One of my friends works with interviewing pedophiles searching for help in Sweden, an interesting job for sure.
We have talked a few times about how they are, and as it is right now he has interviewed about 50.
There is absolutely nothing that they have in common with each other, other than that they were almost all men.
They also don't feel sexually attracted towards children the same way, some likes children exclusively, some likes only young girls, other only young boys, some likes adults and children equally, some like them both but say the way they like them differs and doesn't feel the same.
And it just goes on and on, some like women their own age and young boys, some is vice versa.
The way they like them differs as well, some is purely sexual, some feel it more like a strong love like with adults but hardly any sexual feelings.
The way they discovered that they were pedophiles differs heavely as well, only a small minority said that they hade been abused as kids. The most common was to discover their feelings during puberty but some also discovered it later, around 18-20, some only developed sexual feelings towards children after they themselves became parents.
You can't really claim anything definite about the whole group, it's impossible.