Flow Graph (other)
Flow graph may refer to: * Flow or rooted graph (graph theory), a graph in which a vertex has been distinguished as the root * Control-flow graph (computer science), a representation of paths through a program during its execution * Flow graph (mathematics), a directed graph linked to a set of linear algebraic or differential equations * Flow network, a directed graph where each edge has a capacity and receives a flow * Signal-flow graph, a directed graph with nodes as system variables and branches as node connections See also * Flow diagram, a diagram representing a flow or set of dynamic relationships in a system * Flowchart A flowchart is a type of diagram that represents a workflow or process. A flowchart can also be defined as a diagrammatic representation of an algorithm, a step-by-step approach to solving a task. The flowchart shows the steps as boxes of va ...

Rooted Graph
In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots. Rooted graphs may also be known (depending on their application) as pointed graphs or flow graphs. In some of the applications of these graphs, there is an additional requirement that the whole graph be reachable from the root vertex. Variations In topological graph theory, the notion of a rooted graph may be extended to consider multiple vertices or multiple edges as roots. The former are sometimes called vertex-rooted graphs in order to distinguish them from edge-rooted graphs in this context. Graphs with multiple nodes designated as roots are also of some interest in combinatorics, in the area of random graphs. These graphs are also called multiply rooted graphs. The terms rooted directed graph or rooted d ...
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Control-flow Graph
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a program during its execution. The control-flow graph was discovered by Frances E. Allen, who noted that Reese T. Prosser used boolean connectivity matrices for flow analysis before. The CFG is essential to many compiler optimizations and static-analysis tools. Definition In a control-flow graph each node in the graph represents a basic block, i.e. a straight-line piece of code without any jumps or jump targets; jump targets start a block, and jumps end a block. Directed edges are used to represent jumps in the control flow. There are, in most presentations, two specially designated blocks: the ''entry block'', through which control enters into the flow graph, and the ''exit block'', through which all control flow leaves. Because of its construction procedure, in a CFG, every edge A→B has the property that: : outdegree(A) > 1 or inde ...
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Flow Graph (mathematics)
A flow graph is a form of digraph associated with a set of linear algebraic or differential equations: :"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 elated to the equationsto be obtained." Although this definition uses the terms "signal-flow graph" and "flow graph" interchangeably, the term "signal-flow graph" is most often used to designate the Mason signal-flow graph, Mason being the originator of this terminology in his work on electrical networks. Likewise, some authors use the term "flow graph" to refer strictly to the Coates flow graph. According to Henley & Williams: :"The nomenclature is far from standardized, ...
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Flow Network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. Definition A network is a graph , where is a set of vertices and is a set of 's edges – a subset of – together with a non-negative function , called the capacity function. Without loss of generality, we may assume that ...
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Signal-flow Graph
A signal-flow graph or signal-flowgraph (SFG), invented by Claude 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 SFGs 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. Histo ...
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Flow Diagram
Flow diagram is a collective term for a diagram representing a flow or set of dynamic relationships in a system. The term flow diagram is also used as a synonym for flowchart, and sometimes as a counterpart of the flowchart.Harris. (1999, p. 156) Flow diagrams are used to structure and order a complex system, or to reveal the underlying structure of the elements and their interaction. Overview The term flow diagram is used in theory and practice in different meanings. Most commonly the flow chart and flow diagram are used in an interchangeable way in the meaning of a representation of a process. For example the ''Information Graphics: A Comprehensive Illustrated Reference'' by Harris (1999) gives two separate definitions: :''Flow chart or flow diagram... is a diagram that visually displays interrelated information such as events, steps in a process, functions, etc., in an organized fashion, such as sequentially or chronologically.'' :''Flow diagram sa graphic representa ...
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