Network Effects — Metcalfe's Law

Description

Demonstrates network effects by visually building a graph of nodes and edges as users are added one by one. Shows that connections grow quadratically as n(n-1)/2, contrasting linear cost of new users with the quadratic growth in network value (Metcalfe's Law: V ∝ n²). Includes real-world examples like telephone networks and social media.

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Phases

#	Phase Name	Duration	Description
1	Title	3s	Show title and brief hook about network effects
2	Node Addition	14s	Add nodes 1 through 8 one at a time, drawing all new edges on each addition
3	Connection Count	5s	Display n(n-1)/2 formula and running count of connections
4	Metcalfe's Law	5s	Show V ∝ n² MathTex and highlight the quadratic growth
5	Cost vs Value Chart	10s	Axes showing linear cost line vs quadratic value curve
6	Real Examples	8s	Show telephone, social media examples — first user has no value, millions = huge value

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Layout

+-----------------------------------------------+
|          Network Effects — Metcalfe's Law      |
|                                                |
|    (1)      (1)-(2)   (1)-(2)                 |
|                         |  \ |                 |
|                        (3)-(4)  ...            |
|                                                |
|  Connections: n(n-1)/2                        |
|  n=1: 0    n=2: 1    n=4: 6    n=8: 28        |
|                                                |
|  Value ^       ___/ V ∝ n²                    |
|   Cost |  ____/  — cost                       |
|        +-----------> n (users)                |
|                                                |
|  V ∝ n²   (Metcalfe's Law)                   |
+-----------------------------------------------+

Area Descriptions

• Top: Title
• Center: Growing network graph animation
• Lower-left: Connection count tracker
• Lower-right: Cost vs Value axes chart

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• Nodes: gold circles with number labels
• Edges: thin blue lines, each new batch appears simultaneously
• Connection count updates as integer counter below the graph
• Background: dark navy #1a1a2e