TThe contemporary technologies for personal identity recognition schemes like PIN or password has been adopted and used extensively by the user community. However, these schemes have certain drawbacks; i.e. they can be broken by using bruit force dictionary or by installing key loggers on the system. On the other side, biometric techniques are safer as compared to password identification for security purpose. This paper presents a new biometric security mechanism using accelerometer of smart phone. The use of accelerometer is very common for activity recognition in the researcher community. We have used the basic concepts of graph theory for identification mechanism. The accuracy of identification mechanism was about 80.66%