  In this paper, we examine various types of ${\mathcal F}$-hypercyclic
(${\mathcal F}$-topologically transitive) and disjoint ${\mathcal
F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties
of binary relations over topological spaces. We pay special attention to finite
structures like simple graphs, digraphs and tournaments, providing a great
number of illustrative examples.
