In the context of team Cornet’s seminars, Shane Mannion (University of Limerick) will present his research work on *Correlations on complex networks and their degree distributions*, on April 5, 2023, at 11:35 in the meeting room.

**Abstract:** First we look at long range correlations in complex networks. The assortativity of a network, that is, the correlation between properties of neighboring nodes can have important practical implications. For example, a targeted vaccination program will be less effective in an assortative social network (where high-degree people mix with others of high degree). We are concerned with whether these correlations between nodes extend to nodes that are separated by more than a single edge. In this talk I will discuss how the correlation between properties of connected nodes in a social network changes as the distances between those nodes increases. This lead us to research on fitting degree distributions, where we introduce a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution to which the model is fit. Current methods for fitting to degree distributions in the literature are inconsistent and often assume a priori what distribution the data are drawn from. Much focus is given to fitting to the tail of the distribution, while a large portion of the distribution below the tail is ignored. Here we address these issues, using maximum likelihood estimators to fit to the entire dataset, or close to it. This methodology is applicable to any network dataset (or discrete empirical dataset), and we test it on over 25 network datasets from a wide range of sources, achieving good fits in all but a few cases.