Two classes of bipartite networks: nested biological and social systems.

Bipartite graphs have received some attention in the study of social networks and of biological mutualistic systems. A generalization of a previous model is presented, that evolves the topology of the graph in order to optimally account for a given contact preference rule between the two guilds of the network. As a result, social and biological graphs are classified as belonging to two clearly different classes. Projected graphs, linking the agents of only one guild, are obtained from the original bipartite graph. The corresponding evolution of its statistical properties is also studied. An example of a biological mutualistic network is analyzed in detail, and it is found that the model provides a very good fitting of all the main statistical features. The model also provides a proper qualitative description of the same features observed in social webs, suggesting the possible reasons underlying the difference in the organization of these two kinds of bipartite networks.

Why nestedness in mutualistic networks?

We investigate the relationship between the nested organization of mutualistic systems and their robustness against the extinction of species. We establish that a nested pattern of contacts is the best possible one as far as robustness is concerned, but only when the least linked species have the greater probability of becoming extinct. We introduce a coefficient that provides a quantitative measure of the robustness of a mutualistic system.

Analysis and assembling of network structure in mutualistic systems.

It has been observed that mutualistic bipartite networks have a nested structure of interactions. In addition, the degree distributions associated with the two guilds involved in such networks (e.g., plants and pollinators or plants and seed dispersers) approximately follow a truncated power law (TPL). We show that nestedness and TPL distributions are intimately linked, and that any biological reasons for such truncation are superimposed to finite size effects. We further explore the internal organization of bipartite networks by developing a self-organizing network model (SNM) that reproduces empirical observations of pollination systems of widely different sizes. Since the only inputs to the SNM are numbers of plant and animal species, and their interactions (i.e., no data on local abundance of the interacting species are needed), we suggest that the well-known association between species frequency of interaction and species degree is a consequence rather than a cause, of the observed network structure.

Thermal treatment of the minority game.

We study a cost function for the aggregate behavior of all the agents involved in the minority game (MG) or the bar attendance model (BAM). The cost function allows us to define a deterministic, synchronous dynamic that yields results that have the main relevant features than those of the probabilistic, sequential dynamics used for the MG or the BAM. We define a temperature through a Langevin approach in terms of the fluctuations of the average attendance. We prove that the cost function is an extensive quantity that can play the role of an internal energy of the many-agent system while the temperature so defined is an intensive parameter. We compare the results of the thermal perturbation to the deterministic dynamics and prove that they agree with those obtained with the MG or BAM in the limit of very low temperature.