An alpha city plays a significant role in the global economic network. It's usually a primary hub for finance, commerce, trade, arts & culture etc., having direct impact on global affairs both economically & politically.
Beta City: Cities that are important on a regional or national scale but have less influence globally.
Gamma City: Cities that link smaller economic regions into the world economy.
Global Network: A network of nodes (cities) connected by various economic, political and social links.