Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" (a) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors "radius-resolved saturations" (psi(w)(F), psi(n)(F)) to characterize the distribution of fluid phases within. Small accessivity (alpha -> 0) implies serial connections between different sized pores, while large accessivity (alpha -> 1) corresponds to more parallel arrangements, as the classical capillary bundle model implicitly assumes. Based on these concepts, we develop a statistical theory for quasi-static immiscible drainage-imbibition in arbitrary cycles, and arrive at simple algebraic formulae for updating psi(n)(F) that naturally capture capillary pressure hysteresis, with alpha controlling the amount of hysteresis. These concepts may be used to interpret hysteretic data, upscale pore-scale observations, and formulate new constitutive laws by providing a simple conceptual framework for quantifying connectivity effects, and may have broader utility in continuum modeling of transport, reactions, and phase transformations in porous media. (C) 2018 Elsevier Ltd. All rights reserved.