The performance of materials for electrochemical energy conversion and storage depends upon the number of electrocatalytic sites available for reaction and their accessibility by the transport of reactants and products. For solid oxide fuel/electrolysis cell materials, standard 3-D measurements such as connected triple-phase boundary (TPB) length and effective transport properties partially inform on how local geometry and network topology causes variability in TPB accessibility. A new measurement, the accessible TPB, is proposed to quantify these effects in detail and characterize material performance. The approach probes the reticulated pathways to each TPB using an analytical electrochemical fin model applied to a 3-D discrete representation of the heterogeneous structure provided by skeleton-based partitioning. The method is tested on artificial and real structures imaged by 3-D x-ray and electron microscopy. The accessible TPB is not uniform and the pattern varies depending upon the structure. Connected TPBs can be even passivated. The sensitivity to manipulations of the local 3-D geometry and topology that standard measurements cannot capture is demonstrated. The clear presence of preferential pathways showcases a non-uniform utilization of the 3-D structure that potentially affects the performance and the resilience to alterations due to degradation phenomena. The concepts presented also apply to electrochemical energy storage and conversion devices such as other types of fuel cells, electrolyzers, batteries and capacitors.