The rank-size city rule doesn't seem to apply to Italy. The largest city in Italy, Rome, is smaller than the rule would predict. However, when examining smaller cities, there may be a correlation between city rank and population sizes. 

Some high-order services in Rome, Italy, are financial services such as banking and investment and stock exchange. Rome houses central national and international banks, insurance companies, and investment firms. Borsa Italiana, the Italian Stock Exchange, has its headquarters in Milan, but Rome has a huge presence of stockbrokers and financial analysts. 

Some low-order services in Rome, Italy, are grocery stores, bakeries, pharmacies, and newsstands. Many small shops sell fresh produce, bread, and other daily essentials. Also, some kiosks sell newspapers, magazines, and lottery tickets, providing convenient stores for people to grab their news. 

Rome is an example of a primate city in Italy. It has a population of around 2.8 million within the city limits and reaches over 4.3 million in its broader metropolitan area. Rome houses the national parliament, ministries, and various government agencies. 

We can apply the gravity model to Milan. Considering Milan's role as a financial and business center, the model could show business travel between Milan and other Italian cities. Cities with large populations close to Milan can be predicted to have more frequent business travel interactions. Furthermore, Milan is a major fashion hub, and cities with concentrated fashion-related businesses can result in strong interactions.