Hodge decomposition a Vector calculus: Helmholtz's decomposition ie. vector fields on nice domains may be resolved into irrotational (curl-free and solenoidal(divergence-free) component vector fields F=-Vy+V×A yp scalar potential, A vector potential a Linear algebra: additive orthogonal decomposition of a skew-symmetric matrix into three skew-symmetric matrices W=W1+W2+W3 W,=ve/-ev, W2 clique-consistent, W3 inconsistent Graph theory: orthogonal decomposition of network flows into acyclic and cyclic componentsHodge Decomposition