In this paper we propose a set of necessary and sufficient conditions under which the throughput in an ad-hoc network can remain constant as the number of nodes n increases. Throughput refers to the minimum achievable rate between a source-destination pair for a given routing mechanism and physical model, when the network is shared by \Theta(n) randomly chosen source-destination pairs. The main idea is to use a connectivity graph, that does not represent the actual physical network, but rather the available communication resources.