Types of BGP Topologies

BGP is a very flexible and complex routing protocol. As such, BGP routers may be placed in a large variety of topology settings, such as Internet core routers, intermediary ISP routers, ISP Customer Premises Equipment (CPE), or routers in small private BGP networks. The number of BGP routes required for different topologies varies from greater than 300,000 for core routers, to 0 for ISP customers that use a single ISP and use default routing for all destinations outside of their AS. ISP customers are often required to run BGP from their edge router (the CPE) to the ISP regardless of the number of routes they receive from the ISP. This allows ISP customers to control which networks to advertise to the outside world. There's always the fear that a customer will advertise a network, or network aggregate, not owned by the customer, black-holing Internet traffic to those networks. In reality, ISP providers are careful to filter invalid advertisements from their customers (one of BGP's strengths), so this rarely happens.

There are three basic scales of BGP networks:

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Single-Provider / single-Homed - The network receives a single route (single-homed) from a single ISP (single-provider). The number of routes an ISP customer receives from its ISP depends on the nature of its AS. An ISP customer that uses only one ISP as their Internet provider, and has a single connection to that provider (single-provider / single-homed) has no need to receive any routes - all traffic destined outside of the AS will go to their ISP. These customers may still advertise some or all of their inside network to the ISP.
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Single-Provider / Multi-Homed - The network receives multiple routes (multi-homed) from a single ISP (single-provider). ISP customers that use a single ISP, but have multiple connections to their ISP may only receive the default route (0.0.0.0/0) at each ISP gateway. If an ISP connection goes down, the advertised default route sent from the connected CPE router to internal routers would be withdrawn, and Internet traffic would then flow to a CPE router that has connectivity to the ISP. The customer's inside network would also be advertised to the ISP at each CPE router gateway, allowing the ISP to use alternate paths should a particular connection to a customer go down.
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Multi-Provider / Multi-Homed - ISP customers that use more than one ISP (multi-provider / multi-homed) have one or more separate gateway routers for each ISP. In this case, the customer's AS must be a public AS, and may either be a transit or non-transit AS. A transit AS will receive and forward traffic from one ISP destined for a network reachable through another ISP (the traffic destination is not in the customer's AS). A non-transit AS should only receive traffic destined for its AS - all other traffic would be dropped. BGP routers in a transit AS would often receive a large portion (in many cases, all) of the full BGP route table from each ISP.