Higher-Order Visualization of Causal Structures in Dynamics Graphs

Graph drawing and visualisation techniques are important tools for the exploratory analysis of complex systems. While these methods are regularly applied to visualise data on complex networks, we increasingly have access to time series data that can be modelled as temporal networks or dynamic graphs. In such dynamic graphs, the temporal ordering of time-stamped edges determines the causal topology of a system, i.e. which nodes can directly and indirectly influence each other via a so-called causal path. While this causal topology is crucial to understand dynamical processes, the role of nodes, or cluster structures, we lack graph drawing techniques that incorporate this information into static visualisations. Addressing this gap, we present a novel dynamic graph drawing algorithm that utilises higher-order graphical models of causal paths in time series data to compute time-aware static graph visualisations. These visualisations combine the simplicity of static graphs with a time-aware layout algorithm that highlights patterns in the causal topology that result from the temporal dynamics of edges.