In this work, we address the problem of community detection in a graph whose connectivity is given by probabilities (denoted by numbers between zero and one) rather than an adjacency matrix (only 0 or 1). The graphs themselves come from partitions of a dynamical system's state space where the probabilities denote likely transition pathways for dynamics. We propose a modification of the Leicht-Newman algorithm \cite{Leicht2008} which is able to automatically detect communities of strongly intra-connected points in state space, from which information about the residence time of the system and its principal periodicities can be extracted. Furthermore, a novel algorithm to construct the transition rate matrix of a dynamical system which encodes the time dependency of its Perron-Frobenius operator, is developed. Crucially, it overcomes the issue of time-scale separation stemming from the matrix construction based on {\it{infinitesimal}} generators and the exploration of {\it{long-term}} features of the underlying dynamical system. This method is then tested on a range of dynamical systems and datasets.PDF: Clustering of Dynamical Systems.pdf
