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2GIDEONAMIRANDORIGUREL-GUREVICHallregulartrees.Forunimodulargraphsthefollowingsymmetryprincipleholds:MassTransportPrinciple:LetG=(V;E)beaunimodulargraph,andassumeF:VV![0;1]isautomorphisminvariant(i.e.F(
v;
y)=f(x;y)forany
2Aut(G)),thenforanyv2VwehaveXw2V

2GIDEONAMIRANDORIGUREL-GUREVICHallregulartrees.Forunimodulargraphsthefollowingsymmetryprincipleholds:MassTransportPrinciple:LetG=(V;E)beaunimodulargraph,andassumeF:VV![0;1]isautomorphisminvariant(i.e.F( v; y)=f(x;y)forany 2Aut(G)),thenforanyv2VwehaveXw2V

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4GIDEONAMIRANDORIGUREL-GUREVICHcallxv;0acandidate....

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