Single-cell RNA-sequencing data has revolutionized our ability to understand of the patterns of cell-cell and ligand-receptor connectivity that influence the function of tissues and organs. However, the quantification and visualization of these patterns in a way that informs tissue biology are major computational and epistemological challenges. Here, we present Connectome, a software package for R which facilitates rapid calculation and interactive exploration of cell-cell signaling network topologies contained in single-cell RNA-sequencing data. Connectome can be used with any reference set of known ligand-receptor mechanisms. It has built-in functionality to facilitate differential and comparative connectomics, in which signaling networks are compared between tissue systems. Connectome focuses on computational and graphical tools designed to analyze and explore cell-cell connectivity patterns across disparate single-cell datasets and reveal biologic insight. We present approaches to quantify focused network topologies and discuss some of the biologic theory leading to their design.