Dynamical systems are a contemporary and promising approach to model the computation carried out by neural populations. This perspective hypothesizes that certain dynamical features underlie the computations performed by the system, and characterizing them enables an intuitive understanding of the system. One central feature is the fixed (or slow) point: the fixed points of the system and the linearized dynamics around them can explain important aspects of the computation that is being performed. While successful in many cases, fixed-points analysis has limitations. Finding fixed points is generally hard, and requires knowledge of the full synaptic connectivity. Furthermore, many computations have a transient nature and might be subserved by other dynamical objects. Our goal in this work is to complement fixed-point analysis by providing a general tool for describing the computation performed by a dynamical system during a wide range of controlled tasks. This tool receives as inputs a set of neural trajectories from several trials and produces a directed graph that captures the essence of the calculation, which we call reduced dynamics. The process has two steps: identification of converging trajectories, and rule-based graph compression. In the first step, the algorithm identifies and merges converging trajectories. The second stage accepts a set of criteria from the user that compress the graph to remove redundant information. For instance, different trajectories that lead to the same output might be joined to reflect the final output of the network. A different setting could maintain the duration of these trajectories to allow visualization of delays in the dynamics. This stage is done via an iterative contraction of nodes using the chosen criteria. This tool provides an alternative way to explain task-related computations. Furthermore, the compact and graph-based representations can be used to compare networks one to another and thus allow clustering and other data analyses to be performed on sets of networks.