient of the node, and interprets the product as a connected-aggregated coupling effect, to simultaneously capture the number of direct associations of the node and the compactness of the neighborhood cluster; the method considers the number of independent paths as a diversity factor, and believes that the more parallel and non-interfering paths, the more redundant support the network has when local failure occurs; the method takes the inverse of the average shortest path length from the node to all other nodes, and interprets it as a transmission efficiency indicator, because the shorter the average distance means that information or goods can spread faster in the network.

[0029] After completing the three calculations of the node scale, the method enters the network overall scale processing: first, sum up the connected-aggregated coupling effect, the diversity factor and the transmission efficiency indicator of all nodes respectively, and then divide by the total number of network nodes to obtain the arithmetic mean of the three indicators; then the method implements a quadratic amplification operation on the average value of the connected-aggregated coupling effect and the average value of the transmission efficiency, which emphasizes the contribution of structural strength to resilience in the numerical space, so that the two advantages of high connectivity-high aggregation and high-speed transmission get square-level weight; then, the method adds the amplified result to the average value of the diversity factor, and converges the information in three dimensions into a single scalar, and then applies a natural logarithmic transformation to the scalar to compress the values output by networks of different scales and ensure that the result distribution is closer to normal. The continuous transformation chain starts from the double feature coupling of the node locally, and finally outputs the calibrated value of the topology base resilience index through the average merging, nonlinear weight amplification and logarithmic compression of the network globally. The larger the value, the greater the buffer space that the network can provide on its own without external shocks, because high connectivity-aggregation can reduce the splitting caused by node drop, high diversity can provide alternative paths for failed nodes, and high transmission efficiency can shorten the crawling time required for rewiring or information rerouting, and logarithmic compression ensures that the index of networks with different node numbers can be compared.

[0030] The implementation process requires first traversing all nodes at the data collection level, and generating four mapping tables of node degree, local clustering coefficient, independent path number and average shortest path length in real time or offline; then in the calculation service, the connected-aggregated coupling effect, the diversity factor and the transmission efficiency are derived and generated by node, and then in the aggregation service, the sum and average of the whole network are performed; finally, in the index fusion module, square amplification, addition and logarithmic transformation are performed to obtain the standardized topology base resilience index, and the index is written into the evaluation database for subsequent crisis exposure factor and adaptation-recovery index calling, so that it plays the role of inherent structural health benchmark in the subsequent steps of the whole network resilience index multi-dimensional quantitative evaluation method.

[0031] Specifically, the topology base resilience index is: ; wherein, is the total number of network nodes; is the degree of node ; is the local clustering coefficient of node ; is the independent path number of node to other nodes; is the average shortest path length of node to all other nodes.

[0032] Further, in step 2, the impact intensity and the duration of each crisis phase are multiplied and summed, and the result is divided by the total cumulative value of the sum of the impact intensity and the recovery duration, to obtain the crisis exposure factor; the greater the value of the crisis exposure factor, the more vulnerable the network is in the impact phase.

[0033] The method fully draws on the ideas of risk accumulation and time weighting in the construction of the crisis exposure factor, and regards each external impact as a load segment of the resilience test, and unifies the impact "force" and the impact "quantity" into the same evaluation framework through the two description quantities of the function loss amplitude and the action duration. The method first confirms all identifiable crisis phases in the monitoring period on the time axis, and the division of the crisis phase is automatically intercepted according to the continuous downward trajectory of the network function index. Whenever the network function shows a sustained multi-period decline and the absolute value is lower than the previous period baseline, the system marks a new impact event, and records the starting point, the lowest point and the end point of the recovery to the baseline of the event. For each identified crisis phase, the method extracts three core information: first, the impact intensity, defined as the percentage of the network function decline at the lowest point relative to the pre-crisis baseline, which measures the proportion of instantaneous loss caused by external disturbance to the network function; second, the crisis duration, defined as the time length of the network function from the start of the decline to the lowest point, which reflects the time dimension of the impact maintaining high pressure; third, the recovery duration, defined as the time length of the network function from the lowest point to the pre-crisis baseline, which measures the time cost of the network self-repair, and also indirectly reflects the efficiency of the internal repair mechanism of the network. The joint use of the three indicators can simultaneously describe the depth, breadth of the impact and the recovery speed of the network.

[0034] The method couples the impact intensity and the duration of each crisis phase by multiplying them together, interpreting the product of impact depth and duration as the contribution of a single crisis to the cumulative damage of the network, because a higher loss magnitude exerted over a longer duration implies more functional impairment and resource dissipation. The method then sums the cumulative damage contributions of all crisis phases, accumulating all the impact energy over the historical period to form the numerator. At the same time, the method also sums the impact intensity and the recovery duration of each crisis phase, combining them into the denominator. The physical meaning of this step is to compare the damage contribution and the repair cost on the same scale: when the network suffers greater loss but recovers faster in some phases, the recovery duration in the denominator will weaken the boost of the cumulative damage to the overall vulnerability; on the contrary, if the network suffers less loss but the duration is extremely long or the recovery is extremely slow in some phases, the numerator will be amplified rapidly under the long-time accumulation, while the repair time in the denominator cannot effectively offset this amplification effect because it is increasing, leading to an overall increase in the crisis exposure factor, thus reflecting the vulnerability weighting of the network in the time dimension. The ratio form designed in this way can be regarded as a kind of energy density measurement with a time factor in the algebraic sense, which time-weights the damage impulse of each impact and accumulates it, and then normalizes it with the repair consumption which also has a time attribute. The result will adaptively amplify the comprehensive vulnerability characteristics of long duration, high intensity and slow recovery.

