vector calculus on weighted networks enrique bendito angeles carmona and andr es m encinas e mail enrique bendito upc edu angeles carmona upc edu andres marcos encinas upc edu departament ...
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...Vector calculus on weighted networks enrique bendito angeles carmona and andr es m encinas e mail upc edu andres marcos departament de matem atica aplicada iii universitat polit ecnica catalunya spain fax dept maiii mod c campus nord jordi girona salgado barcelona running head corresponding author abstract we present here a following the guidelines of dierential geometry key to develop an ecient net works which mimetizes in smooth case is adequate construction tangent space at each vertex this allows consider discrete elds inner products general metrics then obtain versions derivative gradi ent divergence curl laplace beltrami operators satisfying analogous properties those veried by their continuous counterparts also construct rham cohomology obtaining particular hodge decomposition theorem type other hand integral that includes integration parts technique green s iden tities as application study variational formulation for boundary value problems version dirichlet principle words net...