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Navigability of Networks

Navigability of Networks. Dmitri Krioukov CAIDA/UCSD M. Boguñá, M. Á. Serrano, F. Papadopoulos, M. Kitsak, A. Vahdat, kc claffy May, 2010. Common principles of complex networks. Common structure Many hubs (heterogeneous degree distributions)

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Navigability of Networks

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  1. Navigability of Networks Dmitri KrioukovCAIDA/UCSDM. Boguñá, M. Á. Serrano,F. Papadopoulos, M. Kitsak,A. Vahdat, kc claffy May, 2010

  2. 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

  3. Navigability • Navigability (or conductivity) is network efficiency with respect to: • targeted information propagation • without global knowledge • Examples are: • Internet • Brain • Regulatory/signaling/metabolic networks

  4. 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 dynamics • It may be vulnerable with respect to network damage

  5. 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

  6. 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

  7. 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

  8. 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.)

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