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  "body": "\n## Summary\n\nAn expander graph is a sparse graph in which every set of at most half of the vertices has many edges leaving it.\nOne usually means a family of [[regular graphs|0KA4S8R39M]] of fixed degree whose [[Cheeger constant|Y7S6W12N64]] stays above a fixed positive bound.\nExpanders combine few edges with strong connectivity, and they are used in network design, error-correcting codes, derandomization and group theory.\n\n## Explanations\n\n### L1 human\n\nPicture a network of computers in which each machine has only three cables.\nIn a good expander, any group of up to half the machines is joined to the rest by many cables, in proportion to the size of the group.\nSo the network has no bottleneck, although it is cheap to build.\nA long cycle is the opposite: half of the cycle is cut off from the other half by just $2$ edges.\n",
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