现实世界中的基础设施系统以及自然生物系统等都是复杂系统的具体例子。这些系统与人们的生活息息相关，是保障社会运行发展的支撑和认识社会自然现象的关键。常常使用复杂网络来描述这些具有相互联系的结构。然而对于现实世界的系统，空间网络是更为准确的概念。此外，就结构信息而言，收集连边信息的难度常常会高于收集节点信息。这使得从节点信息出发，对于空间网络的连边进行预测、重构是一类具有很高应用价值的问题。本文讨论空间网络的重构问题，从两个角度对空间网络重构问题进行探讨：其一，通过估计网络的拓扑性质，尝试使用最大熵方法重构网络结构。其二，讨论网络的演化机制重构网络的拓扑结构。在此基础之上，本文以网络上级联失效现象的例子，说明了基于重构得到的网络确实可以更好地对系统做出分析。
网络重构常常基于最大熵方法，要求首先确定网络的性质。因此本文首先探讨基于已知的、类似系统的结构信息对于未知的目标网络性质做出估计的可能性，讨论了常见的随机节点采样、广度优先搜索以及混合采样方式对于一些网络拓扑性质的影响。本文发现采样对于拓扑性质的偏差主要是网络异质性以及采样方法本身引入的。因此，采样方式对于网络拓扑指标的影响是不同的，无法得到和一个已知网络在各个方面都类似的目标网络。传统的最大熵方法无法在本文的研究场景下实现网络重构的目标。
本文进而研究空间网络的演化模型，讨论了基于已有结构的网络演化机制。相对于以往的模型，这一模型能够更好地生成空间网络中的环结构。具体而言，效率以及成本是主导空间网络演化的两大因素，而节点的异质性以及不同空间条件的制约则进一步导致了不同网络结构的出现。本文首先讨论了强空间以及弱空间条件下的网络的演化策略，并拓展到更为一般的空间条件下得到了经济—效率模型。结果说明早期在现实世界系统中报告的特性，例如基本涌现结构、度分布以及中心-边缘结构均可以通过这一模型重现。这一模型可以更好帮助我们了解、分析、重构真实世界中对应于不同系统的空间网络结构。
在实证方面，本文报告了经济-效率模型在实际数据集上对网络进行重构，并基于重构得到网络进行分析的结果。本文使用航空网络以及电力网络这些具体的例子，首先讨论了从已知的数据中拟合参数的方法。基于拟合得到的参数，模型在航空网络以及电力网络的数据集上均取得了不错的效果。最后，基于重构得到的网络，本文模拟了电力网络中的级联失效，说明了对网络进行重构、引入结构信息可以更有目的性地识别系统中重要节点。

Infrastructure and biological systems are examples of complex systems closely intertwined with people’s lives. They support human society and work as a key to comprehending social and natural phenomena. While complex networks are used to describe structures with interacted relationships, spatial networks are more suitable for real-world systems. Moreover, collecting information about nodes is easier than links in practice, making link prediction and reconstruction critical tasks. In this dissertation, we focus on the reconstruction of spatial networks and tackle the challenge from two perspectives: estimating the network’s topological properties to determine its structure using the Maximum Entropy Principle (MaxEnt) and investigating the evolutionary mechanisms of the networks. Additionally, we take the example of cascading failures to show that the reconstructed network can help us better perform analysis.
In early works, MaxEnt was commonly used to estimate the topology of a target networkbased on known properties. Therefore, we studied the estimation of target properties based on information gathered from networks within the same system. Three sampling methods - Random Node Sampling, Breadth-First Search, and a hybrid method - are discussed. Through empirical and theoretical analysis, we found that the sampling biases are introduced by the sampling methods and network heterogeneity. Moreover, it is difficult to obtain a network with different sizes but similar properties to the target network, since the biases introduced by sampling methods vary.
Then we turned to the evolution of spatial networks and discussed the mechanisms of spatial networks. We proposed a model that can generate loops more reasonably than previous models. Specifically, efficiency and cost are two keys determining the network evolution, whereas node heterogeneity and spatial constraints give rise to distinct network structures. Initially, we discussed the evolutionary mechanisms of systems with strong or weak spatial constraints, which were then expanded into a generalized economical-efficient model. Through this model, many macroscopical properties, such as emergence patterns, degree distributions, and core-periphery structures can be generated by our model using reasonable parameters. To this end, the model can help us understand, analyze, and reconstruct the networks corresponding to different systems.
Moreover, we applied the model to real-world systems and perform analysis based on the reconstructed structures. We examined two examples of airline networks and power grids and studied the method of fitting parameters from known networks. Based on the estimated parameters, the model performs well in both datasets. At last, we simulated cascading failures in power grids using the reconstructed networks. We found that reconstructing networks and introducing structural information can significantly help us estimate the importance of nodes in a system.