  We explore the use of graph networks to deal with irregular-geometry
detectors in the context of particle reconstruction. Thanks to their
representation-learning capabilities, graph networks can exploit the full
detector granularity, while natively managing the event sparsity and
arbitrarily complex detector geometries. We introduce two distance-weighted
graph network architectures, dubbed GarNet and GravNet layers, and apply them
to a typical particle reconstruction task. The performance of the new
architectures is evaluated on a data set of simulated particle interactions on
a toy model of a highly granular calorimeter, loosely inspired by the endcap
calorimeter to be installed in the CMS detector for the High-Luminosity LHC
phase. We study the clustering of energy depositions, which is the basis for
calorimetric particle reconstruction, and provide a quantitative comparison to
alternative approaches. The proposed algorithms provide an interesting
alternative to existing methods, offering equally performing or less
resource-demanding solutions with less underlying assumptions on the detector
geometry and, consequently, the possibility to generalize to other detectors.
