### $\mathcal{F}$-hypercyclic and disjoint $\mathcal{F}$-hypercyclic properties of binary relations over topological spaces

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.