I volunteer for a community justice forum and I'm studying criminology to likely become a probation officer in the future, so let's clear some things up.
According to the DSM-V, pedophilia is a paraphilia ("recurrent, intense sexually arousing fantasies, sexual urges, or behaviors that involve children, nonhuman subjects, or other non-consenting adults, or the suffering or humiliation of oneself or one's partner.") with a sustained sexual orientation toward children, generally aged 13 or younger. That's the psychological definition.
Secondly, sex offenders rarely recidivate. Very low risk, and community witch hunts (legal or otherwise) do more harm than good, it stigmatizes people to the point where they can't get help or lead normal lives. Also, you can be a pedophile without offending, just look back the quote from the DSM where it say "fantasies".
Furthermore, jails aren't the best place for sex offenders, particularly child molesters. In the social hierarchy of prison inmates, convicts who have committed crimes against children, especially sexual abuse are at the bottom. Sentencing is not a adequate deterrent. Rehabilitation would be a better fit.
And like a few other posters have mentioned, criminals are heterogeneous, and not all that different from you or I.