[0035] In actual implementation, the system first constructs a time resolution adjustable function surface through the continuous sampling of the functional index sequence. The surface presents a fluctuation pattern on the time axis, and the drop between each local minimum and adjacent local maximum is regarded as a potential shock event. The algorithm enters crisis mode when a continuous downward trend is detected, accumulates the downward amplitude in real time, and observes the lowest point. Once the function curve rebounds and crosses the baseline before the decline after a number of periods, it is declared that a crisis phase has ended. All divided crisis phases are added to the diagnostic list in chronological order, and each record contains the start time, end time, lowest point time, and corresponding three index values. To reduce the impact of observation errors and data noise on the determination of shock intensity, the system uses sliding median filtering to eliminate accidental spikes for the functional decline amplitude, and uses time window smoothing to eliminate critical point jitter for the duration and recovery time. Then, when calculating the crisis exposure factor, the system multiplies and sums all the smoothed shock intensities and durations, and simultaneously sums all the shock intensities and the sum of the recovery times, and finally divides the former by the latter to output the scaled value of the crisis exposure factor. Since the shock intensity and duration are accumulated in the form of multiplication, both short and intense shocks and long and slow shocks are given appropriate weight, and after comprehensive superposition, a "damage volume" that mixes time depth and loss depth is presented; similarly, the sum of the denominator's repair time and shock intensity couples the recovery speed and loss amplitude, and then adds them all together to ensure that the growth rate of the denominator as a whole follows the network's spontaneous repair ability for damage. When the network exhibits a high recovery rate, the denominator rises faster, and the crisis exposure factor decreases; when the network recovers slowly, the denominator rises slower, and the crisis exposure factor increases; thus, the direction of numerical change perfectly corresponds to the intuitive meaning of "vulnerability", i.e. the larger the value, the more vulnerable the network.

[0036] In terms of index attributes, the crisis exposure factor is a dimensionless, non-negative, and theoretically unlimited quantity. For a network without any historical shock records, the numerator is zero, and the factor value is naturally zero; for a network with very short shocks but very fast recovery, the numerator is not zero but the denominator grows very fast, and the factor value tends to zero; for a network that is subjected to persistent shocks and slow recovery, the ratio of the numerator to the denominator increases rapidly, and the factor value climbs to a higher range. This property allows the crisis exposure factor to be considered as a risk density indicator based on time-accumulated damage and repair capacity, and is also the direct numerator of the anti-shock correction in the subsequent multi-dimensional network resilience comprehensive index. When the topological base resilience index is corrected by the crisis exposure factor, it can present the hedging results of "structural buffer" and "historical load" in the same dimension, further laying the basis for distinguishing the weight amplification of the recovery index in the index fusion link.

[0037] To ensure the cross-network comparability of the indicators, the system adopts a uniform sampling frequency and a uniform crisis determination threshold when evaluating between different networks, ensuring the consistency of the measurement caliber of impact intensity and duration, while adopting the same recovery baseline definition, maintaining the comparable attribute of recovery duration. When real-time updating of the danger situation is needed, the system can continuously introduce the latest monitoring data in a rolling window manner, redraw the crisis phase according to the latest function curve, incrementally update the impact intensity, duration and recovery duration, and recalculate the crisis exposure factor online, so that this phased risk load indicator has real-time traceability in time series. In summary, the crisis exposure factor integrates the depth, breadth of external shocks and network self-healing speed into a single value measure through the dual time weight mechanism of product accumulation and additive normalization, and becomes an indispensable core quantitative link in the multi-dimensional quantitative evaluation method of network resilience index by the consistency of value range direction and vulnerability degree, which evaluates the anti-impact ability.

[0038] Further, step 3 specifically includes: setting an evaluation time window and locking a reference topology snapshot, and assigning a time weight to each node in the reference topology snapshot; under the same reference topology snapshot, calculating the standardized betweenness centrality of all nodes; synchronously calculating the structural hole limitation degree of all nodes, and performing reverse Sigmoid compression on the structural hole limitation degree to make the structural hole advantage present a saturated upper limit in value, avoiding the imbalance of the evaluation result caused by the absolute monopoly node; dividing the standardized betweenness centrality and the structural hole limitation degree node by node to obtain the bridge-hole coupling rate, then taking the time weight as a multiplier to weight and accumulate the bridge-hole coupling rate, and taking the square root of the accumulated result to form the recovery potential indicator at the node level; assigning the same weight or weighting according to the node weight to the recovery potential indicator of each node in the network, calculating the weighted arithmetic mean value, and thus depicting the average recovery potential level of the network as a whole; then, based on the same weight system, calculating the square difference of each node recovery potential indicator and the network weighted average value and summing them up to obtain the weighted square deviation of the distribution, which reflects the uniformity of the distribution of the recovery potential among different nodes; finally, in a harmonic weighting manner, the weighted arithmetic mean value and the weighted square deviation are combined to form a comprehensive measurement indicator that can reflect the average strength and distribution balance of the recovery potential among network nodes, obtaining the adaptation-recovery index.

