Interpolating between random walks and shortest paths: A path functional approach

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7710, Issue , 2012, Pages 68-81

  Bavaud, François ^a   Guex, Guillaume ^a  

^a UNIVERSITY OF LAUSANNE   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ADJUSTABLE PARAMETERS; CONFLICTING OBJECTIVES; ENERGY FUNCTIONALS; ENTROPY FUNCTIONAL; FUNCTIONAL APPROACH; SHORTEST PATH; SPATIAL EXPLORATIONS; THERMODYNAMIC FORMALISM;

GRAPH THEORY;

EID: 84962382935     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-35386-4_6     Document Type: Conference Paper

References (20)

1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Theory, algorithms and applications. Prentice Hall (1993)
2. Alamgir, M., von Luxburg, U.: Phase transition in the family of p-resistances. In: Neural Information Processing Systems (NIPS 2011), pp. 379–387 (2011)
3. Bollobás, B.: Modern Graph Theory. Springer (1998)
4. Borgatti, S.P.: Centrality and network flow. Social Networks 27, 55–71 (2005)
5. Brandes, U., Fleischer, D.: Centrality Measures Based on Current Flow. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 533–544. Springer, Heidelberg (2005)
6. Chebotarev, P.: A class of graph-geodetic distances generalizing the shortest-path and the resistance distances. Discrete Applied Mathematics 159, 295–302 (2010)
7. Dubois-Ferrière, H., Grossglauser, M., Vetterli, M.: Valuable Detours: Least-Cost Anypath Routing. IEEE/ACM Transactions on Networking 19, 333–346 (2011)
8. Iryo, T., Shintaku, H., Senoo, S.: Experimental Study of Spatial Searching Behaviour of Travellers in Pedestrian Networks. In: 1st European Symposium on Quantitative Methods in Transportation Systems, EPFL Lausanne (2012) (contributed talk)
9. Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Springer (1976)
10. Farnsworth, K.D., Beecham, J.A.: How Do Grazers Achieve Their Distribution? A Continuum of Models from Random Diffusion to the Ideal Free Distribution Using Biased Random Walks. The American Naturalist 153, 509–526 (1999)
11. Fouss, F., Pirotte, A., Renders, J.-M., Saerens, M.: Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation. IEEE Transactions on Knowledge and Data Engineering 19, 355–369 (2007)
12. Freeman, L.C.: Centrality in networks: I. Conceptual clarification. Social Networks 1, 215–239 (1979)
13. Freeman, L.C., Borgatti, S.P., White, D.R.: Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks 13, 141–154 (1991)
14. Kirchhoff, G.: On a deduction of Ohm’s laws, in connexion with the theory of electrostatics. Philosophical Magazine 37, 463 (1850)
15. Newman, M.E.J.: A measure of betweenness centrality based on random walks. Social Networks 27, 39–54 (2005)
16. Noh, J.-D., Rieger, H.: Random walks on complex networks. Phys. Rev. Lett. 92, 118701 (2004)
17. Saerens, M., Achbany, Y., Fouss, F., Yen, L.: Randomized Shortest-Path Problems: Two Related Models. Neural Computation 21, 2363–2404 (2009)
18. Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry 32, 425–443 (1969)
19. Yen, L., Saerens, M., Mantrach, A., Shimbo, M.: A Family of Dissimilarity Measures between Nodes Generalizing both the Shortest-Path and the Commute-time Distances. In: Proceedings of the 14th SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 785–793 (2008)
20. Zhou, T.: Mixing navigation on networks. Physica A 387, 3025–3032 (2008)