Two alternative models have been proposed to explain the spread of agriculture in Europe during the Neolithic period. The demic diffusion model postulates the spreading of farmers from the Middle East along a Southeast to Northeast axis. Conversely, the cultural diffusion model assumes transmission of agricultural techniques without substantial movements of people. Support for the demic model derives largely from the observation of frequency gradients among some genetic variants, in particular haplogroups defined by single nucleotide polymorphisms (SNPs) in the Y-chromosome. A recent network analysis of the R-M269 Y chromosome lineage has purportedly corroborated Neolithic expansion from Anatolia, the site of diffusion of agriculture. However, the data are still controversial and the analyses so far performed are prone to a number of biases. In the present study we show that the addition of a single marker, DYSA7.2, dramatically changes the shape of the R-M269 network into a topology showing a clear Western-Eastern dichotomy not consistent with a radial diffusion of people from the Middle East. We have also assessed other Y-chromosome haplogroups proposed to be markers of the Neolithic diffusion of farmers and compared their intra-lineage variation--defined by short tandem repeats (STRs)--in Anatolia and in Sardinia, the only Western population where these lineages are present at appreciable frequencies and where there is substantial archaeological and genetic evidence of pre-Neolithic human occupation. The data indicate that Sardinia does not contain a subset of the variability present in Anatolia and that the shared variability between these populations is best explained by an earlier, pre-Neolithic dispersal of haplogroups from a common ancestral gene pool. Overall, these results are consistent with the cultural diffusion and do not support the demic model of agriculture diffusion.