Graphlet Degree correlations reveal evidence of partial spatial embedding in complex networks

By virtue of most complex networks being comprised of real world objects or entities that can be assigned a location, the interactions that drive edge formation and network growth are affected by the spatial arrangement of the network's nodes. This means that most networks can be considered "partially embedded" in space, and the degree to which the network is embedded is determined by network growth rules. We utilize recent advances in network alignment techniques based on "Graphlet Degree Similarity" (GDS) to quantify how topological quantities change due to varying levels of spatial embedding in simulated complex networks. We demonstrate that the graphlet degree cross correlation matrix can be used to quantify the level of spatial embedding, and discuss how similar measures can be used to investigate the spatial hierarchy of complex networks.