The 3D conformations of chromosomes can encode biological significance, and the implications of such structures have been increasingly appreciated recently. Certain chromosome structural features, such as A/B compartmentalization, are frequently extracted from Hi-C pairwise genome contact information (physical association between different regions of the genome) and compared with linear annotations of the genome, such as histone modifications and lamina association. We investigate how additional properties of chromosome structure can be deduced using an abstract graph representation of the contact heatmap, and describe specific network properties that can have a strong connection with some of these biological annotations. We constructed chromosome structure networks (CSNs) from bulk Hi-C data and calculated a set of site-resolved (node-based) network properties. These properties are useful for characterizing certain aspects of chromosomal structure. We examined the ability of network properties to differentiate several scenarios, such as haploid vs diploid cells, partially inverted nuclei vs conventional architecture, depletion of chromosome architectural proteins, and structural changes during cell development. We also examined the connection between network properties and a series of other linear annotations, such as histone modifications and chromatin states including poised promoter and enhancer labels. We found that semi-local network properties exhibit greater capability in characterizing genome annotations compared to diffusive or ultra-local node features. For example, the local square clustering coefficient can be a strong classifier of lamina-associated domains. We demonstrated that network properties can be useful for highlighting large-scale chromosome structure differences that emerge in different biological situations.