Furthermore, simulated configurations of Lennard-Jones clusters also approximate the findings as well as a simple polymeric system forced into a close-packed structure under extremely high pressure. We also show that model hexagonal close packed structures may be used to reproduce many of the graph properties of the above-mentioned systems. A brief description of the model systems are summarized under the Methods section. This study is a first step towards using statistical characterization in determining the design principles underlying organization of complex molecular networks. However, systems attaining dense core structures do converge to this limit. Such close-packing may be attained by imposing external factors such as the high pressure on PBD; alternatively, the core regions of self-organized systems prefer to realize such an arrangement due to the free energetic requirements of arranging chains with both solvo-phobic and solvo-phillic regions in a solvent that creates the driving force for the Dabrafenib Raf inhibitor formation of the densely packed core. This study is based on the premise that network structures are better classified by the distributions of their network parameters rather than the average values. One previous example has been with approximating residue networks derived from proteins with the regular ring lattice: Although it is relatively easy to generate a corresponding ring lattice with few random rewired links having the same average degree and clustering coefficient as the RN, neither the second degree correlations nor the global properties are reproduced with this approach. However, comparison of distributions of the parameters involved is not straightforward. To make the problem tractable, we derive a relationship between knn and k for networks with arbitrary degree distributions, but with narrowly distributed finite clustering. This subset of constraints is relevant to the study of complex systems, because the results directly apply to the study of self-organized molecular structures which are characterized by Poisson degree distributions, and narrowly distributed clustering coefficients. In randomlypacked chain systems this relationship is expected to be lost, as is observed when the corona region of the micellar networks is also included in the calculations. We validate the derived linear relationship between knn and k on several model networks based on three dimensional regular structures, polymeric melts forced into close-packing by external pressure as well as those constructed from proteins and micelles of self-organizing cooligomers. Excluded volume and close-packing together control the plateau value of the clustering coefficient reached for nodes which are located in the core of the systems studied; i.e. those with high degree. Moreover, they impose a decreasing trend on C with increasing k, as well as providing restrictions on degree distributions. These constraints lead to assortative mixing in the graph structure.