Conductance (probability)

For an ergodic reversible Markov Chain with an underlying graph G, the conductance is a way to measure how hard it is to leave a small set of nodes. Writing $$\Phi_S$$ for the conditional probability of leaving a set of nodes S given that we were in that set to begin with, then the conductance is defined as the minimal $$\Phi_S$$ over sets $$S$$ that have a total stationary probability of at most 1/2. Conductance is related to Markov chain mixing time in the reversible setting.