[0039] The construction of the resilience index is regarded as the key link between the structural resilience and the diachronic shock, because only by accurately depicting the potential of self-healing and regeneration within the network can the "innate buffer" of the structure and the "acquired load" of the shock be effectively coupled at the comprehensive index level. The calculation of the index does not rely on external macro information, but is entirely based on the endogenous characteristics of the network itself in the micro connection relationship and the time evolution trajectory; therefore it has both topological explanatory power and time sensitivity. In order to achieve this goal, the method first introduces the concept of evaluation time window, which strictly limits the observation range of the adaptation-recovery potential to a well-defined time segment, in order to avoid the semantic conflict caused by superimposing structural changes in different time periods on the same projection plane. The upper and lower limits of this time window can be set according to the business cycle of the network, the frequency of topological updates or the policy evaluation period of the manager, and the locking of the benchmark topology snapshot is to freeze the node and edge relationship at a representative time section within the selected time window, so that the subsequent measurement of node attributes is based on the same structure description, in order to exclude the error caused by structural drift. In this way, a "time-topology" fixed analysis framework is formed: the time direction limits the observation depth through the upper and lower boundaries of the evaluation time window, and the structure direction limits the skeleton of node interaction through the benchmark topology snapshot, which together provides the starting point for evaluation.

[0040] On the fixed benchmark topology snapshot, the first step is to assign a time weight to each node. The original intention of the time weight is to give higher contribution to the nodes that have maintained stable bridge role and played a key role in information flow within the evaluation time window, so as to truly reflect the long-term reliable recovery support value of the nodes. The method takes the sequence of intermediate centrality of the node within the entire evaluation time window as the input, calculates the standard deviation of its fluctuation, and makes an inverse mapping on the standard deviation: the smaller the fluctuation, the greater the weight, and the greater the fluctuation, the smaller the weight. This inverse mapping can use linear, logarithmic or other monotonic decreasing conversion, but must ensure that the weight falls within the closed interval of zero to one, so as to be directly multiplied by the normalized intermediate centrality in the following. Through this mechanism, the method makes the nodes with stable and persistent bridge role the main role in the evaluation of recovery potential, while those with occasional peaks but overall dramatic fluctuations are compressed in contribution, avoiding the amplification of short-term fluctuations on the index.

[0041] After the completion of the time weight assignment, the system calculates the normalized betweenness centrality of all nodes on the same base topology snapshot. The normalization process consists of two steps: first, the quartile de-extremum is adopted to cut off the abnormal points beyond a certain distance from the upper quartile and lower quartile, in order to eliminate the extreme high or low values caused by observation noise and data entry abnormalities; then the remaining values are mapped to a unified interval by a zero-one linear transformation, to ensure that the betweenness centrality of networks of different sizes and densities is comparable, and to ensure that any subsequent weighting or division operation is performed in the same numerical space. This normalized betweenness centrality can be regarded as a pure functional measure of the role of a node as a bridge, and the higher the value, the more frequently the node is in the shortest path and the more it can provide alternative channels when information is rerouted.

[0042] Next, the system synchronously calculates the structural hole limitation of all nodes. The structural hole limitation measures the redundancy of a node within its adjacent subgraph, or measures the potential advantage of a node in obtaining non-redundant information. After the calculation is completed, in order to avoid a few nodes from amplifying their contribution infinitely in the subsequent coupling process due to their absolute monopoly position, the method performs reverse Sigmoid compression on the original structural hole limitation. Reverse Sigmoid compression essentially maps the original non-negative value to the zero interval and gives it a smooth upper limit, so that when the original value reaches a very high level, the mapping value gradually converges to one without continuing to rise, so that the structural hole advantage appears to be capped in value. This compression process not only prevents a single super-monopoly node from raising the overall network's recoverability expectations, but also makes it so that when comparing different networks, high redundancy and ultra-high redundancy no longer increase linearly, but maintain a marginal contribution that decreases, which is more in line with the experience rule that actual networks have a decreasing return in an extreme redundancy state.

[0043] The method then divides the standardized betweenness centrality of the node by the compressed structural hole limitation system node by node to obtain the bridge-hole coupling rate. The ratio is proposed to quantify the comprehensive degree of a node's information hub efficiency and redundant information control force: if a node has high betweenness centrality but low structural hole limitation system, it means that it is an information hub, but the alternative redundancy is insufficient, and once it fails, it will cause serious disruption; on the contrary, if the structural hole limitation system is high but the betweenness centrality is low, it means that it controls redundant resources but is not on the key transmission link, and the probability of calling it in the recovery process is limited. Only when both are present, the bridge-hole coupling rate will be high, so as to determine that the node has high replacement value in the post-disaster rerouting scenario. After obtaining the bridge-hole coupling rate, the system weights and accumulates it with time weight as the multiplier, combining the node's stability across time and single-point bridge-hole synergy ability; then takes the square root of the cumulative result to suppress the risk of nonlinear explosion caused by too high time weight or abnormally high bridge-hole coupling rate, and defines the square root result as the node-level recovery potential index. The node-level recovery potential index thus contains both static bridge-hole coupling degree and dynamic stability contribution, with the meaning of "three-dimensional integration": strong bridge, strong redundancy and persistent stability.

