Fragile by Design
How topology shapes resilience, epidemics, and information flow
Not all networks fail the same way. A random network degrades gracefully under attack. A scale-free network - the topology of the internet, airline routes, and social graphs - can survive random failures but collapses catastrophically when its hubs are targeted. These interactive experiments make the mathematics of connection tangible.
Three canonical network topologies with identical node counts, coloured by degree.
80 nodes each. Node size and colour indicate degree (number of connections). Scale-free networks show the characteristic power-law distribution with highly connected hubs.
Random failure removes nodes at random. Scale-free networks survive well because most nodes are peripheral - hubs are unlikely to be hit.
Seed an infection, then run the simulation. Scale-free networks spread faster initially because hubs act as superspreaders. Small-world networks show wave-like propagation through clusters.
The Challenge
Networks are everywhere - social connections, infrastructure grids, biological pathways, the internet. But not all networks are the same. Some are resilient to random failures but collapse when targeted. Others spread information slowly but contain outbreaks. Understanding why requires understanding topology - the shape of connection itself. For Mxwll, we built interactive tools to make these abstract properties tangible.
Background
Three network types dominate the research literature, each with distinct properties:
Random networks (Erdos-Renyi) connect nodes with uniform probability. Degree distribution is narrow - most nodes have similar numbers of connections. Robust to any single failure, but no node is particularly important.
Scale-free networks (Barabasi-Albert) grow through preferential attachment - new nodes connect to already-popular nodes. This creates hubs with many connections and a long tail of peripheral nodes. The degree distribution follows a power law. Hubs make the network efficient but create critical vulnerabilities.
Small-world networks (Watts-Strogatz) combine local clustering with occasional long-range shortcuts. Most connections are to neighbours, but a few bridges span the network. This gives both high clustering (your friends know each other) and short path lengths (six degrees of separation).