CONICET | Buscador de Institutos y Recursos Humanos

The effects of clustering on the structural and dynamical properties of networks have not yet been elucidated. In fact, several studies have reported apparent contradictory results concerning the effects of clustering on the percolation properties of networks and little is known on its effects on dynamical processes running on networks. This is further hindered by the technical difficulties of any analytical treatment. To overcome these problems, a new class of clustered network models has been proposed with the peculiarity that tree-like assumption still holds on them, thus allowing for an analytical treatment. While this is indeed a fair approach to the problem, triangles generated by these models are arranged in a very specific way, with strong correlations between the properties of adjacent edges. In some sense, we can consider this class of models as generators of maximally ordered clustered graphs. At the other side of the spectrum, we can define an ensemble of maximally random clustered graphs such that correlations among adjacent edges are the minimum needed to conform with the degree-dependent clustering coefficient, but no more. These two types of models define ?in a non-rigorous way? the edges of the phase space of possible graphs with given P (k) and c(k). A simple question arises: where are real networks in this phase space? To give an answer to this question, we need to go beyond the local properties of networks and to study their global organization. In this work, we study the global structure induced by the two types of models and compare them with the global structure of real networks with identical local properties. Interestingly enough, real networks tend to be closer to maximally random clustered graphs, although clear differences are evident.