The classification of networks is mostly based on measures such as degree distributions, average clustering, and average path length. Recently, spectral properties of networks gained attention since the distribution of eigenvalues characterize several aspects of the network such as algebraic connectivity and bipartiteness. Although there may be different graphs structures with identical Laplacian BKM120 spectra that define the network, they often show similar characteristics in terms of network parameters. Several heuristic algorithms are proposed to generate networks from their spectra. In recent years, proteins were investigated as networks, by taking the amino-acids as nodes. Termed as residue networks, edges between neighboring nodes are represented by their bonded and non-bonded interactions. Several studies have shown that residue networks have small-world topology, characterized by their logarithmically scaling average path lengths with network size, despite displaying high clustering. Further studies also utilized network models for protein structures to predict hot spots, conserved sites, domain motions, functional residues and protein-protein interactions. The small-world topology of residue networks is established, and various network properties such as the clustering coefficient, path length, and degree distribution are used to account for, e.g. the different fold-types in proteins, interfacial recognition sites of RNA, and bridging interactions along the interface of interacting proteins. In light of these studies, we expect other self-organized molecular systems of synthetic origin to display similar topology. In fact, a hierarchical arrangement of the nodes is expected to occur in self-organization of atoms and molecules under the influence of free energetic driving forces. In graph theory, hierarchies have been quantified by the presence of assortative mixing of their degrees, defined as nodes with high degrees having a tendency to interact with other nodes of high degrees. Analytical and computational models for generating assortatively mixed networks were proposed. Newman has shown that assortatively mixed networks percolate more easily and they are more robust towards vertex removal ; most social networks are examples of these. In this work, we find RN of proteins to also have assortative mixing, although many biological networks such as protein-protein interactions and food webs were found to display disassortative behavior. It is expected that in networks displaying any degree of correlations, local properties of the constructed graphs will have an effect on the global features. However, a connection between the local and global network properties and the underlying structure of molecular systems has yet to be established. In this study, we derive a relationship relating the nearest neighbor degree correlation of nodes, their degree, and clustering coefficient. We next show that a linear relationship is valid for two types of selforganized molecular systems.