Motivated by the need for qualitative investigation of general system properties such as controllability, obser^bility, existence of fixed modes, etc. as the complement of the quantitative approach in analysis, especially of large-scale systems, the problems of pole assignability and stabilizability are considered from the structural point of view. The study is based on the definition of a generic property as a property that holds for almost all values of the nonzero system parameters. Structured matrices and digraphs are used for system description. Both problems are first formulated in an algebraic setting and then translated to a structural framework by means of several graph-theoretic results which give sufficient conditions for solvability, in terms of the existence of particular cycle families in the digraph. Following a similar approach, a graphical investigation of structural observability is presented. Lastly, genericity of several results are reconsidered in the light of these graphical characterizations.