Editing Spectral graph theory (section)

===Cheeger constant===
{{main|Cheeger constant (graph theory)}}
The '''Cheeger constant''' (also '''Cheeger number''' or '''isoperimetric number''') of a [[Graph (discrete mathematics)|graph]] is a numerical measure of whether or not a graph has a "bottleneck". The Cheeger constant as a measure of "bottleneckedness" is of great interest in many areas: for example, constructing well-connected [[Computer networking|networks of computers]], [[Shuffling|card shuffling]], and [[Geometric topology|low-dimensional topology]] (in particular, the study of [[Hyperbolic geometry|hyperbolic]] 3-[[manifold]]s).

More formally, the Cheeger constant ''h''(''G'') of a graph ''G'' on ''n'' vertices is defined as
: <math>h(G) = \min_{0 < |S| \le \frac{n}{2} } \frac{|\partial(S)|}{|S|},</math>
where the minimum is over all nonempty sets ''S'' of at most ''n''/2 vertices and ∂(''S'') is the ''edge boundary'' of ''S'', i.e., the set of edges with exactly one endpoint in ''S''.<ref>Definition 2.1 in {{harvtxt|Hoory|Linial|Wigderson|2006}}</ref>