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A signal-flow graph or signal-flowgraph (SFG), invented by Shannon,〔 but often called a Mason graph after Samuel Jefferson Mason who coined the term,〔 is a specialized flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes. Thus, signal-flow graph theory builds on that of directed graphs (also called digraphs), which includes as well that of oriented graphs. This mathematical theory of digraphs exists, of course, quite apart from its applications.〔 〕〔 i 〕 SFG's are most commonly used to represent signal flow in a physical system and its controller(s), forming a cyber-physical system. Among their other uses are the representation of signal flow in various electronic networks and amplifiers, digital filters, state variable filters and some other types of analog filters. In nearly all literature, a signal-flow graph is associated with a set of linear equations. == History == Wai-Kai Chen wrote: "The concept of a signal-flow graph was originally worked out by Shannon () 〔 Reprinted in 〕 in dealing with analog computers. The greatest credit for the formulation of signal-flow graphs is normally extended to Mason (),〔 〕 ().〔 On-line version found at (MIT Research Laboratory of Electronics ). 〕 He showed how to use the signal-flow graph technique to solve some difficult electronic problems in a relatively simple manner. The term signal flow graph was used because of its original application to electronic problems and the association with electronic signals and flowcharts of the systems under study." Lorens wrote: "Previous to Mason's work, C. E. Shannon〔 worked out a number of the properties of what are now known as flow graphs. Unfortunately, the paper originally had a restricted classification and very few people had access to the material."〔 〕 "The rules for the evaluation of the graph determinant of a Mason Graph were first given and proven by Shannon () using mathematical induction. His work remained essentially unknown even after Mason published his classical work in 1953. Three years later, Mason () rediscovered the rules and proved them by considering the value of a determinant and how it changes as variables are added to the graph. ()" 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Signal-flow graph」の詳細全文を読む スポンサード リンク
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