Flow graph (mathematics)
A flow graph is a form of digraph associated with a set of linear algebraic or differential equations:[1][2]
- "A signal flow graph is a network of nodes (or points) interconnected by directed branches, representing a set of linear algebraic equations. The nodes in a flow graph are used to represent the variables, or parameters, and the connecting branches represent the coefficients relating these variables to one another. The flow graph is associated with a number of simple rules which enable every possible solution [related to the equations] to be obtained."[1]
Although this definition uses the terms "signal flow graph" and "flow graph" interchangeably, the term "signal flow graph" is most ofter used to designate the Mason signal-flow graph, Mason being the originator of this terminology.[3][4] Likewise, some authors use the term "flow graph" to refer strictly to the Coates flow graph.[5][6] According to Henley & Williams:[7]
- "The nomenclature is far from standardized, and...no standardization can be expected in the foreseeable future."
A designation "flow graph" that includes both the Mason graph and the Coates graph, and a variety of other forms of such graphs[8] appears useful, and agrees with Abrahams and Coverley's and with Henley and Williams' approach.[1][2]
A directed network is a particular type of flow graph. A network is a graph with real numbers associated with each of its edges, and if the graph is a digraph, the result is a directed network.[9] A flow graph is more general in that the edges may be associated with gains, branch gains or transmittances, or even functions of the Laplace operator s, in which case they are called transfer functions.[2]
See also
References
- ^ a b c J. R. Abrahams, G. P. Coverley (2014). "Chapter 1: Elements of a flow graph". Signal flow analysis. Elsevier. p. 1. ISBN 9781483180700.
- ^ a b c Ernest J Henley, RA Williams (1973). "Basic concepts". Graph theory in modern engineering; computer aided design, control, optimization, reliability analysis. Academic Press. p. 2. ISBN 9780080956077.
- ^ Mason, Samuel J. (September 1953). "Feedback Theory - Some Properties of Signal Flow Graphs" (PDF). Proceedings of the IRE: 1144–1156.
- ^ SJ Mason (July 1956). "Feedback Theory-Further Properties of Signal Flow Graphs". Proceedings of the IRE. 44 (7): 920–926. doi:10.1109/JRPROC.1956.275147. On-line version found at MIT Research Laboratory of Electronics.
- ^ Wai-Kai Chen (May 1964). "Some applications of linear graphs" (PDF). Coordinated Science Laboratory, University of Illinois, Urbana.
- ^
RF Hoskins (2014). "Flow-graph and signal flow-graph analysis of linear systems". In SR Deards, ed (ed.). Recent Developments in Network Theory: Proceedings of the Symposium Held at the College of Aeronautics, Cranfield, September 1961. Elsevier. ISBN 9781483223568.
{{cite book}}:|editor=has generic name (help) - ^ Ernest J Henley, RA Williams (1973). "Basic concepts". Graph theory in modern engineering; computer aided design, control, optimization, reliability analysis. Academic Press. p. 2. ISBN 9780080956077.
- ^ Kazuo Murota (2009). Matrices and Matroids for Systems Analysis. Springer Science & Business Media. p. 47. ISBN 9783642039942.
- ^ Gary Chartrand (2012). Introductory Graph Theory (Republication of Graphs as Mathematical Models, 1977 ed.). Courier Corporation. p. 19. ISBN 9780486134949.
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