Genetic Structure of the Purebred Domestic Dog
Parker et al. - Genetic Structure of the Purebred Domestic Dog
The study basically did two things: cluster the purebred domestic dogs into several clusters, and determine how exactly individual dogs fit in a cluster. The claim that a certain breed of dogs (say, Shiba Inu) is “genetically closer” to wolf amounts to saying that, in this context, wolfs and Shiba Inu's both fit into the cluster that they're in closely.
The clustering is done based on microsatellites, which
[…] are widely used for DNA profiling in cancer diagnosis, in kinship analysis (especially paternity testing) and in forensic identification. They are also used in genetic linkage analysis to locate a gene or a mutation responsible for a given trait or disease. Microsatellites are also used in population genetics to measure levels of relatedness between subspecies, groups and individuals.