mathematics

Network Science

The hidden structure connecting everything — from the Internet to epidemics, social networks to neural circuits.

networksgraph theoryscale-freesmall worldepidemicspercolation

Network science studies the structure and dynamics of complex systems made of interconnected components. Born from graph theory (Euler, 1736) and transformed by the discoveries of small-world networks (Watts & Strogatz, 1998) and scale-free networks (Barabási & Albert, 1999), it has become essential to understanding the modern world.

Networks are everywhere: the Internet, social media, protein interactions in cells, neural circuits in the brain, airline routes, power grids, and the spread of diseases. These systems share surprising universal properties — the small-world effect (six degrees of separation), the scale-free property (a few hubs with enormous numbers of connections), and phase transitions (sudden emergence of connectivity at critical thresholds).

These simulations let you build and analyze networks, spread epidemics through populations, discover the small-world effect, and watch phase transitions emerge in percolation. Understanding network structure is key to understanding resilience, vulnerability, and the dynamics of complex systems.

5 interactive simulations

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SIR Epidemic Spreading Model

Interactive SIR compartmental model showing how infectious diseases spread through populations, with vaccination and herd immunity dynamics

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Percolation Threshold Simulator

Interactive site percolation on a 2D square lattice demonstrating the critical phase transition at p_c where a giant connected cluster suddenly emerges

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Power-Law Distribution Explorer

Interactive exploration of power-law distributions and Zipf's law across city sizes, word frequencies, wealth distribution, and earthquake magnitudes

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Scale-Free Networks Simulator

Interactive Barabasi-Albert preferential attachment model showing how hub-dominated scale-free networks emerge and respond to targeted vs random attacks

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Small-World Network Model

Interactive Watts-Strogatz model demonstrating how a small amount of random rewiring creates the 'small-world' phenomenon with short paths and high clustering