The geography of collaborative knowledge production: entropy techniques and results for the European Union

In the context of research collaboration addressed here, it is important to note that the
indicator takes into account both intra-national (i=j ) and international (.≠j ) interactions. In
this way, the degree of integration is adjusted for differences in size of countries as measured
by the number of collaborations in which a country participates, as a fraction of the total
number of collaborations. Collaboration patterns are assessed by means of comparing the
observed frequency of collaboration (qij ) to what is expected from the individual shares of
countries (q_i. ∙ q_j ). What follows is that a large country should be expected to collaborate
more intensively at the national level than a small country, because there are more researchers
available in larger countries to interact with at the national level. In this, the indicator
proposed above differs from more other measures that indicate internationalisation either by
looking at international collaboration only (Katz, 2000) or by taking the ratio between
national and international activity (Kearney, 2001). The latter types of indicators typically
show high integration values for smaller countries compared to larger countries as these
indicators do not control for the size of countries.

3.2 Analysing subsets

As explained above, the integration measure is a weighted sum of all intranational and
international T_ij-values weighted for their share in the population. For the European Union,
there are 152 = 225 T_ij-values. By summing non-overlapping subsets of the 225 T_ij-values,
and dividing the sum by the share of the subset in the population, one can focus on the degree
of integration of a subset of the matrix.

In the case of the European Union, one can think of two ways of splitting the matrix into
subsets. First, one can compare the T_ij-values for national (i=j) and international (i≠j)
collaborations to analyse to what extent integration is due to intra-national biases versus
international biases. We get, respectively:

₁          < 15    15

Ti-_i= τr-5;--ΣΣ qj ■^ln

Σ Σ qj ^y-ⁱ =^{1 j} =¹

i =1 j =1

(Leydesdorff, 1991), and the dependence of countries on technologies and markets (Frenken, 2000).
The application of mutual information to simulation data concern the measurement of dependency

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