# Signal-flow graph
## MicroSim spec
### Parameters (tunable controls)
- `Branch gain a` · -2–2 · gain on the forward edge between two nodes
- `Feedback gain b` · -2–2 · gain on the loop edge (sets loop behaviour)
- `Input x` · -10–10 · source-node value propagated through the graph
### What animates
Tokens flow along directed branches; node values update to show the propagated [[Signal|signal]].
### Learning objective
Show how branch and loop gains in a signal-flow graph determine the input-output transfer.
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Signal-flow_graph.json (2026-07-30T02:09:12Z) -->
`Adaptive_control` · `Arthur_Guyton` · `Asymptotic_gain_model` · `Automation_and_Remote_Control` · `Biophysics` · [[Block_diagram]] · `Bode_plot` · [[Claude_Shannon]] · `Closed-loop_controller` · `Closed-loop_transfer_function` · `Coates_graph` · `Coefficient_diagram_method` · `Combinatorics` · `Computer_algebra_system` · `Control_reconfiguration` · [[Control_theory]] · `Controllability` · `Cyber-physical_system` · `Digital_control` · `Digital_filter` · [[Digital_signal_processing]] · `Directed_graph` · `Distributed_control_system` · `Distributed_parameter_system` · [[Electric_motor]] · `Elsevier` · `Embedded_system` · `Energy-shaping_control` · [[Feedback]] · `Flow_graph_(mathematics)` · `Fourier_transform` · `Fractional-order_control` · [[Frequency_response]] · [[Fuzzy_control_system]] · `Fuzzy_logic` · `Gaussian_elimination` · [[Graph_theory]] · `H-infinity_loop-shaping` · `Hankel_singular_value` · `Henry_Paynter` · `Hybrid_computer` · `Industrial_control_system` · `Intelligent_control` · [[Kalman_filter]] · `Krener's_theorem` · `Kronecker_delta` · [[Laplace_transform]] · `Lead–lag_compensator` · `Least_squares` · `Linear_differential_equation` · [[Linear_time-invariant_system]] · [[Lyapunov_stability]] · `Mason's_gain_formula` · `Mathematical_induction` · [[Mechatronics]] · `Minor_loop_feedback` · [[Model_predictive_control]] · `Motion_control` · [[Negative_feedback]] · [[Neuroscience]] · `Nonlinear_control` · [[Observability]] · [[Optimal_control]] · `Orientation_(graph_theory)` · [[PID_controller]] · [[Perceptual_control_theory]] · `Performance` · `Physiology` · [[Positive_feedback]] · `Programmable_logic_controller` · [[Quantization_(signal_processing)]] · [[Real-time_computing]] · `Real_number` · `Regular_polygon` · `Return_ratio` · [[Robotics]] · `Robust_control` · `Root_locus_analysis` · `SCADA` · `Servomechanism` · `Simulation` · `Stability_theory` · `State-space_representation` · `State_diagram` · `State_observer` · `Steady_state` · `Stochastic_control` · [[System_dynamics]] · [[System_identification]] · `System_of_equations` · `System_of_linear_equations` · `Topology` · [[Transfer_function]] · `Two-port_network` · `Wikibooks` · [[Z-transform]]
## From the Real GENERATIVE library
*Signal-flow graph — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Engineering room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Flow_graphs.svg).*
> A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon,[1] but often called a Mason graph after Samuel Jefferson Mason who coined the term,[2] 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-f ([Wikipedia](https://en.wikipedia.org/wiki/Signal-flow_graph))
<!-- REAL-GENERATIVE-MEDIA:END -->
> p5.js MicroSim stub · part of Systems Engineering · [Wikipedia source](https://en.wikipedia.org/wiki/Signal-flow_graph)
## Concept summary
A signal-flow graph is a directed graph whose nodes are variables and whose edges carry gains; Mason's rule reads the overall transfer from it.
## Build checklist
- [ ] Claim it: set `status: in-progress` + `lease` + `leased_at`
- [ ] Write the child page explaining the concept (tie it back to Systems Engineering)
- [ ] Finalize parameter ranges and defaults
- [ ] Implement the p5.js sketch (drawing + control regions)
- [ ] Add caption + the learning objective on the page
- [ ] Set `status: done`
## p5.js sketch
```javascript
// MicroSim: Signal-flow graph
const ARTICLE = "Signal-flow_graph";
let p1, p2, p3;
function setup() {
createCanvas(720, 520);
pixelDensity(2);
// block-diagram sim — create the three sliders described above:
// Branch gain a (-2–2), Feedback gain b (-2–2), Input x (-10–10).
// TODO: build labelled sliders in the control region (below the drawing region).
}
function draw() {
background(248);
// TODO: read p1/p2/p3; render the block-diagram in the drawing region and respond live.
// TODO: HUD — title + en.wikitube.io/wiki/Signal-flow_graph + control hints + live readouts.
}
```
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Back to Systems Engineering
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## Semiotic profile
> *The semiotic universals this article invokes, machine-derived from the crossref — **unverified** (born so). Populated 2026-07-06 for the Systems room.*
**Universals (4):** 🟢 signal (10) · 🟢 flow (5) · 🟡 system (4) · 🟢 feedback (2)
**Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal
<!-- SEMIOTIC-PROFILE:END -->
<!-- REAL-GENERATIVE-MEDIA:START -->
## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Signal-flow_graph) : [Wikitube](https://en.wikitube.io/wiki/Signal-flow_graph)
## Previous hub tags
Tree parents: [[Control_theory]] · [[Systems_engineering]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*