New Way to Build the Distributed System Without Cut Vertexes

In some particular area, such as large-scale distributed systems, especially in peer-to-peer (P2P) system, a small amount of nodes usually restrict the capability of the whole system heavily. These nodes are called ¿Critical Nodes¿ or ¿Cut Nodes¿. This paper is focus on the way of creating the system without the critical node. We regard the distributed system as an undirected graphic. At first, we proposed some theorems, with which we can create the connected graphic without critical node. Then we gave some examples to illustrate the procedure of the creation of the distributed system. Besides, we also make the proof our theorems which will be useful to the distributed system.