With the popularization of Internet, plenty of social networks come into lives. To enjoy different services, users usually take part in multiple social networks simultaneously. Therefore, user identification across social networks has become a hot research topic. In this study, social network structure is used to solve the problem of network alignment. Firstly, the problem of network alignment is formalized as the problem of maximum common subgraph (α-MCS). A method is proposed to determine parameter α adaptively. Compared with the other heuristic methods on determiningα, the proposed method can distinguish matched users and unmatched users effectively on different kinds of social networks. Secondly, in order to fast answer α-MCS, algorithm MCS_INA (α-MCS based iterative network alignment algorithm) is proposed. MCS_INA mainly contains two steps in each iteration. In the first step, MCS_INA aims at selecting candidates in the two networks respectively. In the second step, a mapping algorithm is proposed to match candidates. Compared with other methods, MCS_INA has lower time complexity and higher identification accuracy on different networks. At last, experiments are conducted on real-world and synthetic datasets to demonstrate the effectiveness of the proposed algorithm MCS_INA.