The mole we see in the UK is Talpa Europea, the Eurpoean Mole.
Though the subject of some debate, it is generally believed that moles are solitary creatures. Their territories will quite often overlap, with a common "motorway" tunnel used by two or more moles, linking to their own feeding tunnels. The exceptions to this are (1) during mating in the spring, and (2) later in the summer as the young leave their nests, when there will be quite a lot of movement between territories, and vacant tunnels are likely to be re-inhabited
Normal density is 4 or 5 moles per acre. Having said this, the moles don't read the books, as shown by the fact that I once trapped 11 moles in an area no larger than a cricket pitch!
A large number of mole hills doesn't necessarily indicate a high infestation of moles. Differing soil types and conditions and the density of worms will all have a bearing on the length of feeding tunnels that need to be excavated by the mole.