Interpolating between Random Walks and Shortest Paths: A Path Functional Approach

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7710)


General models of network navigation must contain a deterministic or drift component, encouraging the agent to follow routes of least cost, as well as a random or diffusive component, enabling free wandering. This paper proposes a thermodynamic formalism involving two path functionals, namely an energy functional governing the drift and an entropy functional governing the diffusion. A freely adjustable parameter, the temperature, arbitrates between the conflicting objectives of minimising travel costs and maximising spatial exploration. The theory is illustrated on various graphs and various temperatures. The resulting optimal paths, together with presumably new associated edges and nodes centrality indices, are analytically and numerically investigated.


Random Walk Betweenness Centrality Resistance Distance Uniform Transition Admissible Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Computer Science and Mathematical MethodsUniversity of LausanneSwitzerland
  2. 2.Department of GeographyUniversity of LausanneSwitzerland

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