A centrality measure based on the time of first returns rather than the number of steps is developed and applied to finding proton traps and access points to proton highways in the doped perovskite oxides: AZr 0.875 D 0.125 O 3 , where A is Ba or Sr and the dopant D is Y or Al. The high centrality region near the dopant is wider in the SrZrO 3 systems than the BaZrO 3 systems. In the aluminum-doped systems, a region of intermediate centrality (secondary region) is found in a plane away from the dopant. Kinetic Monte Carlo (kMC) trajectories show that this secondary region is an entry to fast conduction planes in the aluminum-doped systems in contrast to the highest centrality area near the dopant trap. The yttrium-doped systems do not show this secondary region because the fast conduction routes are in the same plane as the dopant and hence already in the high centrality trapped area. This centrality measure complements kMC by highlighting key areas in trajectories. The limiting activation barriers found via kMC are in very good agreement with experiments and related to the barriers to escape dopant traps. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx

Kinetic Monte Carlo (KMC) and graph searches show that proton conduction limiting barriers and trajectories in BaZr 0.875 Y 0.125 O 3 are affected by the presence of other protons. At 1000 K, KMC limiting conduction barriers increase from 0.39 eV to 0.45 eV as the proton number is increased. The proton-proton radial distribution begins to rise at 2 Å and peaks at 4 Å, which is half the distance expected, based on the proton concentration. Density functional theory (DFT) calculations find proton/proton distances of 2.60 and 2.16 Å in the lowest energy two-proton configurations. A simple average of the limiting barriers for 7-10 step periodic long range paths found via graph theory at 1100 K shows an increase in activation barrier from 0.32 eV to 0.37 eV when a proton is added. Both KMC and graph theory show that protons can affect each other's pathways and raise the overall conduction barriers.