An algorithm is presented that defines all the internal meshes of na oriented connected graph described by its incidence matrix. In the case of a planar, connected graph, a mesh matrix is obtained, which allows either nodal or mesh analysis of an active linear network described by its nodes. A further algorithm is developed ehich applies both these types of analysis to networks with ideal elements, such as controlled or uncontrolled current and voltage sources, operational amplifiers and mutual inductances. Owing to the fact that the representation of an element in one of these methods is identical to that of the dual element in the other, a program which performs nodal analysis may easily be adapted to perform mesh analysis. The methods are compared with existing methods of circuit analysis and some conclusions are drawn.