  The uncertainty principle states that a signal cannot be localized both in
time and frequency. With the aim of extending this result to signals on graphs,
Agaskar&Lu introduce notions of graph and spectral spreads. They show that a
graph uncertainty principle holds for some families of unweighted graphs. This
principle states that a signal cannot be simultaneously localized both in graph
and spectral domains. In this paper, we aim to extend their work to weighted
graphs. We show that a naive extension of their definitions leads to
inconsistent results such as discontinuity of the graph spread when regarded as
a function of the graph structure. To circumvent this problem, we propose
another definition of graph spread that relies on an inverse similarity matrix.
We also discuss the choice of the distance function that appears in this
definition. Finally, we compute and plot uncertainty curves for families of
weighted graphs.
