Direct Application B2Bi
Direct application B2Bi is sometimes known as application-to-application B2Bi, which I find to be a mouthful. One way to think about direct application B2Bi is that it is interenterprise EAI, the idea that B2B transactions are enabled when enterprise applications from two or more corporations are directly connected. In this scenario, B2Bi is not occurring as an "open market" interaction among several participants. Instead, it is part of a supply chain between two partners.
For an example, consider the situation in which two companies are related in a reseller-supplier relationship. Corporation A, as the reseller, may use Siebel Sales Automation for sales management, while Corporation B, as the supplier, manages its inventory with SAP. For both companies to participate in a seamless supply chain with sales managed via Siebel and product inventory managed through SAP, both applications need to be integrated together. Integrating these applications through the use of EAI technologies such as integration brokers and adapters over a public network may be the most effective way to get this done. Often when you encounter EAI products claiming to do B2B successfully, the direct application B2Bi pattern is what they have in mind.