ELASTIC GRAPHS
Forum of Mathematics, Sigma, Tome 7 (2019)

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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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     author = {DYLAN~P. THURSTON},
     title = {ELASTIC {GRAPHS}},
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DYLAN P. THURSTON. ELASTIC GRAPHS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.4

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