We investigate networks represented as hypergraphs and propose aa novel measure that captures the relationship between their node degrees and hyperedge sizes. We test the presence of such an association in 36 empirical hypergraphs from diverse domains, with a focus on social networks. Using nested model comparisons, we classify each such relationship as linear, monotonic, non-monotonic, or absent. Results reveal that true absence of this relationship is rare, while nearly half exhibit non-monotonic patterns. We evaluate three correlation measures of this association and find that Pearson correlation best aligns with relationship direction. We also consider three ways to capture this relationship (called: bipartite, node-centric or edge-centric) and show that the bipartite one yields most consistent results. We discuss the implications of existence of relationship between node degrees and hyperedge sizes for dynamic processes on social systems.