基于LMBA策略的鄂尔多斯市生态空间网络优化

在分析鄂尔多斯市生态空间网络拓扑结构和鲁棒性的基础上，提出节点最低和最大介数增加(Low and maximum betweenness addition，LMBA）增边优化策略，同时与采用RA、LDF和SMB 3种增边策略的优化结果进行了对比。结果表明：鄂尔多斯生态空间网络有262个节点、402条边，网络直径为38，节点最大介数为418，最大连通度为25。网络连通度低，重要节点少且均位于网络西部，网络极不均匀，当网络结构遭到破坏时，进行自我恢复的能力比较强，但维持自身连通性的能力非常弱。增边94条后，LMBA策略优化后网络直径为16、节点最大介数为796、最大连通度为49，网络重要节点增多，网络整体效率明显提升；RA、LDF策略也使网络连通度极大增强，SMB策略的网络连通性增强效果不显著，重要节点增多且东移，网络结构比优化前更均匀。遭到攻击后，网络的连接鲁棒性大大增强，恢复鲁棒性也有所提升。与其他策略对比，LMBA策略的连接鲁棒性在两种攻击模式下、节点恢复鲁棒性在随机攻击模式下表现最优，节点恢复鲁棒性在恶意攻击下、边恢复鲁棒性在两种攻击模式下表现较优且稳定，说明该策略网络连通性强、结构均匀，综合表现最优。在遭受攻击过程中，LMBA策略维持自身连通情况的能力较优且稳定，节点和边的恢复能力也较优。

Ecospatial Network Optimization in Ordos Based on LMBA Strategy

Based on the analysis of network topology and robustness, the LMBA edge-adding optimization strategy was proposed, and three strategies of RA, LDF and SMB were adopted to optimize the network and compare the topology and robustness, respectively. It was found that there were 262 nodes and 402 edges in Ordos eco-spatial network, the network diameter was 38, the maximum betweenness was 418, and the maximum connectivity was 25, there were few important nodes which were all located in the west of the network, the network was extremely uneven, the network structure had a strong ability to recover itself when damaged, but the ability to maintain its own connectivity was very weak. After adding 94 edges, the optimized network diameter of LMBA strategy was 16, the maximum betweenness was 796, the maximum connectivity was 49, the number of important nodes was increased, and the overall efficiency of the network was improved significantly. In addition, RA and LDF strategies also greatly enhanced the network, while the network connectivity enhancement effect of SMB strategy was not significant, but the number of important nodes was increased and moved to the east, and the network structure was also more uniform than that before optimization. After being attacked, the connection robustness of the network was greatly enhanced and the recovery robustness was also improved. Compared with other strategies, the connection and recovery robustness of LMBA strategy was decreased slowly and steadily in two attack modes, which meant that the overall performance of the strategy was optimal and the network had strong connectivity and homogeneous structure, and the ability to maintain its own connectivity in the process of being attacked was optimal and stable, and the recovery of nodes and edges was also good.