Handwriting analysis when used as part of a hiring strategy is a complementary piece of the hiring puzzle. Most graphology experts recommend that you use the information gathered as part of the evaluation of a personality profile.
To be fair there is a bit of controversy surrounding the effectiveness and possibly the legality of using this type of personality test. I'll leave that argument to the experts.
Graphology uses information about how a person writes to develop a personality profile. Using such characteristics as shape, slant and pressure of the writing, experts can ascertain aspects of a candidates personality.
I have seen a couple of presentations on this type of personality testing. While I personally find it difficult to develop a comprehensive personality profile based on a writing sample, I do believe there are aspects that make sense.
For instance if someone presses down hard on the paper when they write, I can see how it may signal an intensity or up tight aspect of a personality.
Whether you chose to use this as part of your hiring process, as with any part of the process, be sure to hire an expert. They can give you the right kinds of analysis and interpretations.
It is also important to test everyone in the same way and using the same resource. If you only test young candidates with this method, it is a form of discrimination. Whether or not is a protected class is probably irrelevant. If you use this tool in your hiring process, apply it equally.
Use it on all the applicants or none then at the very least every you are treating each candidate the same.