Page - (000302) - in Knowledge and Networks

299 From this, it follows that the average (distance-weighted) external reach of the city is ADWR c = = 10 7 143. . Of the seven inventors in the city, three perform the function of gatekeepers and are indicated by the octagon shape, in other words, a, e and f. As far as the overall indirect external reach mediated by gatekeepers is con- cerned (expression (14.2) above), this is equal to: 1 1 1 1 1 1 1 1 d d d d d d d dbH bI bJ cH cI cJ dL fK + +       + + +       +       +         = + +       + + +      +       +       = 1 2 1 3 1 3 1 3 1 4 1 4 1 2 1 2 3 The overall direct external reach (expression (14.3) above) is instead equal to: 1 1 1 1 1 1 1 d d d d d daH aI aJ eK eL fL i i GK nc + +       + +       +         = ∈ ∑∑ +       +         = = + j nh ij i i d dK gMd d 1 1 1 1 1 ∉ = ∑∑ = + = GK nc j nh ijd1 1 5 2 7 The share of the overall external reach, which is either directly or indirectly mediated by gatekeepers (expression (14.4) above), is thus given by: 3 5 10 08 + = . Similarly, the share of the overall external reach, which is due to direct external linkages made by gatekeepers (expression (14.5) above), is given by: 5 10 05= . The share of the overall external reach, which is due to indirect external linkages mediated by gatekeepers (expression (14.6) above), is given by: 3 10 033= . As far as network redundancy is concerned, we observed that removing either gatekeeper e or gatekeeper f has no impact on the overall indirect reach of the city. This is because there are two shortest paths (of length 2) linking inventor d to inventor L. On the other hand, removing gatekeeper a reduces the amount of indi- rect external reach by 2 (or 80 %). In this over-simplified context, we can say that the overall indirect reach of the city is concentrated among few (in this case, one) individuals. 14 Are Gatekeepers Important for the Renewal of the Local Knowledge Base?…