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Encyclopedia of Networked and Virtual Or... > Morphology and Entropy in Networks - Pg. 957

957 Morphology and Entropy in Networks Ton van Asseldonk TVA developments bv, The Netherlands Erik den Hartigh Delft University of Technology, The Netherlands Leon Berger Nyenrode University, The Netherlands M IntroductIon This article concerns the relation between the morphol- ogy (concentration and connectivity) and the entropy of networked structures. We will introduce the network morphology concept, we will address two approaches to network characterization--traditional network mea- sures and the concept of entropy--and we will link the entropy concept to the network characteristics. It will be shown that entropy will grow steeply if a certain balance between connectivity and concentration is disturbed. It is known from theory that the morphology of a business network, be within an organization or between organizations, greatly affects the behavior of agents in the network (Ahuja, 2000; Burt, 1992; Coleman, 1988; Gulati, 1999; Powell, Koput, & Smith-Doerr, 1996; Walker, Kogut & Shan 1997). Also it is known that the morphology of networks is an important determinant of the extent of innovation diffusion (Abrahamson & Rosenkopf, 1997; Den Hartigh, 2005). It is therefore important to explore further some basic notions of network morphology. number of connections from one node to all the oth- ers, the higher the concentration. The measurement of concentration has a relationship with the kurtosis of the distribution of connections among the various nodes. MaIn Focus oF tHe artIcle relation between connectivity and concentration We have defined a network as a structure consisting of nodes and links. Concentration and connectivity pro- vide information over the network; they have a certain relationship, as shown in Figure 1. Networks with a high connectivity and a high concentration cannot exist. This would imply that every node is connected to every other node, but still nodes exist that have more connec- tions than others. The same reasoning can be done for medium concentration/high connectivity and medium connectivity/high concentration networks. They also cannot exist. Obviously, the border areas between high, medium, and low are somewhat fuzzy. Let us relate these abstract network measures to economic networks, such as business organizations. The morphology concept can be applied to social systems by analyzing the links between social entities. Different configurations yield different levels of order/disorder. In this way, order in social systems can be seen as an expression of the existence of meaningful and purpose- ful relationships between functional elements of such a system. Without such relationships, the whole of the system can have no meaning or purpose. In such cases, the whole is identical to the sum of parts and no synergy or common purpose can exist. The principles of order through fluctuations were first formulated in thermodynamics. The central idea is that self-organiz- Background Every network has a morphology. Morphology is defined as the form and structure of a network. The morphology of a network can be described by two separate elements: connectivity and concentration. The connectivity of a network can be defined as the relationship between the number of nodes and the number of connections between the nodes. The higher the number of connections with respect to the number of nodes, the higher the connectivity. Concentration defines the number of connections between a certain node and the others. The higher the Copyright © 2008, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.