In order to reinstall cydia without rejailbreaking you need to have terminal or ssh installed. You also need to have some basic linux skills.

1. Open termina/connect via ssh
2. type "su" then enter the default password "alpine"
3. Remove the previous installation of cydia: type "apt-get remove cydia"
4. Install cydia: type "apt-get install cydia'
5. Respring/Restart phone


All done.