AnimG 标志AnimG

Network Effects — Metcalfe's Law

受众: University类别: Economics

简介

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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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.

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

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

Assets & Dependencies

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

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