Biological networks of interacting agents exhibit similar topological properties for a wide range of scales, from cellular to ecological levels, suggesting the existence of a common evolutionary origin. A general evolutionary mechanism based on global stability has been proposed recently [J I Perotti, et al., Phys. Rev. Lett. 103, 108701 (2009)]. This mechanism was incorporated into a model of a growing network of interacting agents in which each new agent's membership in the network is determined by the agent's effect on the network's global stability. In this work, we analyze different quantities that characterize the topology of the emerging networks, such as global connectivity, clustering and average nearest neighbors degree, showing that they reproduce scaling behaviors frequently observed in several biological systems. The influence of the stability selection mechanism on the dynamics associated to the resulting network, as well as the interplay between some topological and functional features are also analyzed.Received: 17 July 2010; Accepted: 27 September 2010; Edited by: D. H. Zanette; Reviewed by: V. M. Eguiluz, Inst. Fisica Interdisciplinar y Sist. Complejos, Palma de Mallorca, Spain; DOI: 10.4279/PIP.020005