This paper presents studies of Bose–Einstein correlations (BEC) in proton–proton collisions at a centre-of-mass energy of 13 TeV, using data from the ATLAS detector at the CERN Large Hadron Collider. Data were collected in a special low-luminosity configuration with a minimum-bias trigger and a high-multiplicity track trigger, accumulating integrated luminosities of 151 μb-1 and 8.4 nb-1, respectively. The BEC are measured for pairs of like-sign charged particles, each with |η|<2.5, for two kinematic ranges: the first with particle pT>100 MeV and the second with particle pT>500 MeV. The BEC parameters, characterizing the source radius and particle correlation strength, are investigated as functions of charged-particle multiplicity ...