There is another study, in addition to that cited by @TumbiSapichu, that establishes a genetic component in canine aggression. This is: Zapata et al. (2016) BMC Genomics 17:572 and is entitled Genetic mapping of canine fear and aggression.
The study did not set out to establish which breeds, if any, are most aggressive, but started from the proposition that there might be a genetic component in canine aggression, and tested this by a genome-wide association (GWA) study on one cohort of different breeds. This established certain candidate genes, which were tested — and confirmed — on a second cohort. The authors of the paper conclude:
“We have mapped many canine fear and aggression traits to single haplotypes at the GNAT3-CD36 and IGSF1 loci. CD36 is widely expressed, but areas of the amygdala and hypothalamus are among the brain regions with highest enrichment; and CD36-knockout mice are known to have significantly increased anxiety and aggression. Both of the other genes have very high tissue-specificity and are very abundantly expressed in brain regions that comprise the core anatomy of fear and aggression – the amygdala to hypothalamic-pituitary-adrenal (HPA) axis. We propose that reduced-fear variants at these loci may have been involved in the domestication process.”
I appreciate that the reader may wish to see a graphic showing that Rottweilers are more aggressive than Yorkies, for example. However the paper clearly answers in the positive the question of whether there is a genetic component in canine aggression, and the paper has 20 pages and eight figures for anyone who wishes to tease out information regarding specific breeds. (I do not own a dog, so lack the incentive to do so myself.)