Morphology and Entropy in Networks

Morphology and Entropy in Networks

Ton van Asseldonk (TVA developments bv, The Netherlands), Erik den Hartigh (Delft University of Technology, The Netherlands) and Leon Berger (Nyenrode University, The Netherlands)
Copyright: © 2008 |Pages: 7
DOI: 10.4018/978-1-59904-885-7.ch126
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Abstract

This article concerns the relation between the morphology (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 measures 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.

Key Terms in this Chapter

Connectivity: of a network is defined as the relationship between the number of nodes and the number of connections between the nodes. The higher the number of connections in relation to the number of nodes, the higher the connectivity.

Hierarchical Structure: A network in which one of the entities is connected to most other entities.

Concentration: of a network defines the number of connections between a certain node and the others. The higher the number of connections from one node to all the others, the higher the concentration.

Networked Structure: A network in which the connectivity is substantially higher than in the hierarchical structure but substantially less than in the chaotic structure.

Network Morphology: The form and structure of a network. It can be described by two separate elements: connectivity and concentration.

Amorphous Structure: A network in which no links exist between the entities.

Chaotic Structure: A network in which all entities are connected to all other entities.

Entropy: is a measure for disorder that can, for organizations, be defined as e = - S [Pi * log Pi] for (i = 1 to m) where Pn is the probability that a certain interaction link in the organization will exist.

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