Foundations of Network Theory

Abstract:
We consider different axiomatizations of network theory with emphasis of Kirchhoff networks. Following a tradition founded by Kirchhoff the topological structure of this class of networks is characterized by means of oriented graphs. Multipole and multiport networks are introduced as alternative variants. A consequent enforcement of the multiport approach leads directly to the class of Paynter networks for which bond graphs deliver an adequate representation. Additionally, Minty networks are discussed briefly as a generalization of Kirchhoff networks. They are based on oriented graphoids instead of oriented graphs. Keywords. networks, multipoles, multiports, graphs, graphoids.