  We present a new metric of link cohesion for measuring the strength of edges
in complex, highly connected graphs. Link cohesion accounts for local small hop
connections and associated node degrees and can be used to support edge scoring
and graph simplification. We also present a novel graph density measure to
estimate the average cohesion across nodes. Link cohesion and the density
measure are employed to demonstrate community detection through graph
sparsification by maximizing graph density. Link cohesion is also shown to be
loosely correlated with edge betweenness centrality.
