Biomolecular condensates are typically maintained by networks of molecular interactions, with canonical examples including those formed by prion-like low complexity domains (LCDs) of proteins. Single-component LCD condensates have been predicted to exhibit small-world network topologies and spatial inhomogeneities in protein compaction. Here, we systematically characterize molecular networks underlying condensates and investigate the relationship between single molecule properties and network topologies. We employ a chemically specific coarse-grained model to probe LCD condensates and generalize our findings by varying sequence hydrophobicity via a generic model that describes "hydrophobic-polar" (HP) polymers. For both model systems, we find that condensates are sustained by small-world network topologies featuring molecular "hubs" and "cliques". Molecular hubs with high network betweenness centrality localize near the centers of condensates and adopt more elongated conformations. In contrast, network cliques-densely interacting molecules that form locally fully connected subgraphs-are bridged by hubs and tend to localize near the condensate interface. Interestingly, we find power-law relationships between the structure and dynamics of individual molecules and network betweenness centrality, which describes molecular connectivity. Thus, our work demonstrates that inhomogeneities in condensate network connectivity can be predicted from single-molecule properties. Furthermore, we find that network cliques have longer lifetimes and that their constituent molecules remain spatially constrained, suggesting a role in shaping interface material properties.