Computation Graph

Definition

A computation graph represents a computation as connected values and operations.

It shows which results are needed to produce later results.

Example:

x -> Add 1 -> Multiply by 2 -> output

Computation graph = graph representation of calculation steps.

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Simple Example

Consider:

y = (x + 1) * 2

This can be represented as:

x -> +1 -> *2 -> y

The graph shows the order of computation:

start with x
add 1
multiply by 2
produce y

A computation graph makes the internal steps visible.

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Operation Nodes

Some computation graphs use operation nodes.

Example:

x ----\
      Add -> z
1 ----/

The Add node takes two inputs and produces one output.

Operation nodes represent rules being applied.

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Value Nodes

Some computation graphs emphasize values.

Example:

x
x + 1
(x + 1) * 2

Edges show which value is derived from which earlier value.

Value nodes represent intermediate results.

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Branching And Reuse

An intermediate result can be used more than once.

Example:

a = x + 1
b = a * 2
c = a * 3

Graph:

x -> a
a -> b
a -> c

The value a is reused by two later computations.

Computation graphs show reuse of intermediate results.

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Why Computation Graphs Matter

Computation graphs help answer:

• what depends on what?
• what must be computed first?
• which intermediate values are reused?
• where does output come from?

They turn a computation into a structure that can be inspected.

Computation graphs make dependency inside computation explicit.

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Final Summary

• A computation graph represents computation as connected values and operations.
• Edges show dependency between steps.
• Nodes can represent operations or values.
• Computation graphs show order, reuse, and intermediate results.
• They make internal computation structure visible.