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== <span style="color: #FFFFFF;">Applying</span> == '''Modeling 'The Six Degrees' (Path Length):''' <syntaxhighlight lang="python"> def estimate_reach(avg_connections, degrees_of_separation): """ Shows the 'Exponential' power of a network. """ return avg_connections ** degrees_of_separation # If every person knows 150 people: # 1 degree: 150 # 2 degrees: 22,500 # 3 degrees: 3,375,000 # 6 degrees: ??? total = estimate_reach(150, 6) print(f"People reached in 6 steps: {total:,}") # This is more than the population of Earth! # We are all 'neighbors'. </syntaxhighlight> ; Network Landmarks : '''The Seven Bridges of Königsberg (1736)''' → Leonhard Euler's proof that started the whole field of "Graph Theory." : '''Google PageRank''' → The algorithm that turned the internet into a searchable library by treating "Links" as "Votes." : '''The Power Grid''' → A complex network where one small error in Ohio can cause a blackout for 50 million people. : '''Neural Networks''' → The biological (brain) and artificial (AI) networks that create intelligence through the interaction of billions of neurons. </div> <div style="background-color: #8B4500; color: #FFFFFF; padding: 20px; border-radius: 8px; margin-bottom: 15px;">
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