Quick implementation of social networking

I need to implement a concept somewhat similar to social networking sites like orkut/linkedIn etc etc... The story is below......

'A' can send request to any other member say 'B' to join his network. The B joins his network. Now 'A' can approach the 'B' 's contacts by 2 ways directly or through 'B' and so on. Now suppose there is 'Z' somewhere in the chain of 'B' , when I search for 'Z' it will display me that you can reach 'Z' from 'B' using the chain or how can I view the chain.

My question is "do i need to write/implement graph theory here or is there any other rapid development approach available for this problem"

After going through the problem and explanation you have detailed above I feel that the best method and approach is to write or implement graph theory for this problem.