@article {43110,
	title = {Finding shortest and nearly shortest path nodes in large substantially incomplete networks by hyperbolic mapping},
	journal = {Nature Communications},
	volume = {14},
	number = {186},
	year = {2023},
	publisher = {Nature},
	abstract = {Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Computing shortest paths is a straightforward task when the network of interest is fully known, and there are a plethora of computational algorithms for this purpose. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions and the Internet at the autonomous system level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks, where numbers of missing links exceed those of observable links. We demonstrate the utility of latent-geometric path finding in problems of cellular pathway reconstruction and communication security.},
	author = {Kitsak, Maksim and Ganin, Alexander and Elmokashfi, Ahmed and Cui, Hongzhu and Daniel A. {Eisenberg} and David L. {Alderson} and Korkin, Dmitry and Linkov, Igor}
}
@article {23835,
	title = {Long-Range Correlations and Memory in the Dynamics of Internet Interdomain Routing},
	journal = {PLoS ONE},
	year = {2015},
	publisher = {Public Library of Science},
	abstract = {Data transfer is one of the main functions of the Internet. The Internet consists of a large number of interconnected subnetworks or domains, known as Autonomous Systems (ASes). Due to privacy and other reasons the information about what route to use to reach devices within other ASes is not readily available to any given AS. The Border Gateway Protocol (BGP) is responsible for discovering and distributing this reachability information to all ASes. Since the topology of the Internet is highly dynamic, all ASes constantly exchange and update this reachability information in small chunks, known as routing control packets or BGP updates. In the view of the quick growth of the Internet there are significant concerns with the scalability of the BGP updates and the efficiency of the BGP routing in general. Motivated by these issues we conduct a systematic time series analysis of BGP update rates. We find that BGP update time series are extremely volatile, exhibit long-term correlations and memory effects, similar to seismic time series, or temperature and stock market price fluctuations. The presented statistical characterization of BGP update dynamics could serve as a basis for validation of existing and developing better models of Internet interdomain routing.},
	doi = {10.1371/journal.pone.0141481},
	url = {http://dx.doi.org/10.1371\%2Fjournal.pone.0141481},
	author = {Kitsak, Maksim and Elmokashfi, Ahmed and Havlin, Shlomo and Krioukov, Dmitri}
}
@article {23836,
	title = {Long-Range Correlations and Memory in the Dynamics of Internet Interdomain Routing},
	journal = {PLoS ONE},
	year = {2015},
	publisher = {Public Library of Science},
	abstract = {Data transfer is one of the main functions of the Internet. The Internet consists of a large number of interconnected subnetworks or domains, known as Autonomous Systems (ASes). Due to privacy and other reasons the information about what route to use to reach devices within other ASes is not readily available to any given AS. The Border Gateway Protocol (BGP) is responsible for discovering and distributing this reachability information to all ASes. Since the topology of the Internet is highly dynamic, all ASes constantly exchange and update this reachability information in small chunks, known as routing control packets or BGP updates. In the view of the quick growth of the Internet there are significant concerns with the scalability of the BGP updates and the efficiency of the BGP routing in general. Motivated by these issues we conduct a systematic time series analysis of BGP update rates. We find that BGP update time series are extremely volatile, exhibit long-term correlations and memory effects, similar to seismic time series, or temperature and stock market price fluctuations. The presented statistical characterization of BGP update dynamics could serve as a basis for validation of existing and developing better models of Internet interdomain routing.},
	doi = {10.1371/journal.pone.0141481},
	url = {http://dx.doi.org/10.1371\%2Fjournal.pone.0141481},
	author = {Kitsak, Maksim and Elmokashfi, Ahmed and Havlin, Shlomo}
}
