We analyze the evolution of the risk of cycling in Seville before and after the implementation of a network of segregated cycle tracks in the city. Specifically, we study the evolution of the risk for cyclists of being involved in a collision with a motor vehicle, using data reported by the traffic police along the period 2000-2013, i.e. seven years before and after the network was built. A sudden drop of such risk was observed after the implementation of the network of bikeways. We study, through a multilinear regression analysis, the evolution of the risk by means of explanatory variables representing changes in the built environment, specifically the length of the bikeways and a stepwise jump variable taking the values 0/1 before/after the network was implemented. We found that this last variable has a high value as explanatory variable, even higher than the length of the network, thus suggesting that networking the bikeways has a substantial effect on cycling safety by itself and beyond the mere increase in the length of the bikeways. We also analyze safety in numbers through a non-linear regression analysis. Our results fully agree qualitatively and quantitatively with the results previously reported by Jacobsen (2003), thus providing an independent confirmation of Jacobsen's results. Finally, the mutual causal relationships between the increase in safety, the increase in the number of cyclists and the presence of the network of bikeways are discussed.