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We generalize the notion of Lagrangian subspaces to self-orthogonal subspaceswith respect to a (skew-)symmetric form, thus characterizing(skew-)self-adjoint and unitary operators by means of self-ortho-gonalsubspaces. By orthogonality preserving mappings, these characterizations can betransferred to abstract boundary value spaces of (skew-)symmetric operators.Introducing the notion of boundary systems we then present a unified treatmentof different versions of boundary triples and related concepts treated in theliterature. The application of the abstract results yields a description of all(skew-)self-adjoint realizations of Laplace and first derivative operators ongraphs.

Boundary systems and (skew-)self-adjoint operators on infinite metric graphs