On network models and the symbolic solution of network equations

This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development in this area of work. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified such as to obtain an admittance representation for all kinds of multi-ports. N -dimensional networks are defined as graphs with the algebraic structure of N -dimensional vectors. In civil engineering, framed structures in two and three spatial dimensions may be modelled as 3-dimensional or 6dimensional networks. The separation of geometry from topology is a characteristic feature of such networks. Finally, extensions of the network concept are discussed which arise when the network graph is replaced by a 3-dimensional complex in the sense of algebraic topology.

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