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Expander graphs 1 introduction expander graphs are sparse yet highly connected graphs Lecture notes on expansion, sparsest cut, and spectral graph theory luca trevisan university of california, berkeley That is, for every subset s of vertices of the graph, there are a lot of edges leaving s
Definitions of expansion, expander mixing lemma kiseki no sedai • 250 views • 1 year ago We will also briefly discuss (without much detail) how these notions are connected to each other. Since expander graphs are meant to mimic the connectivity properties of the complete graph, let’s start by making sure the complete graph itself is very strong expander.
In particular, this implies that not only is the diameter of an expander o(log n), but that after o(log n) random steps, the distribution of a random walk that began at any particular vertex is must have probability of roughly 1=n of being at any vertex.
Now comes the most important de nition of these lectures, that of expander graphs This encapsulate the idea of graphs which are both relatively sparse and highly, and robustly, connected. We will look at 3 types of expansions, namely edge, vertex and spectral expansion, which help to formally define the notion of connectivity
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