Connectivity of material constituents govern the transport, mechanical, chemical, thermal, and electromagnetic properties. Energy storage, recovery and conversion depends on connectivity of material constituents. High-resolution microscopy image of a material captures the microstructural aspects describing the distribution, topology and morphology of various material constituents. In this study, six metrics are developed and tested for quantifying the connectivity of material constituents as captured in the high-resolution microscopy images. The six metrics are as follows: geobody connectivity metric based on percolation theory, Euler number based on integral geometry, indicator variogram based on geostatistics, two-point cluster function, connectivity function, and travel-time histogram based on fast marching method. The performances of these metrics are tested on 3000 images representing six levels of connectivity. The metrics are also evaluated on the organic constituent captured in the scanning electron microscopy (SEM) images of organic-rich shale samples. The connectivity function and travel-time histogram based on fast-marching method are the most robust and reliable metrics. Material constituents exhibiting high connectivity result in large values of average travel time computed using fast-marching method and average connected distance computed using connectivity function. The proposed metrics will standardize and speed-up the analysis of connectivity to facilitate the characterization of properties and processes of energy-relevant materials.