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  1. ; ; (, Groups, Geometry, and Dynamics)
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  2. (, Forum of Mathematics, Sigma)
    An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy . We characterize when a homotopy class of maps from one elastic graph to another is loosening , that is, decreases this elastic energy for all possible targets. This fits into a more general framework of energies for maps between graphs. 
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