If $P$ is the Markov transition matrix of a graph, the matrix $A=P\pi^{-1}$ is called the affinity matrix and $R=\pi^{1/2}A\pi^{1/2}=\pi^{1/2}P\pi^{-1/2}$ is called the *normalized affinity matrix*, see for example section 3 of <A HREF="http://papers.nips.cc/paper/2665-hierarchical-eigensolver-for-transition-matrices-in-spectral-methods.pdf">this paper.</A> Other papers simply call $R$ the symmetrized transition matrix, see for example <A HREF="http://arxiv.org/abs/1511.08100">here.</A>