Event broker networks are basically overlay networks formed over the underlying physical network. In modern distributed applications, ensuring high availability in the face of the runtime failures is a major issue. This paper presents an asynchronous distributed algorithm for constructing and maintaining an underlay aware overlay which ensures high availability in the presence of node and link failures in the underlying physical network. We prove theoretically that our algorithm is correct. The time complexity of the algorithm is estimated to be O(diameter*degree)2 of the network and the message complexity is O(diameter*degree). A model for availability of an underlay aware overlay network and a classification of available overlays are the other important contributions of this paper.