The heartbeat central pattern generator (CPG) in medicinal leeches controls blood flow within a closed circulatory by programming the constrictions of two parallel heart tubes. This circuit reliably produces a stereotyped fictive pattern of activity and has been extensively characterized. Here we determined, as quantitatively as possible, the strength of each inhibitory synapse and electrical junction within the core circuit of the heartbeat CPG. We also examined the animal-to-animal variability in strengths of these connections and, for some, determined the correlations between connections to the same postsynaptic target. The core CPG is composed of seven bilateral pairs of heart interneurons connected via both inhibitory chemical synapses and electrical junctions. Fifteen different connections within the core CPG were measured for strength using extracellular presynaptic recordings and postsynaptic voltage-clamp recordings across a minimum of seven individuals each, and the animal-to-animal variability was characterized. Connection strengths within the core network varied three to more than sevenfold among individuals (depending on the specific connection). The balance between two inputs onto various postsynaptic targets was explored by within-individual comparisons and correlation across individuals. Of the seven comparisons made within the core CPG, three showed a clear correlation of connection strengths, while the other four did not. We conclude that the leech heartbeat CPG can withstand wide variability in connection strengths and still produce stereotyped output. The network appears to preserve the relative strengths of some pairs of inputs, despite the animal-to-animal variability.