Network Complexity Measures. an Information-theoretic Approach

Quantitative graph analysis by using structural indices has been intricate in a sense that it often remains unclear which structural graph measures is the most suitable one, see [1, 12, 13]. In general, quantitative graph analysis deals with quantifying structural information of networks by using a measurement approach [5]. As special problem thereof is to characterize a graph quantitatively, that means to determine a measure that captures structural features of a network meaningfully. Various classical structural graph measures have been used to tackle this problem [13]. A fruitful approach by using information-theoretic [21] and statistical methods is to quantify the structural information content of a graph [1, 8, 18]. In this note, we sketch some classical information measures. Also, we briefly address the problem what kind of measures capture structural information uniquely. This relates to determine the discrimination power (or also called uniqueness) of a graph measure, that is, how is the ability of the measures to discriminate non-isomorphic graphs structurally.