  A majority of real life networks are weighted and sparse. The present article
aims at characterization of weighted networks based on sparsity, as a measure
of inherent diversity, of different network parameters. It utilizes sparsity
index defined on ordered degree sequence of simple networks and derives further
properties of this index. The range of possible values of sparsity index of any
connected network, with edge-count in specific intervals, is worked out
analytically in terms of node-count; a pattern is uncovered in corresponding
degree sequences to produce highest sparsities. Given the edge-weight frequency
distribution of a network, we have formulated an expression of the sparsity
index of edge-weights. Its properties are analyzed under different
distributions of edge-weights. For example, the upper and lower bounds of
sparsity index of edge-weights of a network, having all distinct edge-weights,
is determined in terms of its node-count and edge density. The article
highlights that this summary index with low computational cost, computed on
different network parameters, is useful to reveal different structural and
organizational aspects of networks for performing analysis. An application of
this index has been demonstrated through overlapping community detection of
networks. The results validated on artificial and real-world networks show its
efficacy.