[0044] After obtaining the recovery potential index of all nodes in the network, the system first calculates the weighted arithmetic mean under the unified node weight system to depict the average recovery potential level of the network as a whole. The node weight can be set to one, or it can be allocated according to the importance of the node, such as capacity weight or asset weight, as long as it remains consistent throughout the evaluation process. A high weighted arithmetic mean indicates that the network has a high self-healing ability in a broad sense, but this mean value cannot identify whether the distribution of recovery potential among nodes is uniform, so the system proceeds to the next step to calculate the weighted squared deviation. Under the same weight system, the system subtracts the network average from each node's recovery potential index, then multiplies it by the corresponding weight and sums it up to obtain the dispersion of the recovery potential distribution. The greater the deviation, the more concentrated the recovery potential is in a few key nodes, and the majority of nodes contribute less, which is a potential vulnerability from the perspective of resilience, because the key nodes will be difficult to replace if they fail. The smaller the deviation, the more dispersed the recovery potential is, and the network has bridge-hole synergy ability at multiple node levels, with high redundancy.

[0045] To integrate the average level and dispersion into a single indicator, the system uses a harmonic weighting method for combination. The idea of harmonic weighting is to regard the weighted arithmetic mean and the weighted square deviation as positive and negative factors, respectively, and to realize the negative punishment of the deviation term through the reciprocal or fractional structure. Specifically, the method maintains the linear positive contribution of the average level to the index, while introducing the deviation term as the denominator or exponential decay term, so that when the deviation becomes large, the index as a whole decreases. When the average level and the deviation are input into the index generation function, the system finally obtains a dimensionless and monotonically increasing resilience-recovery index. The index continuously changes between zero and the theoretical upper limit, and the larger the value, the better the network performs in fast recovery and regeneration, and this advantage comes from the sharing of multiple nodes, which will not be severely attenuated by the failure of a single node in the same time window. On the contrary, when the network average recovery potential is high but the deviation is large, the index will be significantly lowered by the penalty term, indicating that the self-healing ability of the network is highly dependent on a few nodes, and redundancy compensation needs to be made in terms of structural stability.

[0046] In terms of implementation, in order to deal with the high computational complexity brought by large-scale networks, the system stores the node bridge coupling rate and the time weight in a column memory table, and completes the weight multiplication, accumulation and square root operation at one time through vectorization instruction. Then, the average value and the deviation are calculated in a single round of traversal using high-performance aggregation functions. Since the harmonic weighting itself involves a fractional form, the system uses high-precision floating-point numbers to ensure numerical stability and prevent the risk of division by zero caused by too small deviation. After the index generation is completed, the system not only records the historical trajectory of the resilience-recovery index in the index library, but also records the node-level recovery potential indicators, providing micro support for subsequent strategy analysis. Managers can discover weak links with insufficient recovery potential based on node ranking, implement link addition or redundancy optimization, monitor the change trend of the index in the rolling time window, identify early signs of structural faults, and intervene in time in the context of a sharp rise in crisis exposure factors to improve overall resilience. When linked with the simulation module, the resilience-recovery index can also be used as an objective function to evaluate the immediate gain of network resilience under different fault injection or repair strategies, helping to form a fast closed loop. Through this set of precise, fine-grained and time-series and topology perspective construction logic, the invention effectively fills the gap in traditional resilience evaluation, which only focuses on static structure or only focuses on average level while ignoring the uniformity of distribution, and provides a new tool for resilience improvement in the whole life cycle of the network, which is quantifiable, traceable and intervenable.

[0047] Further, the time weight is determined by the node in the most recent The standard deviation of the sequence of betweenness centrality in each period is reverse-scaled to emphasize the leading role of structural stable nodes in the recovery process; the normalized betweenness centrality is transformed by quartile de- outliers, 0-1 linear stretching and power-law reduction to ensure that the bridge effect can maintain the distribution difference without being hidden by extreme values.

[0048] Specifically, for each node, the system takes the betweenness centrality observations of the last τ periods from the monitoring data lake, calculates the sample standard deviation to obtain the structural fluctuation amplitude; in order to avoid mapping zero fluctuation to infinite weight, and also to prevent the fluctuation maximum node from being given almost zero weight, the method uses a reverse monotonic function with lower and upper limits to map the standard deviation to between zero and one, for example, a commonly used transformation is to take the first inverse of the standard deviation plus one as the denominator, and then compress it by logarithm or hyperbolic tangent, which ensures that the weight decreases monotonically and keeps the boundary continuous. After the mapping is completed, the weight is directly multiplied by the result of the node in the bridge-hole coupling rate calculation link to achieve time emphasis on the contribution of the stable bridge; since the weight definition is based on the standard deviation rather than the mean, nodes that have short-term spikes but are not stable in the long term will be automatically de-weighted due to high fluctuations, thus allowing nodes that consistently provide hub services in the long term to dominate the overall recovery potential.

