1. A system connecting multiple hosts in a computing network by at least one heartbeat link to each host comprising: a) a first set of heartbeat links between said multiple hosts such that each host is connected by the heartbeat link to a first adjoining neighbor host and a second adjoining neighbor host; and b) a second set of heartbeat links between said multiple hosts such that each host is connected by a heartbeat link to the first adjoining neighbor host's adjoining neighbor host and to the second adjoining neighbor host's adjoining neighbor host; and c) wherein a failure of one of said multiple hosts comprises a resulting action of: d) the failed host's first adjoining neighbor host remaining connected by a heartbeat link to said failed host's second adjoining neighbor host; and e) the failed host's second adjoining neighbor host remaining connected by a heart beat link to said failed host's second adjoining neighbor host's second adjoining neighbor; and f) the failed host's first adjoining neighbor host, using said remaining connected heartbeat link from said first adjoining neighbor host to failed host's second adjoining neighbor host, and said remaining connected heartbeat link from said second adjoining neighbor host to said second adjoining neighbor host's adjoining neighbor host, to connect a new heartbeat link to said failed host's second adjoining neighbor host's adjoining neighbor host; and g) the failed host's first adjoining neighbor host remaining connected by a heartbeat to said failed host's first adjoining neighbor host's first adjoining neighbor; and h) the failed host's second adjoining neighbor host connecting a new heartbeat link to said failed host's first adjoining neighbor host's first adjoining neighbor host by using said remaining connected heartbeat link from failed host's first adjoining neighbor host to the failed host's second adjoining neighbor host and said remaining heartbeat link from the first adjoining neighbor host to the first adjoining neighbor's first adjoining neighbor host; i) thereby establishing a heartbeat linking structure similar to a heartbeat linking structure prior to the failure of the failed host, with an exception that the failed host is no longer in the structure.