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

Authors:
François Bavaud;Guillaume Guex
Affiliations:
Department of Computer Science and Mathematical Methods, University of Lausanne, Switzerland, Department of Geography, University of Lausanne, Switzerland;Department of Computer Science and Mathematical Methods, University of Lausanne, Switzerland, Department of Geography, University of Lausanne, Switzerland
Venue:
SocInfo'12 Proceedings of the 4th international conference on Social Informatics
Year:
2012

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Abstract

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.