Network Geometry Inference using Common Neighbors

F. Papadopoulos, R. Aldecoa, and D. Krioukov
Physical Review E
v.92, 022807, 2015
August 12, 2015


We introduce and  explore a new method for inferring hidden geometric coordinates of nodes in  complex networks based on the number of common neighbors between the nodes.  We compare this approach to the HyperMap method, which is based only on the  connections (and disconnections) between the nodes, i.e., on the links that  the nodes have (or do not have). We find that for high degree nodes the  common-neighbors approach yields a more accurate inference than the  link-based method, unless heuristic periodic adjustments (or "correction  steps") are used in the latter. The common-neighbors approach is  computationally intensive, requiring O(t4) running time to map a network of t  nodes, versus O(t3) in the link-based method. But we also develop a hybrid method  with O(t3) running time, which combines the common-neighbors and link-based  approaches, and explore a heuristic that reduces its running time further to  O(t2), without significant reduction in the mapping accuracy. We apply this  method to the Autonomous Systems (AS) Internet, and reveal how soft  communities of ASes evolve over time in the similarity space. We further  demonstrate the method's predictive power by forecasting future links between  ASes. Taken altogether, our results advance our understanding of how to  efficiently and accurately map real networks to their latent geometric  spaces, which is an important necessary step towards understanding the laws  that govern the dynamics of nodes in these spaces, and the fine-grained  dynamics of network connections.

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