Social networks are analyzed as graphs under the scope of discrete mathematics which have a great range of applications in different contexts such as: technology, social phenomena and biological systems. At the present this theory gives a set of tools for a phenomenological analysis that would be difficult or almost impossible with a different approach. In this work social networks for different technical communities from electronic mail and ``News'' in Spanish language are constructed. The algorithm was based on the use of RFC2822 standards and RFC1036 to arm threads of messages. The results are quite different from that obtained by another kind of community as the jazz musicians community. Nevertheless they show an analogy to random graphs obtained by the ``Configuration Model'' method. This points the attention that some generalization assumptions are not correct.

Among the several findings deriving from the application of complex network formalism to the investigation of natural phenomena, the fact that linguistic constructions follow power laws presents special interest for its potential implications for psychology and brain science. By corresponding to one of the most essentially human manifestations, such language-related properties suggest that similar dynamics may also be inherent to the brain areas related to language and associative memory, and perhaps even consciousness. The present work reports a preliminary experimental investigation aimed at characterizing and modeling the flow of sequentially induced associations between words from the English language in terms of complex networks. The data is produced through a psychophysical experiment where a word is presented to the subject, who is requested to associate another word. Complex network and graph theory formalism and measurements are applied in order to characterize the experimental data. Several interesting results are identified, including the characterization of attraction basins, association asymmetries, context biasing, as well as a possible power-law underlying word associations, which could be explained by the appearance of strange loops along the hierarchical structure underlying word categories.

The widespread occurrence of an inverse square relation in the hierarchical distribution of sub-communities within communities (or sub-species within species) has been recently invoked as a signature of hierarchical self-organization within social and ecological systems. Here we show that, whether such systems are self-organized or not, this behavior is the consequence of the tree-like classification method. Different tree-like classifications (both of real and truly random systems) display a similar statistical behaviour when considering the sizes of their sub-branches.

The extreme eigenvalues of connectivity matrices gover 920 n the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by ensemble averages. Here we investigate this question explicitly and validate the concept of ensemble averageability in random scale-free networks by showing that the ensemble distributions of extreme eigenvalues converge to peaked distributions as the system size increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.

We investigate precursors and predictability of extreme events in time series, which consist in large increments within successive time steps. In order to understand the predictability of this class of extreme events, we study analytically the prediction of extreme increments in AR(1)-processes. The resulting strategies are then applied to predict sudden increases in wind speed recordings. In both cases we evaluate the success of predictions via creating receiver operator characteristics (ROC-plots). Surprisingly, we obtain better ROC-plots for completely uncorrelated Gaussian random numbers than for AR(1)-correlated data. Furthermore, we observe an increase of predictability with increasing event size. Both effects can be understood by using the likelihood ratio as a summary index for smooth ROC-curves.