A person which is sexually attracted predominantly by preadolescent children.
Description:That means, it is not a person with actual or previous sexual relations with children. Thus, if a person is pedophile may be established only by the person itself, not by their behaviour.
There may be other persons (sadists, persons with fear of contact with adults, persons in a situation without the preferred sexual partner) which have sexual contacts with children but are not pedophile.
There may be also pedophiles which have even never touched a child for different reasons (fear of persecution, fear of contact, no possibility of contact, internalization of prejudices that it is harmful for the child, religious reasons and so on).
See also about paraphilia
Pedophiles, under the biological definition, are those who are attracted to pre-pubescent children.
The law, on the other hand, is usually cast in terms of age alone.
The paper contains some interesting historical background.
The paper is valuable in that it highlights certain distinctions that, if not made, would make clear thinking about pedophilia impossible.
Then there is also the Report of the Australian Parliamentary Joint Committee on the National Crime Authority:
On "Organised criminal paedophile activity" November 1995.
"To be a paedophile is not, as such, a crime". page 7
and
"Expert opinion seems to favour the view that the term "paedophile" should not be used to cover all adults who commit sexual offences against children (of whatever age). For example, under the American Psychiatric Association criteria, a person can be a paedophile without ever having sexually molested or abused a child, and can sexually molest a child without being a paedophile. The categories of child molester and paedophile overlap, but are not identical. Some paedophiles simply phantasise or act out their fantasies in ways that are not illegal. Conversely, some persons sexually abuse children without having any attraction to them, as the Victorian Government's submission explained.