  Physical distancing, as a measure to contain the spreading of Covid-19, is
defining a "new normal". Unless belonging to a family, pedestrians in shared
spaces are asked to observe a minimal (country-dependent) pairwise distance.
Coherently, managers of public spaces may be tasked with the enforcement or
monitoring of this constraint. As privacy-respectful real-time tracking of
pedestrian dynamics in public spaces is a growing reality, it is natural to
leverage on these tools to analyze the adherence to physical distancing and
compare the effectiveness of crowd management measurements. Typical questions
are: "in which conditions non-family members infringed social distancing?",
"Are there repeated offenders?", and "How are new crowd management measures
performing?". Notably, dealing with large crowds, e.g. in train stations, gets
rapidly computationally challenging.
  In this work we have a two-fold aim: first, we propose an efficient and
scalable analysis framework to process, offline or in real-time, pedestrian
tracking data via a sparse graph. The framework tackles efficiently all the
questions mentioned above, representing pedestrian-pedestrian interactions via
vector-weighted graph connections. On this basis, we can disentangle distance
offenders and family members in a privacy-compliant way. Second, we present a
thorough analysis of mutual distances and exposure-times in a Dutch train
platform, comparing pre-Covid and current data via physics observables as
Radial Distribution Functions. The versatility and simplicity of this approach,
developed to analyze crowd management measures in public transport facilities,
enable to tackle issues beyond physical distancing, for instance the
privacy-respectful detection of groups and the analysis of their motion
patterns.
