In many optimization problems, regardless of the domain to which it belongs, the structural component that the interactions among variables provides can be seen as a network. The impact that the topological characteristics of that network has, both in the hardness of the problem and in the performance of the optimization techniques, constitutes a very important subject of research. In this paper, we study the behavior of estimation of distribution algorithms (EDAs) in functions whose structure is defined by using different network topologies which include grids, small-world networks and random graphs. In order to do that, we use several descriptors such as the population size, the number of evaluations as well as the structures learned during the search. Furthermore, we take measures from the field of complex networks such as clustering coefficient or characteristic path length in order to quantify the topological properties of the function structure and analyze their relation with the behavior of EDAs. The results show that these measures are useful to have better understanding of this type of algorithms which have exhibited a high sensitivity to the topological characteristics of the function structure. This study creates a link between EDAs based on Bayesian networks and the emergent field of complex networks.