In pattern recognition, graphs become alluring more and more as structural pattern representations due to their richer representability than feature vectors. However, there are many challenging problems using graphs for pattern recognition. One is that it is difficult to investigate the relationships of graphs effectively, even of trees. In this paper, we focus on the structure relationship analysis of trees, such as tree and subtree isomorphism, maximum common subtree, minimum common supertree, etc., which is almost suffered from all kinds of tree recognition problems. For investigating the relationships of structures of trees, we propose a structure network to represent the evolutional relationships of structures of trees. Moreover, for a lot of tree isomorphism problems appearing in the application of structure network, we propose a method that encodes the structure of tree as a numerical sequence, and illustrate its efficiency by comparing it with traditional matching method for tree isomorphism problem.