Flow-Graph Solutions of Linear Algebraic Equations

On the Use of Graph Theory for Railway Power Supply Systems Characterization

“…It can be observed that the edge representing the adjacency (6,7), is e 19 in both cases. Furthermore, the adjacencies appearing in both cases ((1, 5), (3,5) and (2, 7)) are represented by the same edges (e 4 , e 13 and e 11 ). Table 4 shows the "active" and "non active" edges at each instant and Fig.…”

“…The bulk of these improvements took place in the decades of 1950's and 1960's, when the classical topological formulas were modified to fit passive networks containing mutual couplings and active networks. For example, methods for solving a system of indefinite linear algebraic equations by applying a directed weighted graph, known as a signal-flow graph, were proposed in [7,12,13,16,18,23]. Successive efforts were done to develop the graph description by means of matrix techniques [4,31].…”

Circuit complexity reduction for symbolic analysis of analog integrated circuits

“…with G x D g n2b nout g oM2b g n4b C g n4b nout g oM4b g n2b g n2b nout g n4b (12) In equation (12) we can clearly find as summing terms the parallel action of the two cascode loops. The second graph indicates the elements that determine the first non dominant pole/zero pair.…”

“…The transformation of a linearized electrical network model in a (connected, directed) signal flow graph can be performed in numerous ways [11], [12]. The key decision to be made is the set of vertices and thus the signal entities to build the graph on.…”

“…As a final step the graph still needs some rearrangement in order to ensure validity and avoid redundancy, but we won't discuss this in detail here. The signal flow graph defined that way is closely related to the Coates flow graph built on the modified nodal admittance matrix [12]. This type of graph closely resembles a designer's way of thinking, for it clearly indicates where voltages generate currents and vice versa.…”