In May 2017, The Belt and Road Initiative First International Cooperation Forum, which once again highlighted China's efforts and contributions in the construction of the "community of human destiny," was held in Beijing. We have drawn up the strategic conception of building the 21st Century Maritime Silk Road, thus paving the maritime passage of elements flow in Eastern and Western countries, and expanding the new trade route for China to connect the world economy. Based on the relationship of shipping between the Chinese and international ports and social network analysis (SNA), this study mapped the connection network of Chinese and international ports along the 21st Century Maritime Silk Road. The study also used the SNA method to analyze the overall network spatial structure and its core-periphery structure. We considered the network centrality and the actual shipping capability of the Chinese and international port nodes, thus identifying the functional nodes in the shipping network. The main conclusions are as follows. (1) The 21st Century Maritime Silk Road shipping network presents a spatial pattern of the pickaxe shape, and the close connection between the Chinese and Southeast Asian ports is the core of this pattern. Shanghai, Shenzhen, Singapore, and Port Klang constitute the hub and spoke network structure of the port of high efficiency and low consumption. (2) We derived the backbone network and core network through filtering, and identified special nodes and core nodes of international ports with different breadth and intensity. (3) There are two ways for ports to enter the shipping network. One is the hierarchical embedding mode (breadth, depth, intermediary function), such as China and Southeast Asia, and the other is homogeneous embedding mode, such as Africa, south West Asia-Middle East, South Asia, and Europe. (4) We identified five types of Chinese port nodes: potential composite hub port, export-oriented trunk port, inward direct port, intermediary branch port, and marginal feeder port. Then, the development proposals for these five types of ports are put forward, in order to effectively coordinate the port organization pattern and node functions so that ports can complement each other and enhance the value of the 21st Century Maritime Silk Road.