  Recently, the first author proposed a measure to calculate Pearson
correlations for node values expressed in a network, by taking into account
distances or metrics defined on the network. In this technical note, we show
that using an arbitrary choice of distances might result in imaginary or
unbounded correlation values, which is undesired. We prove that this problem is
solved by restricting to a special class of distances: negative type metrics.
We also discuss two natural classes of negative type metrics on graphs, for
which the network correlations are properly defined.
