Measures of Network Structure

Networked systems, natural or designed, have always been part of life. Their sophistication degree and complexity have increased through either natural evolution or technological progress. However, recent theoretical results have shown that a previously unexpected number of different classes of networks share similar network architectures and universal laws. Examples of such networks include metabolic pathways and ecosystems, the Internet and the World Wide Web, and organizational, social, and neural networks. Complex systems-related research questions investigated by researchers nowadays include: how consciousness arises out of the interactions of the neurons in the brain and between the brain and the environment (Amaral & Ottino, 2004; Barabási, 2005; Barabási & Oltvai, 2004; Neuman, 2003b) and how this understanding could be used for designing networked organizations or production networks whose behavior satisfies a given specification. The aim of this article is to review the main measures of network structure and their applicability and to discuss future trends on this topic. The article is structured as follows. The Background section gives background information on networks. The Properties, Topologies, and Measures of Networks Structure section reviews the main properties and measures of network structure, mainly for graphbased representations of networks. It also includes several representative examples of networks. Next, the Discussion section briefly reviews the measures and their applicability, and the last section concludes the article.