Bottlenecks can drastically reduce transport through porous materials. Previous work has concentrated on constriction-bottlenecks caused by variations in pore size. Here we study connectivity-bottlenecks, which are caused by many paths in the pore network passing through the same small part of the material. We develop three new connectivity descriptors, geodesic channel-strength, pore size-channels, and the closed pore-tortuosity that capture these effects. Five sets of computer-generated pore geometries with a wide variation in characteristics were used to evaluate the effect bottlenecks have on diffusive transport. We show that low connectivity as measured by the new bottleneck descriptors, can decrease diffusive transport drastically, but that in these data sets constriction-bottlenecks had a smaller effect. We also show that path-lengths and connectivity-bottlenecks can be highly correlated and adjustments using theoretical models of diffusive transport can help separate the effects. We provide a freely available software MIST that can be used to measure connectivity-bottleneck effects.