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Quantitative Concepts and Measures

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Innovation Networks in the German Laser Industry

Part of the book series: Economic Complexity and Evolution ((ECAE))

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Abstract

A broad range of concepts and measures are needed to provide a quantitative description of the industry and to analyze the initially raised research questions. Focus is on using applied methods in calculating geographical and network-related measures. Chapter 5 is divided into three sections: Section 5.1 presents some general graph theoretical concepts. Section 5.2 provides an overview of techniques and measures for the structural analysis of interorganizational networks. More precisely, we present most commonly used network measures at three analytical levels: actor level, subgroup level and overall network level. Finally, in Sect.5.3 we outline a selection of spatial proximity and geographical concentration concepts that were applied in the analytical part of the study.

Measure what is measurable, and make measurable what is not so.

(Galileo Galilei).

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Notes

  1. 1.

    Vertexes are also called “nodes”, “actors”, “agents”, “players” and “entities”.

  2. 2.

    Edges are also called “ties”, “links”, “connections” and “relationships”.

  3. 3.

    Isomorphic means in this context that subgraphs are structurally indistinguishable from one another (Wasserman and Faust 1994, p. 560).

  4. 4.

    According to this scheme, the first character specifies the number of mutual dyads, the second character gives the number of asymmetric dyads, the third character displays the number of null-dyads, and the last character gives a further characterization of how the ties are directed at each other within these specific isomorphism classes by using the characters “D” (for down), “U” (for up), “T” (transitive), “C” (cyclic). For details, see Wasserman and Faust (1994, pp. 559–575).

  5. 5.

    The graph theoretical terminology can be somewhat misleading in this context. Note that the term “group” refers to the overall graph. The term “subgroup” addresses subsets of actors in the overall network.

  6. 6.

    The historical roots of this concept are located in the field of sociological research. In this study the terms “social network analysis” and “quantitative network analysis” are used interchangeably.

  7. 7.

    General system theory (Bertalanffy 1968) provides the general theoretical foundation for socio-economic and other systems by describing the general nature of a system by explicitly referring to system elements and some kind of relationships or forces between them.

  8. 8.

    Jackson (2008, p. 39) suggests that decay centrality is a richer way of measuring closeness. Instead of a simple distance function d (ni, nj) a so-called decay parameter with δd(ni, nj).0 < δ < 1 is introduced. The specific feature of this measure is that distances get weighted by the decay parameter.

  9. 9.

    For an in-depth discussion on the Katz prestige measure, see Jackson (2008, pp. 40–41) or Newman (2010, pp. 172–175).

  10. 10.

    For an in-depth discussion on further egocentric concepts and measures see: Marsden (2002) or Knoke and Yang (2008, pp. 53–56).

  11. 11.

    In the case of unconnected graphs, the index can be applied to at least the main component.

  12. 12.

    These measures are especially required for analyzing the emergence of large-scale properties at the overall network level (cf. Sect. 8.3.2).

  13. 13.

    Newman (2010, p. 235) reports that the main component usually fills more than 90 % of the entire network in the majority of real world networks such as social networks, biological networks, information networks or technological networks. For the German laser industry network, we found that the main component fills 94.51 % of the network on average (cf. Sect. 8.3.3).

  14. 14.

    If not otherwise stated, in this section we follow the methodological concept proposed by Sorenson and Audia (2000, pp. 433–435).

  15. 15.

    To account for the heterogeneity of organizations in our PRO sample we put all universities and technical universities into one group, and all other public research organizations into another. These measures were predominantly used to check for consistency and robustness in our estimation results (for instance, an additional consistency check of estimation results in Chap. 12).

  16. 16.

    According to Whittington et al. (2009) the weighting factor x in the numerator of the originally proposed LD measure was taken to equal one.

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Authors and Affiliations

  1. Stifterverband, Essen, Germany

    Muhamed Kudic

  2. Halle Institute for Economic Research, Halle (Saale), Germany

    Muhamed Kudic

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Kudic, M. (2015). Quantitative Concepts and Measures. In: Innovation Networks in the German Laser Industry. Economic Complexity and Evolution. Springer, Cham. https://doi.org/10.1007/978-3-319-07935-6_5

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