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

FIGURE 1. The heat map of the Pearson’s correlations results among variables for each edition and complex network model. Predominantly, the weighted links between Medalists had highest values than the weighted links of non-medalists athletes, with significant differences between groups (One-way ANOVA followed by Tukey HSD post hoc test, p < 0.01 at 2000, 2004, and 2008 editions and p < 0.05 at 2012 and 2016 editions). In this figure, A, age; W, weight (kg); H, height (cm); B, body mass index (kg/m2); N, number of Olympic medals and R, reaction time (s).

FIGURE 2. Complex network model parameters (nodes and links) representation proposed for Medalists (yellow) and non-medalists (red) athletes. Every edition of the games results in two complex models. They are: The 2000 Olympic Games, which took place at Australia, in Sydney; 2004 Olympic Games, which took place in Greece, at Athens city; the 2008 Olympic Games, which took place in China, in Beijing; the 2012 Olympic Games, which took place in United Kingdom, in London; and the 2016 Olympic Games, which took place in Brazil, in the city of Rio de Janeiro. The finalists of the 50 m freestyle male swimmers were considered, relating 6 transformed variables into nodes – colored (Age, Height, Weight, BMI, Number of Olympic Medals and Reaction Time) and their weighted links (black) through the resulting correlation. The links of the Medalists complex models had higher weighted links.

FIGURE 3. The Spectral Radius (SR) network (y-axis) by Olympic edition, comparing Medalists result (white) and non-medalists result (black). The Medalists – Winners network of each edition had the highest SR values at all competitions. It is worth mentioning that the winners always resulted in higher SR values at all editions analyzed, with significantly differences between groups (One-way ANOVA followed by Tukey HSD post hoc test, p < 0.05).

FIGURE 4. The SR results (y-axis) by Olympic edition versus mean eigenvalues (x-axis) represented by the triangle with the coordinates (x; y). It is important to note that the Medalists SR results were always above 2.91 and the non-medalists’ results are under 2.51. This point to a common behavior among Medalists-Winners (highest values) at all 5 editions of the games analyzed, with significant differences (One-way ANOVA followed by Tukey HSD post hoc test, p < 0.05).