Exploring spatial networks with greedy navigators

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

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Optimizing spatial networkfor greedy navigators

Fixed vertices, growing

Boston roads

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graph distance

Euclidean distance

Optimizing spatial networkfor greedy navigators

Fixed vertices

Optimizing spatial networkfor greedy navigators

Not fixed vertices

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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.