Navigability of Networks Dmitri Krioukov CAIDA/UCSD M. Boguñá, M. Á. Serrano, F. Papadopoulos, M....
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Transcript of Navigability of Networks Dmitri Krioukov CAIDA/UCSD M. Boguñá, M. Á. Serrano, F. Papadopoulos, M....
Navigability of Networks
Dmitri KrioukovCAIDA/UCSD
M. Boguñá, M. Á. Serrano,F. Papadopoulos, M. Kitsak,
A. Vahdat, kc claffy
May, 2010
Common principlesof complex networks
Common structure Many hubs (heterogeneous degree distributions) High probability that two neighbors of the same
node are connected (many triangles, strong clustering)
Small-world property (consequence of the two above + randomness)
One common function Navigability
Navigability
Navigability (or conductivity) is network efficiency with respect to: targeted information propagation without global knowledge
Examples are: Internet Brain Regulatory/signaling/metabolic networks
Potential pitfallswith greedy navigation
It may get stuck without reaching destination (low success ratio)It may travel sup-optimal paths, much longer than the shortest paths (high stretch)It may require global recomputations of node positions in the hidden space in presence of rapid network dynamicsIt may be vulnerable with respect to network damage
Results so far
Hidden metric spaces do exist even in networks we do not expect them to exist Phys Rev Lett, v.100, 078701, 2008
Complex networks are navigable large numbers of hubs and triangles improve navigability
do networks evolve to navigable configurations? Nature Physics, v.5, p.74-80, 2009
Regardless of metric space structure, all greedy paths are shortest in complex networks (stretch is 1) Phys Rev Lett, v.102, 058701, 2009
The success ratio and navigation robustness do depend on metric space structure
But if the metric space is hyperbolic then also (PRE, v.80, 035101(R), 2009)
Greedy navigation almost never gets stuck (the success ratio approaches 100%)
Both success ratio and stretch are very robust with respect to network dynamics and even to catastrophic levels of network damage
Both heterogeneity and clustering (hubs and triangles) emerge naturally as simple consequences of hidden hyperbolic geometry
Agenda: mapping networksto their hidden metric spaces
Mapped the Internet used maximum-likelihood techniques very messy and complicated, does not scale
Need rich network data on network topological structure intrinsic measures of node similarity
New mapping methods
If we map a network, then we can
Have an infinitely scalable routing solution for the Internet
Estimate distances between nodes (e.g., similarity distances between people in social networks) “soft” communities become areas in the hidden space
with higher node densities
Tell what drives signaling in networks, and what network perturbations drive it to failures (e.g., brain disorders, cancer, etc.)