1 INTRODUCTION

Global and regional ecological security patterns are facing grand challenges (Xie & Wu, 2020). The rapid urbanization and industrialization in most countries had led to various ecological problems (Bai et al., 2018; Ma, Bo, Li, Fang, & Cheng, 2019; Xie, He, Choi, Chen, & Cheng, 2020), such as ecological sources encroachment and destruction (Han, Liu, & Wang, 2015), habitat fragmentation (Ng, Xie, & Yu, 2011), biodiversity loss (Kong, Yin, Nakagoshi, & Zong, 2010), ecosystem deterioration (Ernstson, 2013), and ecological function and service value deterioration (Costanza et al., 1997). A well-performing ecological security network (ESN) is necessary to enhance landscape connectivity, protect biodiversity, mitigate ecosystem degradation, improve ecological security patterns, and promote sustainable development (Cui, Wang, Sun, & Lv, 2020; Dai, Liu, & Luo, 2020; Dame & Christian, 2008; Zhao, Ma, Wang, & You, 2019). As one of the most important concepts and methods of landscape ecology (Forman, 1995), the ESN is a spatial organization system that identifies the characteristics of linear ecological corridors (i.e., network edges), connects various ecological sources (i.e., network nodes), and reflects the combinations of spatial elements with structural and functional characteristics in a specific space (i.e., the overall network). The ESN couples network structure, function, and ecological processes.
Since the 1970s, scholars have been studying different aspects of ESNs, such as network construction (Fath, Scharler, Robert, & Hannon, 2017), network planning and assessment (Cook, 2002), nature conservation (Hepcan, Hepcan, Bouwma, Jongman, & Ozkan, 2009), collaborative environmental governance (Bodin et al., 2016), species interactions (Delmas, 2018), and biodiversity conservation (Modica et al., 2021). However, most studies in the literature have focused on the development of the methods for ESN identification, reconstruction, and optimization (Hu et al., 2018; Kong et al., 2010; Shen, Wang, & Fu, 2014; Shi et al., 2020; Xie, Zhou, & Guan, 2014; Yin et al., 2011; Zhang, Yang, & Fath, 2010). A few studies have dealt with spatial and temporal evolution and systematic assessment of the constructed ESNs (Fan & Yang, 2019; Wang et al., 2020; Yu et al., 2018; Zhou, Lin, Ma, Qi, & Yan, 2020). In China, assessing the constructed ESNs is still at the exploratory stage by using landscape pattern index or traditional network structure index of graph theory (Liu et al., 2019; Pascual-Hortal & Saura, 2006), apparently lacking a systematic evaluation index system based on the complex network theory. In addition, a few studies had explored the scale effect (Dong et al., 2021), especially on network stability and connectivity under different disturbance mechanisms (Fu, Mo, Peng, Xie, & Gao, 2019; Pocock, Evans, & Memmott, 2012). It is necessary to develop a set of scientifically defensible index systems for ESN assessment that will help to discover the similarities and differences between different ecosystems and to provide decision-makers with science-based network optimization strategies.
In the recent years, complex network analysis derived from graph theory has been widely used to assess the pattern and process of various networks (Yong, Donner, Marwan, Donges, & Kurths, 2018), such as urban networks (Fang, Yu, Zhang, Fang, & Liu, 2020), social networks (Vahidzadeh, Bertanza, Sbaffoni, & Vaccari, 2021), water networks (Sitzenfrei, 2021), transportation networks (Soh et al., 2016), ecological networks (Pocock, Evans, & Memmott, 2012), energy metabolism (Zhai, Huang, Liu, & Zhang, 2019), economic performance (Gao, Tian, Zhang, Shi, & Shi, 2021), land use decision-making (Xia, Li, Zhou, Zhang, & Xu, 2020), land use effects (Xia & Chen, 2020), and CO2 transfer (Wang et al., 2021). A complex network is often understood as a distributed system that consists of multiple interconnected components with the network functionality being largely influenced by its structure, which, in turn, depends on the complexity of the network and the level of the interactions among components (Sitzenfrei, 2021). The network’s ubiquity, importance, and complexity intrigued the scientific community to study the formation and the growth dynamics of the network, as well as to explore the security of the network, the vulnerability of the network’s structure, and its robustness to random disaster and targeted disturbances (Callaway, Newman, Strogatz, & Watts, 2000; He, Liu, & Zhan, 2013; Yazdani & Jeffrey, 2011). Many statistical parameters have been proposed to describe the topology of complex networks (Jing & Wang, 2020), among which, degree, aggregation degree, betweenness centrality, closeness centrality, and network diameter are the most important parameters (Chen, Lu, Shang, Zhang, & Zhou, 2012; Liu, Slotine, & Barabási, 2011; Xia et al., 2018). These parameters cover many aspects of the network, such as static statistical characteristics, relatedness, connectivity, robustness, and resilience. In addition, some scholars have also evaluated the cluster characteristics of the network (Liu, Cao, Liu, Shi, & Liu, 2020).
The purpose of this study is to develop a framework and index system to assess the spatial topological structure of the ecological security network by integrating landscape ecology theory, graph theory, and complex network analysis for a rapid urbanization region in China, the urban agglomeration around Hangzhou Bay (UAHB) (see Supplemental Information (SI) Study area & Figure S1). The specific tasks include: (i) to construct a four-dimension assessment index system in terms of the network’s nodes, edges, connectivity, and robustness; (ii) to explore the stability and anti-disturbance ability of the network through scenario simulation; (iii) to propose the feasible measures for the optimization of the UHAB’s ecological security network. The framework and the technical roadmap of this study are shown in Figure 1.
The potential innovation of our study include: (i) evaluating the ESNs from the perspective of the network’s topological structure by integrating landscape ecology theory, graph theory, and complex network analysis; (ii) comparing the characteristics of the ESNs under two different disturbance scenarios to reveal the dynamic evolution process of the connectivity and stability of the ESNs; and (iii) proposing measures for the optimization of the ESNs.