Complex Networks Models and Spectral Decomposition in the Analysis of Swimming Athletes' Performance at Olympic Games

This study aims to present complex network models which analyze professional swimmers of 50-m freestyle Olympic competitions, comparing characteristics and variables that are considered performance determinants. This comparative research includes Olympic medalists' versus non-medalists' behavior. Using data from 40 athletes with a mean age, weight and height of 26 ± 2.9 years, 87 ± 5.59 kg, 193 ± 3.85 cm, respectively, at the Olympics of 2000, 2004, 2008, 2012, and 2016 (16-year interval), we built two types of complex networks (graphs) for each edition, using mathematical correlations, metrics and the spectral decomposition analysis. It is possible to show that complex metrics behave differently between medalists and non-medalists. The spectral radius (SR) proved to be an important form of evaluation since in all 5 editions it was higher among medalists (SR results: 3.75, 3.5, 3.39, 2.91, and 3.66) compared to non-medalists (2.18, 2.51, 2.23, 2.07, and 2.04), with significantly differences between. This study introduces a remarkable tool in the evaluation of the performance of groups of swimming athletes by complex networks, and is relevant to athletes, coaches, and even amateurs, regarding how individual variables relate to competition results and are reflected in the SR for the best performance. In addition, this is a general method and may, in the future, be developed in the analysis of other competitive sports.