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Network problems that involve finding an optimal way of doing something are studied as combinatorial optimization.Examples include network flow, shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing problem, critical path analysis, and program evaluation and review technique.
Network theory is an area of applied mathematics. This page is a list of network theory topics. Network theorems. Max flow min cut theorem; Menger's theorem;
Reciprocity of electrical networks is a special case of Lorentz reciprocity, but it can also be proven more directly from network theorems. This proof shows reciprocity for a two-node network in terms of its admittance matrix, and then shows reciprocity for a network with an arbitrary number of nodes by an induction argument .
Indeed, certain neural network families can directly apply the Kolmogorov–Arnold theorem to yield a universal approximation theorem. Robert Hecht-Nielsen showed that a three-layer neural network can approximate any continuous multivariate function. [22] This was extended to the discontinuous case by Vugar Ismailov. [23]
Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values; however, for the most part, the techniques assume linear components.
In direct-current circuit theory, Norton's theorem, also called the Mayer–Norton theorem, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel.
The network consequently must consist entirely of inductors and capacitors and the impedance will be purely an imaginary number with zero real part. Foster's theorem applies equally to the admittance of a network, that is the susceptance (imaginary part of admittance) of a passive, lossless one-port monotonically increases with frequency. This ...
In 1933, A. T. Starr published a generalization of Thévenin's theorem in an article of the magazine Institute of Electrical Engineers Journal, titled A New Theorem for Active Networks, [13] which states that any three-terminal active linear network can be substituted by three voltage sources with corresponding impedances, connected in wye or ...