Cheeger inequalities for unbounded graph Laplacians
  We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded. 
Frank Bauer, Matthias Keller, Rados{\l}aw K. Wojciechowski
math.SP math.CO math.DG