  We focus on the problem of analyzing multiagent interactions in traffic
domains. Understanding the space of behavior of real-world traffic may offer
significant advantages for algorithmic design, data-driven methodologies, and
benchmarking. However, the high dimensionality of the space and the
stochasticity of human behavior may hinder the identification of important
interaction patterns. Our key insight is that traffic environments feature
significant geometric and temporal structure, leading to highly organized
collective behaviors, often drawn from a small set of dominant modes. In this
work, we propose a representation based on the formalism of topological braids
that can summarize arbitrarily complex multiagent behavior into a compact
object of dual geometric and symbolic nature, capturing critical events of
interaction. This representation allows us to formally enumerate the space of
outcomes in a traffic scene and characterize their complexity. We illustrate
the value of the proposed representation in summarizing critical aspects of
real-world traffic behavior through a case study on recent driving datasets. We
show that despite the density of real-world traffic, observed behavior tends to
follow highly organized patterns of low interaction. Our framework may be a
valuable tool for evaluating the richness of driving datasets, but also for
synthetically designing balanced training datasets or benchmarks.
