1. Petter Holme
Umeå University, Sungkyunkwan University,
Stockholm University, Institute for Future Studies
Sang Hoon Lee
Umeå University, Oxford University

4. How can we measure
navigability?
What does optimally
navigable networks look
like?

5. Full information
Shortest paths

6. 3 t 4
6
2 5
1 8 7
s 9

7. 3 t 4
6
2 5
1 8 7
s 9

8. 3 t 4
6
2 5
1 8 7
s 9

9. 3 t 4
6
2 5
1 8 7
s 9

10. 3 t 4
6
2 5
1 8 7
s 9

11. Partial information
Greedy navigators

12. 3 t 4
6
2 5
1 8 7
s 9

13. 3 t 4
6
2 5
1 8 7
s 9

14. 3 t 4
6
2 5
1 8 7
s 9

15. 3 t 4
6
2 5
1 8 7
s 9

16. 3 t 4
6
2 5
1 8 7
s 9

17. 3 t 4
6
2 5
1 8 7
s 9

18. 3 t 4
6
2 5
1 8 7
s 9

19. (Greedy navigator) navigability
Avg. distance
Rg =
Avg. distance for greedy
navigators

20. (Greedy navigator) navigability
Avg. distance
Rg =
Avg. distance for random
navigators
random navigators
perform a random DFS

23. Rg = 33% Rr = 24%

24. Network N M dg d dr Rg Rr
Boston* 88 155 6.8 5.7 30.8 84% 19%
null
8.6 3.7 23.2 43% 16%
model
New
125 217 8.3 6.8 44.4 82% 15%
York*
null
11.7 4.0 33.5 34% 12%
model
LCM 184 194 62.8 20.6 86.2 33% 24%
* from Youn, Gastner, Jeong, PRL (2008)

25. Navigator essentiality

26. 0
–2
–4
1 –6
–8
ln |e|
–5
2 4 –6
3 –7
–8

27. 1 0
2
–5
3 –10
4
ln |e|
–5
–6
–7

28. Optimizing spatial network
for greedy navigators
Fixed vertices, growing

29. Boston roads

30. MST

31. graph distance

32. Euclidean distance

33. Optimizing spatial network
for greedy navigators
Fixed vertices

37. Optimizing spatial network
for greedy navigators
Not fixed vertices

40. 0.2
BA
deviation from shortest path 0 optimized HK
WS
–0.2 Karate Club
2D square
–0.4 1D ring
–0.6
–0.8
–1
–1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
relative position f in greedy paths

41. 0.2
deviation from shortest path BA
0 KK HK
WS
–0.2 Karate Club
2D square
–0.4 1D ring
–0.6
–0.8
–1
–1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
relative position f in GSN paths

42. 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.