i) terrorists are, almost by definition "crazy" (as in: on a rapid trajectory towards death, ignominy, or both)
ii) terrorists do not *need* "links" to known terrorist organisations. Proving any such links only has value in that it increases the urgency with which we need to dispatch organisationally competent individuals within such an organisation or, preferably, the organisation in toto.
Surely a terrorist must belong to some organisation that threatens, or poses a threat, to a group or groups of people over a period of time. That group causes people to change their behaviour because of the threat, such as changing holiday plans because the intended destination is under threat; or even emigrating because you belong to the target group.
This country is on high alert because of there is a real possibility that we might be attacked by a terrorist organisation, currently ISIS.
One deranged madman with a gun is not a terrorist, no more than Brenda Spencer was a terrorist.