[0049] The triple transformation process of standardized intermediary centrality aims to shape the bridge effect on the numerical scale, both preserving relative differences and suppressing excessive dependence on extreme values. The process first performs quartile de-extremization, which calculates the upper quartile and lower quartile of the network intermediary centrality distribution, then multiplies the common one or one-five internal distance threshold to define the abnormal area, and all observations higher than the upper threshold or lower than the lower threshold are truncated to the threshold boundary, eliminating sampling noise and abnormal structure injection outliers from the source; the sequence after de-extremization enters the zero-one linear stretching, which maps the minimum value to zero and the maximum value to one, and the rest of the values are distributed proportionally and linearly, ensuring that the intermediary centrality distribution under different network size or density is in the same interval, avoiding dimensional inconsistency in subsequent numerical interactions with structural hole limit system, time weight and other dimensions; finally, through power law reduction, the high interval after stretching is gradually compressed, specifically, each value in the zero to one interval is raised to a power, and the power index is selected as a positive number less than one, commonly in the range of zero point five to zero point eight, so that the difference in the middle-high segment is gradually converged, while the difference in the low segment remains the original linear slope. This can preserve the ordering between nodes while limiting the exponential amplification of extreme high values in the accumulation and multiplication process, preventing a few super hubs from dominating the bridge-hole coupling rate or node-level recovery potential. When the standardized intermediary centrality obtained after the triple transformation is divided by the compressed structural hole limit system, the numerical fluctuations in the numerator are within a controllable range, and the denominator will not be excessively scaled due to the inverse Sigmoid saturation mechanism, so the bridge-hole coupling rate distribution is smoother overall; combined with the continuous suppression of the time weight, nodes with high stability and high bridge are also high in redundancy, and are given significant recovery potential, while the single-point contribution of extreme nodes is weakened to a reasonable range by a series of nonlinear compression functions. Through this temporal-scale double calibration, the method ensures that the adaptation-recovery index not only measures strength, but also accurately reflects the spatial distribution of strength between nodes, in principle avoiding the distortion of recovery potential by "super nodes" and truly connecting to the core mechanism of network self-organization regeneration.

[0050] Further, step 3 also includes: in parallel, traversing all possible two-by-two combinations between nodes, counting the number of independent parallel paths between each pair of nodes, and calculating the ratio with the maximum number of parallel paths between the two nodes in theory to quantify the link diversity of the network; at the same time, calculating the modularity coefficient of the Louvain community partition result of the network, and converting it into an attenuation factor using inverse translation to reflect the positive contribution of partition isolation to diffusion suppression; multiplying the primary recovery coefficient with the link diversity ratio, and then adding the attenuation factor in an additive manner to obtain the comprehensive recovery potential without scale compression; if the comprehensive recovery potential exceeds the theoretical upper limit of resilience, map and compress it using a hyperbolic tangent function to ensure consistency in the index interval; to offset the index comparability deviation caused by network size differences, introduce the node number logarithm term as the denominator adjustment, so that larger networks with more dispersed structures will not be overestimated in recovery potential due to the large number of nodes, and obtain the size-standardized result; based on the size-standardized result, perform numerical normalization processing, and finally output the adaptability-recovery index, which is continuous and monotonic between 0 and the theoretical maximum value, and maintains a first-order positive correlation with the bridge-cave synergy degree, link diversity, and partition isolation.

[0051] After completing the bridge-hole coupling rate and node-level recovery potential indicators, a parallel process is also started to measure the network's regeneration potential at the macro-topological redundancy and community isolation levels, and the two processes are connected into a continuous recovery potential measurement chain in the numerical space. The parallel process first traverses all possible two-by-two combinations between nodes for the reference topology snapshot, and here it does not distinguish between directed and undirected, as long as the node pair has connection potential under the current structure. For each pair of nodes, the system calls the multi-source shortest path and flow allocation algorithm to enumerate all topologically independent and parallel paths between the two nodes, and excludes any path combination that conflicts at the level of transit nodes or transit edges, leaving only the truly independent redundant paths, and then records the number of paths. After the traversal is complete, the system holds a sparse matrix with node pairs as keys and independent parallel path numbers as values, and then divides each record's path number by the maximum number of parallel paths that the node pair can theoretically reach in the full graph to obtain a proportion between zero and one, which is defined as the local entry of the link diversity ratio for that node pair. All local entries are averaged or weighted averaged in the network range to obtain the link diversity ratio of the entire network. Since the theoretical maximum number of parallel paths increases rapidly with the network size and density, this step of proportioning can automatically eliminate the scale effect to some extent, ensuring that the link redundancy measurement focuses on "utilization" rather than "absolute number".

[0052] Meanwhile, the system performs Louvain community partition on the same baseline topology snapshot. Louvain community partition algorithm aims to maximize modularity, and alternately advances by local greedy merging and macro-level compression, to split the network into several sub-communities with dense internal connections and sparse external connections. After the algorithm outputs community labels, the system immediately calculates the modularity coefficient based on the same topology, and the larger the coefficient, the clearer the community structure, the weaker the coupling between communities, and the more the network can rely on community boundaries to block the chain diffusion when facing local failure. In order to convert the positive effect of strong community isolation into a clear numerical contribution, the system converts the modularity coefficient into a decay factor by reciprocal translation: the larger the coefficient, the smaller the factor obtained after reciprocal translation, but the factor is then additively stacked in the next step, so the larger the coefficient means the weaker the penalty to the comprehensive recovery potential, in other words, the more positive the contribution; the smaller the coefficient means that the community structure is scattered and the isolation effect is poor, and the larger the factor obtained after reciprocal translation, which is equivalent to adding a larger burden to the index when stacking the comprehensive recovery potential, reducing the self-healing evaluation. The purpose of reciprocal translation is to let the partition isolation advantage be expressed in a negative way, rather than multiplying an additional weight to cause scale amplification, so as to maintain the link diversity in the same positive scale semantic as the node-level recovery potential.

