The Curl of a Weighted Network

In this work we introduce an accurate definition of the curl operator on weighted networks that completes the discrete vector calculus developed by the authors. This allows us to define the circulation of a vector field along a curve and to characterize the conservative fields. In addition, we obtain an adequate discrete version of the De Rham cohomology of a compact manifold, giving in particular discrete analogues of the Poincaré and Hodge’s decomposition theorems.