  Potential energy landscapes can be represented as a network of minima linked
by transition states. The community structure of such networks has been
obtained for a series of small Lennard-Jones clusters. This community structure
is compared to the concept of funnels in the potential energy landscape. Two
existing algorithms have been used to find community structure, one involving
removing edges with high betweenness, the other involving optimization of the
modularity. The definition of the modularity has been refined, making it more
appropriate for networks such as these where multiple edges and
self-connections are not included. The optimization algorithm has also been
improved, using Monte Carlo methods with simulated annealing and basin hopping,
both often used successfully in other optimization problems. In addition to the
small clusters, two examples with known heterogeneous landscapes, LJ_13 with
one labelled atom and LJ_38, were studied with this approach. The network
methods found communities that are comparable to those expected from landscape
analyses. This is particularly interesting since the network model does not
take any barrier heights or energies of minima into account. For comparison,
the network associated with a two-dimensional hexagonal lattice is also studied
and is found to have high modularity, thus raising some questions about the
interpretation of the community structure associated with such partitions.
