In the present paper we describe an approach to the dynamical clustering of fMRI resting state networks and their connections, in which we use two known mathematical methods for data analysis: topological data analysis and k-means method. With these two methods we found about 4 stable states in group analysis. Dynamics of these states is characterized by periods of stability (blocks) with subsequent transition to another state. Topological data analysis method allowed us to find some regularity in subsequent transitions between blocks of states for individuals but it was not shown that the regularity repeats in all subjects. Topological method gives smoother distribution of dynamic states comparing to k-means method, highlighting about 4 dominant states in percentage, while k-means method gives 1–2 such states.