~/tedtes/writing/math-foundations-for-reasoning-models

~/writing/math-foundations-for-reasoning-models $ ls

Graphs and Computation

Data Flow Graph

A data flow graph shows how data moves from one step to another.

~/writing/math-foundations-for-reasoning-models $ cat topic.md

Data Flow Graph

Definition

A data flow graph shows how data moves through a system.

Nodes represent steps, values, or storage locations.

Edges represent data moving between them.

Example:

Input -> Clean -> Transform -> Output

Data flow graph = graph of where data comes from and where it goes.


Simple Example

Suppose a process does this:

number -> add 1 -> multiply by 2 -> result

As a data flow graph:

Input -> Add 1 -> Multiply by 2 -> Result

The output of one step becomes the input to the next step.

Data flow makes step-to-step dependency visible.


Nodes As Operations

In many data flow graphs, nodes are operations.

Example:

Read file -> Parse text -> Count words -> Print result

Each node performs a step.

Each edge carries the data needed by the next step.

Operation nodes show what happens to data.


Nodes As Values

Sometimes nodes can represent values instead.

Example:

x -> x + 1 -> (x + 1) * 2

Here each node can be read as a value produced during the process.

The graph still shows how one value leads to another.

Data flow can be represented using operation nodes or value nodes.


Branching Data Flow

Data can move to more than one later step.

Example:

Input -> Cleaned Data
Cleaned Data -> Summary
Cleaned Data -> Chart

The same intermediate data supports multiple outputs.

Data flow graphs can branch when one result is reused.


Final Summary

  • A data flow graph shows how data moves through a system.
  • Nodes can represent operations, values, or storage locations.
  • Edges represent data movement.
  • The output of one step can become the input to another.
  • Data flow can branch when one result supports multiple later steps.

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Continue the series.

Computation Graph