This study's main objective is to analyse the relationship between network-based centrality measures and physical demands in elite football players. Thirty-six matches from La Liga, the Spanish league, were analysed in the 2017/18 season. The analysis of networks formed by team players passing the ball included: degree-prestige (DP), degree-centrality (DC), betweenness-centrality (BC), page-rank (PRP) and closeness-centrality (IRCC). A video-based system was used for analysing total distance (TDpos) and distance run >21Km/h (TD21pos) when the team was in possession of the ball. A magnitude-based inference and correlation analysis were applied. There were different styles of play, team-A was characterized by greater ball circulation (e.g. higher values of DP, DC, BC and IRCC) while team-B used a more direct game (lower values in centrality-metrics except with PRP). Furthermore, TDpos was higher in team-A than in team-B, but those differences disappeared for TD21pos between teams with the exception of the forwards. Finally, the correlation among centrality measures and physical performance were higher in team-B. Coaches could identify the key opponents and players who are linked to them, allowing to adjust performance strategies. Furthermore, interaction patterns between teammates can be used to identify preferential paths of cooperation and to take decisions regarding these relations in order to optimize team performance.