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Title: Network Mapping by Replaying Hyperbolic Growth
Authors: Papadopoulos, Fragkiskos 
Psomas, Constantinos 
Krioukov, Dmitri 
Major Field of Science: Engineering and Technology
Field Category: Electrical Engineering - Electronic Engineering - Information Engineering
Keywords: Applications;Ιnference;Νetwork geometry
Issue Date: 1-Feb-2015
Source: IEEE/ACM Transactions on Networking, 2015, vol. 23, no. 1, pp. 198-211
Volume: 23
Issue: 1
Start page: 198
End page: 211
Journal: IEEE/ACM Transactions on Networking 
Abstract: Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society. However these promises cannot be readily fulfilled and lead to important practical applications, without a simple, reliable, and fast network mapping method to infer the latent geometric coordinates of nodes in a real network. Here we present HyperMap, a simple method to map a given real network to its hyperbolic space. The method utilizes a recent geometric theory of complex networks modeled as random geometric graphs in hyperbolic spaces. The method replays the network's geometric growth, estimating at each time step the hyperbolic coordinates of new nodes in a growing network by maximizing the likelihood of the network snapshot in the model. We apply HyperMap to the AS Internet, and find that: 1) the method produces meaningful results, identifying soft communities of ASs belonging to the same geographic region; 2) the method has a remarkable predictive power: using the resulting map, we can predict missing links in the Internet with high precision, outperforming popular existing methods; and 3) the resulting map is highly navigable, meaning that a vast majority of greedy geometric routing paths are successful and low-stretch. Even though the method is not without limitations, and is open for improvement, it occupies a unique attractive position in the space of trade-offs between simplicity, accuracy, and computational complexity.
ISSN: 1558-2566
DOI: 10.1109/TNET.2013.2294052
Rights: © IEEE
Type: Article
Affiliation : Cyprus University of Technology 
University of California 
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