  The task of semi-supervised classification aims at assigning labels to all
nodes of a graph based on the labels known for a few nodes, called the seeds.
One of the most popular algorithms relies on the principle of heat diffusion,
where the labels of the seeds are spread by thermoconductance and the
temperature of each node at equilibrium is used as a score function for each
label. In this paper, we prove that this algorithm is not consistent unless the
temperatures of the nodes at equilibrium are centered before scoring. This
crucial step does not only make the algorithm provably consistent on a block
model but brings significant performance gains on real graphs.
