With the deepening of reform and opening-up, China’s economy has been further developed, but there is still a problem of uneven development. It is of great significance to completely construct China’s economic spatial correlation network, to clarify the role and status of each province in the whole network, and to study the influencing factors of the national spatial economic network. In this paper, we employ the network analysis method to analyze China’s economic development in the past 20 years. Based on the modified gravity model, we construct China’s spatial economic network and explore the network structure from three aspects: the whole network structure feature, characteristics of individual provinces in the network, and block model analysis. The results show that (1) China’s spatial economic network has strong internal cohesion, and the hierarchy of the network is becoming less and less obvious. However, the network density is low, and the overall network relationship still needs to be strengthened. (2) The different levels in economic development illustrate the obvious economic unbalance among provinces. (3) The block model analysis results demonstrated that coastal areas are more attractive to other provinces and are playing an important role in driving China’s economy. Finally, we employ Quadratic Assignment Procedure (QAP) regression analysis to analyze the influential factors on spatial economic network. Numerical results show that the geographic proximity and the differences in six factors (industrial structure, level of economic development, degree of opening to the outside world, medical level, size of labor market, and infrastructure) have significant impact on the spatial economic network. Moreover, the influence of these factors on the economic relation among provinces has been gradually strengthened in recent years.

Let $G$ be a connected graph with vertex set $V\left(G\right)$. The degree distance of $G$ is defined as $D^{\prime }\left(G\right)={\sum }_{\{u,v\}\subseteq V\left(G\right)}({\mathrm{deg}}_G\left(u\right)+{\mathrm{deg}}_G\left(v\right))d(u,v)$, where ${\mathrm{deg}}_G\left(u\right)$ is the degree of vertex $u$, and $d(u,v)$ denotes the distance between $u$ and $v$. Here we characterize $n$-vertex unicyclic graphs with girth $k$, having minimum and maximum degree distance, respectively. Furthermore, we prove that the graph $B_n$, obtained from two triangles linked by a path, is the unique graph having the maximum degree distance among bicyclic graphs, which resolves a recent conjecture of Tomescu.

Photovoltaic industry trade has become a global trade activity, and a wide range of photovoltaic trade relations have been formed between countries. In order to further strengthen and balance trade relations, this paper analyzes global photovoltaic (PV) trade from the perspective of complex networks. We employ network indicators and the cascading process of risk propagation to analyze the evolution features and the vulnerability of the PV trade network. Firstly, we establish the global PV trade networks from 2000 to 2021 based on the PV trade flow between countries. We then explore evolution features and analyze the influencing factors of the trade network structure. Finally, we simulate the cascading process of risk propagation on the trade network based on an improved bootstrap percolation model. The evolution features reveal the following three results: (1) the scale of global PV trade continues to grow, and the participation of some countries has increased significantly; (2) the global PV trade network has small-world characteristics, and the related products have high circulation efficiency; and (3) the global PV trade network has a core-periphery structure, while a few countries drive most of the trade. China, Germany, and the U.S. are the top PV traders. Some Asian countries, such as Vietnam, are gradually increasing their share of the market. The QAP regression analysis shows that the gaps in GDP and electricity access rate are the biggest facilitating and hindering factors in the global PV trade, respectively. The simulation results show that the global PV trade network is vulnerable to targeted risk and is robust to randomness risk.