Complex systems and interaction phenomena are usually described as networks in which the individuals (nodes) interact (link) to each other. Examples of these systems can be found in a daily basis, e.g. air traffic, world trade market, social networks, spread of diseases and so on. Thus, it is important to understand the behaviour of such systems and the random processes to which they are bound. Random Graphs are one of the tools that help us analyse this particular - yet general - behaviour. A particular case of these complex systems is the protein-protein interaction (PPI) network for which despite of its recent good results on small virus PPI networks (Hayes et al., 2013) - around 50 to 120 nodes- current models seem to fail in representing PPI networks for more complex organisms (Shao et al., 2013; Rito et al., 2010) such as the yeast PPI network, which has more than 5000 nodes - more than 40 times the number of nodes in the mentioned virus PPIs - therefore a good model for this networks is still needed. Thus, I’m currently developing new random graph models that aim to fit PPIs among others.