Page - (000301) - in Knowledge and Networks

298 that performing effectively as a gatekeeper requires special attributes that are not widely distributed in the population, then a higher concentration of that function in few (possibly large) firms might lead to a superior outcome. On the other hand, as long as access to external knowledge is concentrated in few local firms, any benefit that might derive from the activity of gatekeepers does not spread (or spreads more slowly) across all firms in the local economy. A Hypothetical Example Figure 14.1 below illustrates the measures derived above by using a highly simpli- fied, hypothetical example of a city with seven inventors (from a to g), who are connected either directly or indirectly to six inventors located outside the boundar- ies of the city (from H to M). By applying the expression (14.1) above, it is straightforward to check that i n j n ij aH aI aJ bH bI bJ c h d d d d d d d= = ∑∑ = + +       + + +       1 1 1 1 1 1 1 1 1 + + +       + +       + +       + 1 1 1 1 1 1 1 1 d d d d d d d d cH cI cJ dK dL eK eL fK fL gMd d +         + = + +      + + +       + + + 1 1 1 1 2 1 2 1 2 1 3 1 3 1 3 1 4 1 4       + +       + +( )+ +      + = 1 1 2 1 1 1 2 1 1 10 Fig. 14.1 Hypothetical example of external relations and gatekeepers (Source: Design by authors) S. Breschi and C. Lenzi