[0053] When both link diversity ratio and primary recovery coefficient are ready, the system multiplies them to get a composite value that combines both microscopic bridge-cave synergy and macroscopic redundant path potential. Then the aforementioned decay factor, which is translated from the inverse of modularization coefficient, is added to the composite value in an additive way to get the comprehensive recovery potential without scale compression. Numerically, the combination order of multiplication first and addition later is adopted here because both node-level recovery potential and link diversity ratio are positive multipliers, and the higher the coupling between them, the smoother the overall network redundancy and re-routing. While partition isolation is essentially not about amplifying transmission efficiency but weakening cascading failure, so it is introduced in an additive way after multiplication to better reflect the meaning of "reducing burden". If the comprehensive recovery potential exceeds the preset theoretical upper limit, to avoid losing resolution in the high value region, the system uses the hyperbolic tangent function for monotonic mapping compression. The hyperbolic tangent function has upper and lower bound characteristics, which can gradually converge when the value is close to the extreme, while still maintaining nearly linear response in the middle segment, so it can avoid overflow of large values without destroying monotonicity. After mapping, the comprehensive recovery potential falls into the compressed interval between zero and one, but there is still a hidden danger: the number of nodes in different scale networks varies greatly, and the product of node-level recovery potential and link diversity ratio often underestimates in large-scale sparse networks and overestimates in large-scale dense networks; in order to offset the comparability bias caused by scale difference, the method introduces the logarithm of node number as the denominator adjustment, that is, taking the natural logarithm of the total number of nodes plus one, and then dividing the compressed comprehensive recovery potential by the logarithm. The logarithm grows slower than linear but faster than constant, which can moderately balance the numerical inflation caused by scale expansion, and ensure that the scale of the network is not too small to get an unreasonable high value due to the small denominator.

[0054] After the scale standardization result is completed, the system performs a numerical normalization process, which can be based on historical extreme values or theoretical extreme values using zero-one normalization, or using mean-variance scaling; no matter which one, it is only required to be consistent when comparing horizontally across networks. The normalized result is officially named the adaptation-recovery index, and is hard-coded as a continuous monotone between zero and the theoretical maximum value, ensuring that any input that logically improves the bridge-cave synergy, link diversity, or partition isolation will cause the index to monotonically increase; if any of the three dimensions decreases while the others remain unchanged, the index will inevitably decrease, achieving a first-order positive correlation. The system records the integrated recovery potential before compression, the scale standardization result, and the normalization weight parameter when the index is persistent, providing a basis for subsequent tracing and sensitivity analysis. The entire process completes the three-dimensional coupling of microstructure stability, macroscopic redundancy, and community isolation elasticity at the algorithm design level, and introduces multiple compression and scale correction at the numerical level to ensure cross-network comparability. The final output of the adaptation-recovery index can not only reflect the average recovery strength, but also present the distribution balance among nodes, thereby providing a high-confidence self-healing potential description for the fusion of multi-dimensional network resilience index quantification evaluation methods.

[0055] Further, the process of numerical normalization based on the scale standardization result includes: taking the scale standardization result as a benchmark, performing Box-Cox transformation and multiplying it by a constant Performing numerical stretching, finally outputting the adaptation-recovery index.

[0056] Further, step 4 specifically includes: taking the topological base resilience index divided by the value of the crisis exposure factor plus one as the structure-impact correction term; setting the exponential weight of the structure-impact correction term as the ratio of the adaptation-recovery index and the adaptation-recovery index plus one to reflect the amplification effect of recovery ability on overall resilience, to obtain the correction adjustment result; selecting the latest year as the time window, calculating the standard deviation of all topological base resilience indices in the time window to represent the long-term fluctuation amplitude of the base resilience; taking the negative topological base resilience index standard deviation value of the natural exponential function as the stability correction term; multiplying the correction adjustment result and the stability correction term to obtain the multi-dimensional network resilience comprehensive index; the larger the value of the network resilience comprehensive index, the stronger the network resilience.

[0057] Firstly, a structure-shock correction term is introduced to put the inherent structural health of the network and the historical cumulative shock load in the same fractional framework by dividing the topological base resilience index by the value of the crisis exposure factor plus one. This fractional construction can be seen as a direct deduction between the "buffer total amount" and the "shock density". When the topological base resilience index is much larger than the crisis exposure factor, the correction term is higher than one, indicating that the structure remains sufficient. When the two are close or the crisis exposure factor rises rapidly, the correction term will drop to a level close to one or even below one, reflecting that the shock almost exhausts the structural buffer. Next, in order to make the recovery capacity have a multiplier effect on the overall resilience, the method applies the ratio of the adaptation-recovery index to the adaptation-recovery index plus one as an exponential weight to the structure-shock correction term. The selection of the exponential weight takes advantage of the concave increasing feature of the exponential function in a certain interval, so that when the adaptation-recovery index is high, the structure-shock correction term will be amplified exponentially, reflecting that strong recovery potential can compensate for the impact load by a multiple; when the adaptation-recovery index is low, the exponential weight tends to one, and the amplification effect of the correction term is weak or even almost none, reflecting that the insufficient recovery potential cannot significantly alleviate the impact pressure. This amplification mechanism converts node-level bridge cooperation, link diversity, and community isolation into an overall resilience accelerator, giving a nonlinear bonus to high-recovery-capacity networks.

