exploring spatial networks with greedy navigators
TRANSCRIPT
Petter HolmeUmeå University, Sungkyunkwan University,Stockholm University, Institute for Future Studies
Sang Hoon LeeUmeå University, Oxford University
How can we measurenavigability?
What does optimallynavigable networks look like?
Full informationShortest paths
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Partial informationGreedy navigators
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(Greedy navigator) navigability
Avg. distanceAvg. distance for greedy navigators
Rg =
(Greedy navigator) navigability
Avg. distanceAvg. distance for random navigators
Rg =
random navigators perform a random DFS
Rg = 33% Rr = 24%
Network N M dg d dr Rg Rr
Boston* 88 155 6.8 5.7 30.8 84% 19%null model 8.6 3.7 23.2 43% 16%New York* 125 217 8.3 6.8 44.4 82% 15%null model 11.7 4.0 33.5 34% 12%
LCM 184 194 62.8 20.6 86.2 33% 24%
* from Youn, Gastner, Jeong, PRL (2008)
Navigator essentiality
–8–7–6–5
–6–4–20
–81
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ln |e|
–7–6–5
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–104 3
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ln |e|
Optimizing spatial networkfor greedy navigators
Fixed vertices, growing
Boston roads
MST
graph distance
Euclidean distance
Optimizing spatial networkfor greedy navigators
Fixed vertices
Optimizing spatial networkfor greedy navigators
Not fixed vertices
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BAHKWS
Karate Club2D square
1D ring
relative position f in greedy paths
devia
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relative position f in GSN paths
BAHKWS
Karate Club2D square
1D ring
KK
Thank you!SH Lee & P Holme, 2012. Exploring maps with greedy navigators. Phys. Rev. Lett. 108:128701.
SH Lee & P Holme, 2012. A greedy-navigator approach to navigable city plans. To appear in Eur. J. Phys. Spec. Top.
SH Lee & P Holme, 2012. Geometric properties of graph layouts optimized for greedy navigation. Under review Phys. Rev. E.