  Network (or graph) sparsification compresses a graph by removing inessential
edges. By reducing the data volume, it accelerates or even facilitates many
downstream analyses. Still, the accuracy of many sparsification methods, with
filtering-based edge sampling being the most typical one, heavily relies on an
appropriate definition of edge importance. Instead, we propose a different
perspective with a generalized local-property-based sampling method, which
preserves (scaled) local \emph{node} characteristics. Apart from degrees, these
local node characteristics we use are the expected (scaled) number of wedges
and triangles a node belongs to. Through such a preservation, main complex
structural properties are preserved implicitly. We adapt a game-theoretic
framework from uncertain graph sampling by including a threshold for faster
convergence (at least $4$ times faster empirically) to approximate solutions.
Extensive experimental studies on functional climate networks show the
effectiveness of this method in preserving macroscopic to mesoscopic and
microscopic network structural properties.