[0058] However, resilience is not only instantaneous buffer and self-healing speed, but also the ability to maintain stable performance in a longer period of time, so the method further sets up long-term fluctuation penalty logic. The system selects the last y years as the time window, extracts all topological base resilience index sequences in the window, calculates the standard deviation of the sequence, and takes it as the statistical scale of the base resilience fluctuation over time. The larger the standard deviation, the more dramatic the inherent structure of the network has been in recent years, and the more unstable the available structural buffer; the smaller the standard deviation, the more stable the structural strength, providing more predictable protection for risk management and resource allocation. After obtaining this fluctuation amplitude, the system sends it as a negative exponential variable of the exponential function to the natural exponential function and outputs a stability correction term. Since the natural exponential function decays rapidly on the negative half-axis, the stability correction term quickly shrinks as the standard deviation of the structural fluctuation increases, directly reducing the adjusted result of the correction after exponential amplification; when the standard deviation tends to zero, the correction term approaches one, almost not compressing the comprehensive index. Through this external parameter-free exponential decay design, the method introduces long-term structural stability into resilience evaluation, ensuring that networks that rely on short-term high peaks to support resilience but oscillate overall are appropriately penalized, while networks that are stable and steadily improving over the long term receive exponential complete addition.

[0059] In the last step, the system multiplies the correction adjustment result with the stability modifier to obtain the multi-dimensional network resilience composite index, which is defined as a unified non-negative and dimensionless scale. The correction adjustment result interweaves structural buffer, impact load, and recovery potential as positive multipliers, while the stability modifier, as an absolute multiplier factor not greater than one, down-regulates the overall score, making the upper bound of the composite index limited by the theoretical extreme value, and the lower bound zero, and monotonically increasing when structural buffer, impact mitigation, recovery potential, or volatility decrease. The numerical logic of the composite index thus realizes the fusion of the four physical meanings: when the topology base resilience index rises while the crisis exposure factor remains unchanged or decreases, the index rises, reflecting the innate structural strengthening; when the adaptation-recovery index increases, the index is nonlinearly amplified by the exponential weight, reflecting the acquired recovery addition; when the long-term volatility amplitude is compressed, the index is exponentially attenuated to retain more original values, reflecting the advantage of stable operation; if any dimension changes inversely, the index is immediately adjusted downward, ensuring monotonic consistency. When persisting the multi-dimensional network resilience composite index, the system also synchronously writes the structure-impact correction term, the exponential weight, the stability modifier, and the sequence of topology base resilience indices within the y-year window into the analysis warehouse, providing bottom support for subsequent sensitivity analysis and scenario simulation; on the real-time monitoring panel, the composite index curve and its three components are displayed in parallel, which can help operation or decision-making personnel identify the source of index changes and timely intervene in structural strengthening, recovery acceleration, or volatility control.

[0060] In particular, the multi-dimensional network resilience composite index is: ; wherein: ; Here, is the topology base resilience index; is the crisis exposure factor; is the adaptation-recovery index; is the standard deviation of all topology base resilience indices in the last years; is the topology base resilience index in the year; is the mean of all topology base resilience indices in the last years; is the starting year of the time window.

[0061] The above-described embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing embodiments can still be modified, or some technical features can be replaced by equivalent replacements; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for multi-dimensional quantitative evaluation of network resilience index, characterized in that, The method comprises: Step 1: obtaining original topology data of a target network, and constructing a topology base resilience index of the network in a case without external impact, wherein the greater the value of the topology base resilience index, the healthier the network is in an inherent structure layer; Step 2: identifying all crisis stages based on historical monitoring records to obtain a total number of crisis stages; for each crisis stage, counting a percentage of network function decline as an impact strength, counting a continuous network function decline time length as a crisis duration, and counting a time for the network function to recover from a lowest point to a pre-crisis baseline as a recovery time; and calculating a crisis exposure factor according to the total number of crisis stages, the impact strength, the crisis duration and the recovery time; Step 3: calculating an intermediate centrality of each node to measure a bridge role of the node in a whole network information flow, and calculating a structural hole limitation system of each node to measure an information redundancy degree controlled by the node; and combining the intermediate centrality and the information redundancy degree to generate an adaptation-recovery index for measuring self-healing and regeneration capabilities of the network; Step 4: performing anti-impact correction on the topology base resilience index and the crisis exposure factor, then performing index weight amplification according to the adaptation-recovery index, and finally generating a multi-dimensional network resilience comprehensive index by combining stability correction of network resilience fluctuation.

2. The network resilience index multi-dimensional quantitative assessment method of claim 1, wherein, The original topology data comprises a degree, a local clustering coefficient, an independent path number and an average shortest path length to all other nodes of each node.

