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.

中文翻译：

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加权网络的稀疏性：措施和应用

大多数现实生活中的网络都是加权和稀疏的。本文旨在表征基于稀疏性的加权网络，作为不同网络参数的固有多样性的度量。它利用定义在简单网络的有序度序列上的稀疏指数并推导出该指数的进一步属性。任何连接网络的稀疏指数的可能值范围，在特定区间的边数，是根据节点数解析得出的；在相应的度序列中发现一种模式以产生最高的稀疏性。给定网络的边缘权重频率分布，我们制定了边缘权重稀疏指数的表达式。在不同的边权重分布下分析其属性。例如，具有所有不同边权重的网络的边权重稀疏指数的上限和下限是根据其节点数和边密度确定的。这篇文章强调，这个在不同网络参数上计算的具有低计算成本的汇总指数对于揭示网络的不同结构和组织方面进行分析很有用。已经通过网络的重叠社区检测证明了该指数的应用。在人工和现实世界网络上验证的结果显示了其有效性。有助于揭示网络的不同结构和组织方面以进行分析。已经通过网络的重叠社区检测证明了该指数的应用。在人工和现实世界网络上验证的结果显示了其有效性。有助于揭示网络的不同结构和组织方面以进行分析。已经通过网络的重叠社区检测证明了该指数的应用。在人工和现实世界网络上验证的结果显示了其有效性。