According to the NIST 800-145 guide1, a community cloud is a cloud infrastructure that is provisioned for exclusive use by a specific community of consumers from organizations that have shared concerns (e.g., mission, security requirements, policy, and compliance considerations). It may be owned, managed, and operated by one or more of the organizations in the community, a third party, or some combination of them, and it may exist on or off premises. A community cloud is different from a hybrid cloud, which is a composition of two or more distinct cloud infrastructures (private, community, or public) that remain unique entities, but are bound together by standardized or proprietary technology that enables data and application portability (e.g., cloud bursting for load balancing between clouds). A private cloud is a cloud infrastructure that is provisioned for exclusive use by a single organization comprising multiple consumers (e.g., business units). It may be owned, managed, and operated by the organization, a third party, or some combination of them, and it may exist on or off premises. A public cloud is a cloud infrastructure that is provisioned for open use by the general public. It may be owned, managed, and operated by a business, academic, or government organization, or some combination of them. It exists on the premises of the cloud provider. References :=

Some possible references are:

1: NIST SP 800-145, The NIST Definition of Cloud Computing, 1 2: Evaluation of Cloud Computing Services Based on NIST SP 800-145, 3 3: What Is Community Cloud? Definition, Architecture, Examples, and Best Practices, 6