For the purpose of further exploring the correlations among RF, SH and MD, the network in the constructed CSR evolution model was divided into 7 accident subnets, namely coal mine fire accidents, coal dust explosion accidents, gas explosions, coal and gas outburst accidents, rock burst accidents, roof accidents, and water accidents. Subsequently, key parameters were obtained through continuous experimentation and analysis of proven literature references. Feature analysis was conducted on the 8 networks using Pajek software to obtain the values of characteristic parameters for both the complex network of CSR evolution (referred to as the CSR network) and its 7 accident subnets (Table 4).
Size and density of the network
The network size refers to the numbers of nodes and edges in a complex network26. Based on experiments and literature27,28,29, the constructed CSR network model contains 44 nodes and 184 edges, and the theoretical maximum number of all connected edges in the network is 1,840, which means that the density of this complex network is 0.10. Given that the density of a random network with the same network structure is about 0.34, it can be concluded that the CSR network is a sparse one. The CSR network is characterized by a relatively dispersed structure, uncomplicated evolution paths among RF, SH and MD, and influencing factors that slightly interact with each other.
On the other hand, the number of edges in the 7 accident subnets is larger than that in the CSR network, demonstrating that the CSR network is not formed by simple combination of the subnets. Failure in controlling one inherent risk can easily lead to complex changes in the overall network, thus developing into causes of multiple types of accidents. In addition, among the 7 subnets, those corresponding to gas explosion accidents and coal and gas outburst accidents occupy the highest density, 26%, while that of water accidents has the lowest density, 18%. This indicates that in the accident subnets, the correlation between risk factors and potential hazards is relatively closer and the interaction between risk factors is more significant, i.e., the evolution process is more complex.
Average node degree and centralization
The node degree is a major evaluation indicator for the influence of nodes in complex networks, while the average node degree of a network reflects the average influence of the nodes in this network[30]. According to Table 4, the average node degree of the CSR network is 8.36, which means that each hazard in the network is correlated with other 8.36 hazards on average, that is, a change in one hazard in the network may lead to changes of the other 8.36 hazards. Among the 7 accident subnets, the highest average node degree is 6.71 corresponding to coal and gas outburst accidents, and the lowest is 3.2 to water accidents. Therefore, particular attention should be paid to potential hazards of coal and gas outburst accidents to avoid the failure of control measures.
The centralization reflects the aggregation of hazards in the network and subnets. It can be seen from Table 4 that the out-degree is lower than the in-degree for centralization of both the CSR network and the 7 subnets. This means that the evolution is more concentrated in the RF-SH path than in the SH-MD path, i.e., many factors can affect coal mine accidents, but few types of accidents may occur.
Characteristic path length and network diameter
The characteristic path length is the average distance between all node pairs in a complex network19. When the characteristic path is shorter, the risks and hazards need to go through fewer steps in a complex network, and thus the risks propagate faster in this network. The characteristic path length of the CSR model is 1.73, indicating that a risk or hazard can affect the other nodes correlated with it through an average of 1.73 edges. In other words, a change in a risk or hazard in the CSR network can trigger changes of its associated risks or hazards after an average of 1.73 steps. Among the 7 accident subnets, the largest characteristic path length is 1.63 corresponding to fire accidents, and the smallest is 1.49 to rock burst accidents and roof accidents. Both values are smaller than 1.73, suggesting that mine accidents are more susceptible to safety risks and potential hazards.
The network diameter refers to the maximum distance between two connected nodes in a complex network. The diameter of the CSR network is 5, which demonstrates that in the network model, it takes at most 5 steps for a risk or hazard to affect another one, namely, the incidence of risks and hazards can be determined to be within [0, 5]. Moreover, the diameters of the 7 subnets are all smaller than or equal to 5, suggesting that the triggering of mine accidents also requires at most 5 steps.
Global efficiency
The propagation rate of risks and hazards in the CSR network reflects its global efficiency19. In Table 4, the global efficiency of the CSR network is lower than or equal to that of the 7 subnets, indicating that the connectivity of the CSR network is lower than that of the subnets, that is, risks and hazards propagate more slowly in the CSR network. Particularly, the subnets of coal dust accidents and gas explosion accidents have the highest global efficiency among the 7 subnets, the lowest being the water accident subnet. Hence, vital risks and potential hazards related to coal dust accidents and gas explosion accidents should be especially concerned in prevention and control of coal mine disasters and accidents.
Clustering coefficient
The clustering coefficient manifests the importance of certain nodes in the CSR network, its value lying in the range of [0,1]21. According to Table 4, the clustering coefficient of the CSR network is 0.11, signifying that the correlation between nodes in the overall network is relatively uniformly distributed. Meanwhile, the clustering coefficients of the 7 subnets are all larger than or equal to that of the overall network. Among them, the highest clustering coefficient is 0.22 corresponding to rock burst accidents, and the lowest is 0.11 to water accidents. Changes in the risk and hazard nodes with higher clustering coefficients can easily lead to sudden changes in the nodes associated with them, even resulting in strong coupling and chain reactions within the network.
Small-world properties
The small-world properties of complex networks feature a short average path length (no longer than 10) and a high clustering coefficient (no lower than 0.1)21. The two values of the constructed CSR model are 4.8 and 0.11, respectively, both conforming to the small-world properties of complex networks. Therefore, the small-world properties of the CSR network can be determined.
The small-world properties of the CSR network suggest that most risks or hazards in the network are not necessarily directly correlated, yet they are accessible through short paths, indicating the propensity for rapid CSR evolution and sudden mine accidents. Moreover, the good connectivity between risk and hazard factors in the CSR network also increases the randomness of mine accidents, resulting in the broadscale propagation of safety risks and easy triggering of chain accidents. Following that, the controllability of safety risks is decreased, and safety production in coal mines is severely affected.
Scale-free properties
In a scale-free complex network, most nodes are only correlated with a few nodes, while some are correlated with numerous nodes. Therefore, BA scale-free networks are usually symbolized by high clustering coefficients of local nodes. Considering the small size of the CSR network, the cumulative degree distribution was taken as the indicator for identification of its scale-free properties.
According to the calculation results of the relevant parameters of the CSR network, its cumulative degree distribution follows the power-law distribution of function \(P(x)\sim 1.358 \times {x^{ – 0.337}}({R^2}=0.961)\) (Fig. 2). Consequently, it is identified to be a scale-free network, suggesting that risk and hazard nodes in the CSR network are concentrated. Therefore, CSR can be controlled more effectively by targeting the key risk and hazard nodes with high clustering coefficients and centrality in the network. Such targeted control can cut off the risk propagation chain and prevent the spread of risks and hazards in the network, thus reducing the probability of accidents.
Cumulative degree distribution of coal mine safety risk evolution complex network.
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