The measured transport critical current densities, Jc, of MgB2 superconductors fall short of their intrinsic Jcs on account of the grain boundary blockage, sausaging, and porosity seen in most powder-processed wire samples. Hence, it becomes important to understand and to be able to measure the degree of what can be referred to as “connectivity” in order to be able to assess the highest attainable Jc in a given class of samples. In this paper connectivity is determined with the aid of normal state resistivity in an extension of the model originally proposed by Rowell. The normal-state resistivity temperature dependence is fitted to a standard Bloch–Grüneisen (B-G) equation in the range 50–300 K. Such an approach leads not only to a connectivity parameter but also to other useful data: the actual intragrain residual resistivity (indirectly related to the upper critical field) and a resistively determined Debye temperature, θR. The latter quantity, coupled to the transition temperature, Tc, provides a measure (by way of the McMillan formula) of the electron-phonon coupling constant, usually designated λ. The B-G-based connectivity model was applied to our own experimental data on binary and heavily doped MgB2 samples as well as published resistivity data. To complete the study, low temperature specific heat measurements, performed on binary and doped bulk samples provided calorimetrically determined Debye temperatures, θD, for comparison to the resistively determined values and excellent agreement was found. Calorimetric measurements also probed the homogeneity of the doped samples in terms of the roundness of the electronic specific heat jump near Tc.