Network depth: identifying median and contours in complex networks

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as the `centre' of a complex network. In fact, this problem corresponds to finding the median of a complex network. The median is a non-parametric and robust estimator of the location parameter of a probability distribution. In this work, we present the most natural generalisation of the concept of median to the realm of complex networks, discussing its advantages for defining the centre of the system and percentiles around that centre. To this aim, we introduce a new statistical data depth and we apply it to networks embedded in a geometric space induced by different metrics. The application of our framework to empirical networks allows us to identify median nodes which are socially or biologically relevant

Robust Estimation of the Generalized Loggamma Model. The R Package robustloggamma

robustloggamma is an R package for robust estimation and inference in the generalized loggamma model. We briefly introduce the model, the estimation procedures and the computational algorithms. Then, we illustrate the use of the package with the help of a real data set.Comment: Accepted in Journal of Statistical Softwar