Page - (000298) - in Knowledge and Networks

295 as direct, whenever a local inventor is directly connected to an external inventor, and indirect, whenever a local inventor needs the intermediation of another co-localized inventor to reach external inventors. As far the indirect linkages are concerned, these are defined as those shortest paths between inventors such that the geodesic distance dij between inventor i (located in focal city c) and inventor j (not located in city c) goes through some other inventor also located in city c. Accordingly, the latter inventor can be defined as a gatekeeper, in the sense this inventor performs a bridging function between inventors located in a given city and other inventors located in other cities. This definition of gatekeeper is consistent with the original one proposed by Gould and Fernandez (1989), Allen (1977), and Tushman and Katz (1980). If we take all indirect linkages defined in this way and we aggregate them up to the city level, we can formally define the overall indirect reach of city c as: INDREACH dc i n j n ij ind c h = = = ∑∑ 1 1 1 (14.2) where dij ind is the distance in the co-invention network between inventor i (in city c) and inventor j (not in city c) and the apex “ind ” indicates that the shortest paths linking i and j involve the intermediation of at least one inventor (i.e., a gate- keeper) located in city c.4 As far as direct linkages are concerned, these are symmetrically defined as those paths between inventors such that the distance dij) between inventor i (located in focal city c) and inventor j (not located in city c) does not pass through any other inventor located in city c. In other words, direct linkages, in the sense used in this paper, are those that do not involve the intermediation of other inventors located in the same city. In this respect, any type of actors, including gatekeepers, can under- take direct linkages. As before, if all direct linkages defined in this way are aggre- gated up to the city level, the overall direct reach of city c can be formally defined as: DIRREACH d dc i i GK n j n ij i i GK n j n ij c h c h = + = ∈ = = ∉ = ∑∑ ∑∑ 1 1 1 1 1 1 (14.3) where dij is the distance in the co-invention network between inventor i (in city c) and inventor j (not in city c) ; the first term of the summation refers to the subset of inventors in city c who perform the function of gatekeepers for some other co- located inventor, while the second term of the summation refers to the subset of inventors in city c who do not perform the function of gatekeepers for any other co-located inventor. 4 Note that by definition dij ind ≥2 and thus 1 1 2/ / .dij ind£ Paths of length 1, in fact, cannot involve any gatekeeper, in other words, they are direct linkages. 14 Are Gatekeepers Important for the Renewal of the Local Knowledge Base?…