Abstract: Mechanical and flexible structural orders emerge in the Internet topology. The researches describing the dissipative structural order and related topics are very important in the redesign of the Internet， and it is also of great importance in the field of predicting the evolution of Internet topology. IPv4， IPv6 and AS-level network topologies data which authorized by cooperative association for Internet data analysis (CAIDA) are used in this paper， and the relationships among the network structural orders and the size and connectivity of the network are discussed， the results show that all the 3 kinds of network are of dissipative structures， which behave both centralization and equalization， and their orders are continuously evolving in the process of dissipation. The positive correlativity among the network structural orders and the size and connectivity of the network size shows that the network structural order is gradually dissipated in the development process of the Internet.

Key words: Internet topology evolution, structural order, dissipation, IPv4, IPv6, Internet AS-level