Measures of Network Structure

Measures of Network Structure

Ani Calinescu, Janet Efstathiou
Copyright: © 2008 |Pages: 7
DOI: 10.4018/978-1-59904-885-7.ch122
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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.

Key Terms in this Chapter

Network: A system which has a large number of components capable of interacting with each other and with the environment, and which may act according to rules change over time and may not be well understood by an external observer.

Degree Distribution: A distribution function P(k) that characterizes the spread in the node degree and gives the probability that a randomly selected node has exactly k edges.

Scale-Free Network: A network that contains hubs, that is, vertices which have a seemingly unlimited number of links and in which no vertex is typical of the others. Scale-free networks are remarkably resistant to accidental failures but extremely vulnerable to coordinated attacks. The scale-free model assumes that the network grows continuously by adding new vertices. New vertices would connect with higher probability to higher connected vertices, a phenomenon called preferential attachment.

Self-Organization: The components of a system make local decisions that have a coherent, organizing impact on the system as a whole. Therefore, the system displays organization without any external organizing principle being applied.

Clustering Coefficient: The clustering coefficient Ci for a vertex vi is the proportion of edges between the vertices within its neighborhood divided by the number of edges that could possibly exist between them.

Complex Systems: Network-based systems characterized by feedback-driven flow of information, openness, self-organization, and emergence.

Random Network: A network in which the probability that two vertices are connected is random and uniform.

Emergence: The process of complex pattern formation from simpler rules; emergent properties are neither properties had by any parts of the system taken in isolation nor a resultant of a mere summation of properties of parts of the system.

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