Optimal navigation in complex networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 4, 2009, Pages

  Cajueiro, Daniel O ^a  

^a National Institute of Science and Technology for Complex Systems   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; CRITICAL POINTS; RANDOM NAVIGATIONS; RANDOM WALKERS;

EQUATIONS OF STATE;

NAVIGATION;

EID: 65549136527     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.046103     Document Type: Article

References (28)

1. J. D. Noh and H. Rieger, Phys. Rev. Lett. 92, 118701 (2004). 10.1103/PhysRevLett.92.118701
2. S. J. Yang, Phys. Rev. E 71, 016107 (2005). 10.1103/PhysRevE.71.016107
3. L. F. Costa and G. Travieso, Phys. Rev. E 75, 016102 (2007). 10.1103/PhysRevE.75.016102
4. K. Sneppen, A. Trusina, and M. Rosvall, Europhys. Lett. 69, 853 (2005). 10.1209/epl/i2004-10422-0
5. M. Rosvall, A. Trusina, P. Minnhagen, and K. Sneppen, Phys. Rev. Lett. 94, 028701 (2005). 10.1103/PhysRevLett.94.028701
6. M. Rosvall, A. Gronlund, P. Minnhagen, and K. Sneppen, Phys. Rev. E 72, 046117 (2005). 10.1103/PhysRevE.72.046117
7. A. Trusina, M. Rosvall, and K. Sneppen, Phys. Rev. Lett. 94, 238701 (2005). 10.1103/PhysRevLett.94.238701
8. M. Rosvall, P. Minnhagen, and K. Sneppen, Phys. Rev. E 71, 066111 (2005). 10.1103/PhysRevE.71.066111
9. I. Rodriguez-Iturbe, A. Rinaldo, R. Rigon, R. L. Bras, E. Ijjaszvasquez, and A. Marani, Geophys. Res. Lett. 19, 889 (1992). 10.1029/92GL00938
10. D. O. Cajueiro, Phys. Rev. E 72, 047104 (2005). 10.1103/PhysRevE.72. 047104
11. A. E. Motter and Z. Toroczkai, Chaos 17, 026101 (2007). 10.1063/1.2751266
12. R. Carvalho and G. Iori, Phys. Rev. E 78, 016110 (2008). 10.1103/PhysRevE.78.016110
13. D. O. Cajueiro and W. L. Maldonado, Phys. Rev. E 77, 035101 (R) (2008). 10.1103/PhysRevE.77.035101
14. L. Dall'Asta, M. Marsili, and P. Pin, J. Stat. Mech.: Theory Exp. 2008, P02003. 10.1088/1742-5468/2008/02/P02003
15. Here, we are not assuming such as in that P (i,t) is the shortest path from node i to node t.
16. D. P. Bertsekas, Dynamic Programming and Optimal Control (Athena Scientific, Belmont, 2001), Vol. II.
17. R. Bellman, Dynamic Programming (Princeton University Press, New Jersey, 1957).
18. R. S. Suton and A. G. Barto, Reinforcement Learning (MIT, Cambridge, MA, 2002).
19. A. L. Barabasi and R. Albert, Science 286, 509 (1999). 10.1126/science.286.5439.509
20. S. Maslov and K. Sneppen, Science 296, 910 (2002). 10.1126/science. 1065103
21. S. Maslov, K. Sneppen, and A. Zaliznyak, Physica A 333, 529 (2004). 10.1016/j.physa.2003.06.002
22. A. Trusina, S. Maslov, P. Minnhagen, and K. Sneppen, Phys. Rev. Lett. 92, 178702 (2004). 10.1103/PhysRevLett.92.178702
23. V. Latora and M. Marchiori, Physica A 314, 109 (2002). 10.1016/S0378-4371(02)01089-0
24. It is worth noting that the subgraphs used to explore navigation in the Swedish cities were built using the following procedure. Start with an empty subgraph. Add to this subgraph a randomly selected node of the network (we will call this node "1"). Then add one of the neighbors of node 1 (we will call this neighbor node "2") to the subgraph. If the desired number of nodes of the subgraph is not reached, add another neighbor of node 1 and so on. If the desired number of nodes of the subgraph is not reached, after all the neighbors of node 1 are included in the subgraph, repeat the procedure to node 2 and so on. After choosing the desired number of nodes, connect these nodes with the original edges.
25. V. Batagelj and A. Mrvar, PAJEK datasets, 2006 (http://vlado.fmf.uni-lj. si/pub/networks/data/).
26. W. W. Zachary, J. Anthropol. Res. 33, 452 (1977).
27. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-dynamic Programming (Athena Scientific, Belmont, 1996), Vol. II.
28. The only modification in the framework needed to deal with weighted networks is to replace the cost CN in Eq. 2 by the size of the edge.