The border separates the inside from the outside and defines the organisation as such. At the same time a border has no relevance when there is no interaction over it, in whatever form. Borders without interaction are nonexistent as an object of study or design.
That interaction implies also a kind of connections between the actors.
Taking this idea a little further, you could argue that it are the networked connections that make up the organisation. An organisation defined by a commonality in the nature of the connections instead of by an enclosing borderline.