3. The network resilience index multi-dimensional quantitative assessment method of claim 2, wherein, Step 1 specifically comprises: at a node scale, multiplying the node degree and the local clustering coefficient to represent a connectivity-aggregation coupling effect, directly taking the independent path number as a diversity factor, and taking an inverse of the average shortest path length to represent a transmission efficiency; at a network overall scale, summing and averaging the three types of node factors respectively, then amplifying the connectivity-aggregation coupling effect and the transmission efficiency twice, and performing logarithmic conversion on a result and a sum of the diversity factor to obtain the topology base resilience index in the case without external impact.

4. The network resilience index multi-dimensional quantitative assessment method of claim 3, wherein, In step 2, the impact strength and the duration of each crisis stage are multiplied and summed, and the result is divided by an overall cumulative value of the sum of the impact strength and the recovery time to obtain the crisis exposure factor; the greater the value of the crisis exposure factor, the more fragile the network is in the impact stage.

5. The network resilience index multi-dimensional quantitative assessment method of claim 4, wherein, The step 3 specifically comprises: setting an evaluation time window and locking a reference topology snapshot, in which a time weight is assigned to each node; under the same reference topology snapshot, the normalized betweenness centrality of all nodes is calculated; the structural hole limitation of all nodes is calculated synchronously, and inverse Sigmoid compression is performed on the structural hole limitation to make the structural hole advantage present a saturated upper limit in value, so as to avoid that the absolute monopoly node leads to unbalanced evaluation results; the normalized betweenness centrality and the structural hole limitation are divided by node by node to obtain the bridge-hole coupling rate, then the bridge-hole coupling rate is weighted and accumulated with the time weight as a multiplier, and the square root of the accumulated result is taken to form the recovery potential index of the node level; the recovery potential index of each node in the network is given the same weight or weighted according to the node weight, and the weighted arithmetic mean value is calculated to depict the average recovery potential level of the whole network; then, based on the same weight system, the square difference of the recovery potential index of each node and the weighted average value of the network is calculated and summed to obtain the weighted square deviation of the distribution, which is used to reflect the uniformity of the distribution of the recovery potential among different nodes; finally, in a harmonic weighting manner, the weighted arithmetic mean value and the weighted square deviation are combined to form a comprehensive measurement index that can reflect the average strength and distribution balance of the recovery potential among network nodes, and the adaptation-recovery index is obtained.

6. The network resilience index multi-dimensional quantitative assessment method of claim 5, wherein, The time weight is obtained by the standard deviation of the sequence of betweenness centrality in the last The time weight is obtained by the standard deviation of the sequence of betweenness centrality in the last The time weight is obtained by the standard deviation of the sequence of betweenness centrality in the last 7. The network resilience index multi-dimensional quantitative assessment method of claim 6, wherein, The step 3 further comprises: in parallel, all possible two-by-two combinations between nodes are traversed, the number of independent parallel paths existing between each pair of nodes is counted, and a ratio calculation is performed between the number and the maximum number of parallel paths between two nodes in theory, so as to quantify the link diversity of the network; at the same time, the modularity coefficient of the Louvain community division result of the network is calculated, and the reciprocal translation is used to convert it into an attenuation factor to reflect the positive contribution of partition isolation to diffusion suppression; the primary recovery coefficient is multiplied by the link diversity ratio, and then the attenuation factor is added in an additive manner to obtain the comprehensive recovery potential without scale compression; if the comprehensive recovery potential exceeds the theoretical upper limit of resilience, a hyperbolic tangent function is used for mapping compression to ensure that the index interval is consistent; in order to offset the index comparability deviation caused by the difference in network size, a node number logarithm term is introduced as a denominator adjustment, so that a network with larger size and more dispersed structure will not be overestimated in recovery potential due to the large number of nodes, and a size standardized result is obtained; based on the size standardized result, numerical normalization processing is performed, and finally the adaptation-recovery index is output, which is continuous and monotonic between 0 and the theoretical maximum value, and maintains a first-order positive correlation with the bridge-hole synergy degree, the link diversity and the partition isolation.

8. The network resilience index multi-dimensional quantitative assessment method of claim 7, wherein, The process of numerical normalization based on the scale standardization result includes: taking the scale standardization result as a benchmark, performing Box-Cox transformation and multiplying by a constant Numerical stretching is performed, and finally the adaptation-recovery index is output.

9. The network resilience index multi-dimensional quantitative assessment method of claim 8, wherein, The step 4 specifically comprises: taking the value of the topological base resilience index divided by the crisis exposure factor plus one as a structure-shock correction term; setting the exponential weight of the structure-shock correction term as the ratio of the adaptation-recovery index and the adaptation-recovery index plus one to reflect the amplification effect of the recovery capability on the overall resilience, to obtain a correction adjustment result; selecting the latest year as a time window, calculating the standard deviation of all topological base resilience indexes in the time window to represent the long-term fluctuation amplitude of the base resilience; taking the standard deviation value of the negative topological base resilience index of the natural exponential function as a stability correction term; multiplying the correction adjustment result and the stability correction term to obtain a multi-dimensional network resilience comprehensive index; the larger the value of the network resilience comprehensive index, the stronger the network resilience.

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