Closure in inter-regional knowledge networks: An application to the European co-publication network

The question of the determinants of inter-regional knowledge flows has received a growing interest in the recent past. Particularly, the question of the relationship between geography and networks has been debated. Yet, at the inter-regional level, there is no study assessing the effect of networks on the the value of knowledge flows. This may come from the fact that methodological tools assessing network characteristics at the dyadic level are lacking for aggregated networks (such as the network of inter-regional knowledge flows). This paper aims to fill this gap and contribute to the debate on the determinants of knowledge flows. To do so we first define a new measure to assess 'network proximity' at the level of the regional dyad, based on the concept of inter-regional bridging path. Here a bridging path is a path at the micro-level between two regions via a third one. For instance, if an agent from region B has collaborated with an agent from region A and an agent from region C, then there is a bridging path between A and C via B. By using the information at the aggregated level, and assuming a 'random matching process' of the agents at the micro level, we are able to derive a closed form of the total expected number of bridging paths between two given regions. By the concept of triadic closure at the micro-level, the regional pairs having a high number of bridging paths should be more prone to collaborate. We then illustrate the measure theoretically defined by making use of co-publications data from chemistry journals for the period 2001-2005, within the five largest European countries (France, Germany, Italy, Spain, the United Kingdom). The studied network is then composed of all the regional pairs among 386 active NUTS3 regions. Using a zero-inflated negative binomial regression model along gravity equations, we then assess the effect of geographical distance, spatial contiguity and national borders. We also assess the effect of 'network proximity' by using the expected number of bridging paths as a proxy. As in previous studies, the effects of the geographical distance or the national borders are negative. But we show that the measure of 'network proximity' has a positive and significant effect. All the more, it also significantly alleviates the impeding effect of national borders on cross-countries collaborations, then suggesting that 'network proximity' is a channel favored for international collaborations.