We present a general approach for evaluating and visualizing evolutionary dynamics of self-replicators using a graph-based representation for genealogy. Through a transformation from the space of species and mutations to the space of nodes and links, evolutionary dynamics are understood as a flow in graph space. A formalism is introduced to quantify such genealogical flows in terms of the complete history of localized evolutionary events recorded at the finest level of detail. Represented in a multidimensional viewing space, collective dynamical properties of an evolving genealogy are characterized in the form of aggregate flows. We demonstrate the effectiveness of this approach by using it to compare the evolutionary exploration behavior of self-replicating loops under two different environmental settings.