1 / 10

Navigability of Networks

Explore the concept of navigability in complex networks, discussing efficiency in information propagation, potential pitfalls of greedy navigation, and the evolving nature of networks towards navigable configurations. Learn about mapping networks to hidden metric spaces and the implications for routing solutions and understanding network dynamics. 8 Relevant

brendar
Download Presentation

Navigability of Networks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.)

More Related