  Sparsification reduces the size of networks while preserving structural and
statistical properties of interest. Various sparsifying algorithms have been
proposed in different contexts. We contribute the first systematic conceptual
and experimental comparison of \textit{edge sparsification} methods on a
diverse set of network properties. It is shown that they can be understood as
methods for rating edges by importance and then filtering globally or locally
by these scores. We show that applying a local filtering technique improves the
preservation of all kinds of properties. In addition, we propose a new
sparsification method (\textit{Local Degree}) which preserves edges leading to
local hub nodes. All methods are evaluated on a set of social networks from
Facebook, Google+, Twitter and LiveJournal with respect to network properties
including diameter, connected components, community structure, multiple node
centrality measures and the behavior of epidemic simulations. In order to
assess the preservation of the community structure, we also include experiments
on synthetically generated networks with ground truth communities. Experiments
with our implementations of the sparsification methods (included in the
open-source network analysis tool suite NetworKit) show that many network
properties can be preserved down to about 20\% of the original set of edges for
sparse graphs with a reasonable density. The experimental results allow us to
differentiate the behavior of different methods and show which method is
suitable with respect to which property. While our Local Degree method is best
for preserving connectivity and short distances, other newly introduced local
variants are best for preserving the community structure.
