## Theoretical Condensed Matter Physics

### Dmitri Krioukov

Associate Professor

PhD Old Dominion University, 1998

(617) 373-2934

dima@neu.edu

### Research Summary

Prof. Krioukov’s research focuses on networks. Within network science, his interests range from big data analytics and practical applications, to mathematical physics of networks.

Prof. Krioukov’s past research dealt with the analysis of massive Internet datasets, and the design of efficient Internet routing algorithms. He introduced a systematic basis (*dK*-series) for network topology analysis and generation, generalizing a series of standard statistical properties of networks, such as degree distribution, degree correlations, clustering, etc. One outcome of his routing research is the Internet routing algorithm that is as efficient as theoretically possible. Due to its exceptional efficiency, this algorithm is now being considered as a foundation for routing in future Internet designs. The maximum efficiency of routing, navigation, and transport processes on complex networks is due to latent hyperbolic geometry of these networks, discovered in Krioukov’s research. This geometry not only governs flows of information and other media through complex networks, but also shape their structure as they grow. Hyperbolic geometry of complex networks finds a simple interpretation as an extension of preferential attachment that emerges as a by-product of certain trade-off optimization processes between popularity and similarity forces that drive network growth. More recently, Prof. Krioukov and his collaborators have shown that asymptotically the same network growth mechanisms describe the growth of the causal network structure of the universe at the Planck scale. Simply put, the growth rules of the universe and the Internet, or even the brain, are asymptotically identical—a result that led to a great deal of enthusiasm among the general public worldwide.

These and other results of Prof. Krioukov’s research suggest that the canonical approach in theoretical physics may, to a certain extent, be applicable to networks. If true, this hypothesis may help to predict and control network dynamics. The lack of fundamental theory of this dynamics is one of many factors making the network prediction and control tasks extremely challenging in many practically relevant applications. Some other focus areas of Prof. Krioukov’s current/recent research include brain networks, mathematical connections between different ensembles of random graphs, and certain networks in pure mathematics, such as networks of numbers and Apollonian sphere packings.

### Relevant Publications

D. Krioukov, M. Kitsak, R. Sinkovits, D. Rideout, D. Meyer, and M. Boguna,

**Network Cosmology**,

*Nature Scientific Reports, v.2, p.793, 2012* (DOI, arXiv),

Press: UCSD, SDSC, Space, Time, TheRegister, CBS, HuffingtonPost, HuffingtonPostUK, PopularScience, LiveScience, Slashdot, Robots.Net, PhysOrg, ScienceDaily, TGDaily, DigitalJournal, Vesti, MK, LifeNews, theRunet,…

One-sentence abstract: The large-scale structure and dynamics of complex networks and the universe are asymptotically identical.

F. Papadopoulos, M. Kitsak, M. Angeles Serrano, M. Boguna, and D. Krioukov,

**Popularity versus Similarity in Growing Networks**,

*Nature, v.489, p.537, 2012* (DOI, arXiv),

Press: UCSD, SDSC, Nature, Nature Physics, PhysOrg, ScienceDaily, AMS, Le Scienze, STRF, Elsevier, …

One-sentence abstract: Trade-offs between popularity and similarity shape the structure and dynamics of growing complex networks, with preferential attachment emerging from local optimization processes, casting these networks as random geometric graphs growing in hyperbolic spaces.

D. Krioukov, F. Papadopoulos, M. Kitsak, A. Vahdat, and M. Boguna,

**Hyperbolic Geometry of Complex Networks**,

*Physical Review E, v.82, 036106, 2010* (DOI, arXiv)

One-sentence abstract: A framework to study the structure and function of complex networks in purely geometric terms.

M. Boguna, F. Papadopoulos, and D. Krioukov,

**Sustaining the Internet with Hyperbolic Mapping**,

*Nature Communications, v.1, p.62, 2010* (DOI, arXiv, data),

Press: UCSD, SDSC, U. Barcelona, Nature, New Scientist, IEEE Spectrum, Communications of the ACM, Computerworld, MIT Scope, The Register, CBC, El Pais, TOVIMA, Electronics Weekly, PhysOrg, ACMEscience, Science Daily, I Programmer, ISPreview, PC Pro, R&D Mag, EnterTheGrid, CNews, Daily UA, …

One-sentence abstract: Mapping the Internet to its underlying hyperbolic space enables optimal routing in the Internet.

M. Boguna, D. Krioukov, and K.C. Claffy,

**Navigability of Complex Networks**,

*Nature Physics, v.5, p.74-80, 2009* (DOI, arXiv),

Press: UCSD, Nature, DailyTech, Science Daily, Voice of San Deigo, Technology Review, news:lite, Lenta.ru, …

One-sentence abstract: Complex networks have navigable topologies.

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