Connection among the vertices on a plane or hyperplane

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Hi,

I am solving a problem where I want know that whether certain vertices on a hyperplane are connected to each other or not. Say in a 2D plane, if I have 3 or more vertices (points), how can I decide that if all these vertices are connected to each other? Similar is the problem for a hyperplane. Do we have any function/class is sage that can do it? I heard about convex hull algorithms but I don't know how to apply them to this problem. OR can we use graphs to solve this problem?

Any help/hint in this regard will be highly appreciated.

Thanks