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 this paper. Other papers simply refer to a symmetrized transmission matrix, see for example here.

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 this paper. Other papers simply call $R$ the symmetrized transition matrix, see for example here.