  A Random Geometric Graph (RGG) ensemble is defined by the disordered
distribution of its node locations. We investigate how this randomness drives
sample-to-sample fluctuations in the dynamical properties of these graphs. We
study the distributional properties of the algebraic connectivity which is
informative of diffusion and synchronization timescales in graphs. We use
numerical simulations to provide the first characterisation of the algebraic
connectivity distribution for RGG ensembles. We find that the algebraic
connectivity can show fluctuations relative to its mean on the order of $30
\%$, even for relatively large RGG ensembles ($N=10^5$). We explore the factors
driving these fluctuations for RGG ensembles with different choices of
dimensionality, boundary conditions and node distributions. Within a given
ensemble, the algebraic connectivity can covary with the minimum degree and can
also be affected by the presence of density inhomogeneities in the nodal
distribution. We also derive a closed-form expression for the expected
algebraic connectivity for RGGs with periodic boundary conditions for general
dimension.
