Structure constrained by metadata in networks of chess players

Physical Review E, 2004

Although being a very popular sport in many countries, soccer has not received much attention from the scientific community. In this paper, we study soccer from a complex network point of view. First, we consider a bipartite network with two kinds of vertices or nodes: the soccer players and the clubs. Real data were gathered from the 32 editions of the Brazilian soccer championship, in a total of 13, 411 soccer players and 127 clubs. We find a lot of interesting and perhaps unsuspected results. The probability that a Brazilian soccer player has worked at N clubs or played M games shows an exponential decay while the probability that he has scored G goals is power law. Now, if two soccer players who have worked at the same club at the same time are connected by an edge, then a new type of network arises (composed exclusively by soccer players nodes). Our analysis shows that for this network the degree distribution decays exponentially. We determine the exact values of the clustering coefficient, the assortativity coefficient and the average shortest path length and compare them with those of the Erdös-Rényi and configuration model. The time evolution of these quantities are calculated and the corresponding results discussed.

2004

We live in the world of information, where huge amounts of data of diverse nature and origin arise in various spheres of life, including sports. To get useful information from this data, one should apply special techniques of summarizing and visualizing the information contained in a certain dataset. In many practical situations, a real-life dataset can be represented as a large graph (network)-a structure that can be easily understood and visualized [3]. A graph is a set of vertices (dots) and edges (links) connecting them.

2007

The paper proposes an alternative way to observe and extract the multiple matches games of sports, i.e.: tennis tournament in the Athlete's Historical Relative Performance Index and its representation as graph. The finding of the small world topology is elaborated along with further statistical patterns in the fashion of the weighted and directed network. The explanation of the sport tournament system as a highly optimized system is hypothetically proposed. Finally, some elaborations regarding to further directions of the usability of the proposed methodology is discussed.

2009

Although being very popular all around the globe, soccer has not received much attention from the scientific community. In this paper we will study the Dutch Soccer Team from the perspective of complex networks. In the DST network every node corresponds to a player that has played an official match for the Dutch Soccer Team. A node is connected with another node if both players have appeared in the same match. The aim of this paper is to study the topological properties of the Dutch Soccer Team network. The motivation for studying the DST network is twofold. The first reason is the immense popularity of the DST, in the Netherlands. Through our study we obtain all kind of new statistics about the DST. Secondly, our results could also be used by the coach of the DST, for instance by determining the optimal line-up. Using data available from a public website we have computed the topological metrics for the DST. Furthermore, we have looked at the evolution of the topological metrics over time and we compared them with those of other real-life networks and of generic network models. We found that the DST is a small world network and that the player with the highest degree also has the lowest clustering coefficient.

Scientific Reports, 2019

The application of Network Science to social systems has introduced new methodologies to analyze classical problems such as the emergence of epidemics, the arousal of cooperation between individuals or the propagation of information along social networks. More recently, the organization of football teams and their performance have been unveiled using metrics coming from Network Science, where a team is considered as a complex network whose nodes (i.e., players) interact with the aim of overcoming the opponent network. Here, we combine the use of different network metrics to extract the particular signature of the F.C. Barcelona coached by Guardiola, which has been considered one of the best teams along football history. We have first compared the network organization of Guardiola’s team with their opponents along one season of the Spanish national league, identifying those metrics with statistically significant differences and relating them with the Guardiola’s game. Next, we have f...

PLoS ONE, 2011

The sport of football is played between two teams of eleven players each using a spherical ball. Each team strives to score by driving the ball into the opposing goal as the result of skillful interactions among players. Football can be regarded from the network perspective as a competitive relationship between two cooperative networks with a dynamic network topology and dynamic network node. Many complex large-scale networks have been shown to have topological properties in common, based on a small-world network and scale-free network models. However, the human dynamic movement pattern of this network has never been investigated in a real-world setting. Here, we show that the power law in degree distribution emerged in the passing behavior in the 2006 FIFA World Cup Final and an international ''A'' match in Japan, by describing players as vertices connected by links representing passes. The exponent values c*3:1 are similar to the typical values that occur in many real-world networks, which are in the range of 2vcv3, and are larger than that of a gene transcription network, c*1. Furthermore, we reveal the stochastically switched dynamics of the hub player throughout the game as a unique feature in football games. It suggests that this feature could result not only in securing vulnerability against intentional attack, but also in a power law for self-organization. Our results suggest common and unique network dynamics of two competitive networks, compared with the large-scale networks that have previously been investigated in numerous works. Our findings may lead to improved resilience and survivability not only in biological networks, but also in communication networks.

Journal of Science and …, 2010

This paper describes and evaluates the novel utility of network methods for understanding human interpersonal interactions within social neurobiological systems such as sports teams. We show how collective system networks are supported by the sum of interpersonal interactions that emerge from the activity of system agents (such as players in a sports team). To test this idea we trialled the methodology in analyses of intra-team collective behaviours in the team sport of water polo. We observed that the number of interactions between team members resulted in varied intra-team coordination patterns of play, differentiating between successful and unsuccessful performance outcomes. Future research on small-world networks methodologies needs to formalize measures of node connections in analyses of collective behaviours in sports teams, to verify whether a high frequency of interactions is needed between players in order to achieve competitive performance outcomes.

Motriz: Revista de Educação Física, 2014

The aim of this pilot study was propose a set of network methods to measure the specific properties of football teams. These metrics were organized on "meso" and "micro" analysis levels. Five official matches of the same team on the First Portuguese Football League were analyzed. An overall of 577 offensive plays were analyzed from the five matches. From the adjacency matrices developed per each offensive play it were computed the scaled connectivity, the clustering coefficient and the centroid significance and centroid conformity. Results showed that the highest values of scaled connectivity were found in lateral defenders and central and midfielder players and the lowest values were found in the striker and goalkeeper. The highest values of clustering coefficient were generally found in midfielders and forwards. In addition, the centroid results showed that lateral and central defenders tend to be the centroid players in the attacking process. In sum, this stud...

Journal of Systems Science and Complexity, 2013

In this paper we analyze the network of passes among the players of the Spanish team during the last FIFA World Cup 2010, where they emerged as the champion, with the objective of explaining the results obtained from the behavior at the complex network level. The team is considered a network with players as nodes and passes as (directed) edges. A temporal analysis of the resulting passes network is also done, looking at the number of passes, length of the chain of passes, and to network measures such as player centrality and clustering coefficient. Results of the last three matches (the decisive ones) indicate that the clustering coefficient of the pass network remains high, indicating the elaborate style of the Spanish team. The effectiveness of the opposing team in negating the Spanish game is reflected in the change of several network measures over time, most importantly in drops of the clustering coefficient and passing length/speed, as well as in their being able in removing the most talented players from the central positions of the network. Spain's ability to restore their combinative game and move the focus of the game to offensive positions and talented players is shown to tilt the balance in favor of the Spanish team.

Statistical Modelling

In this work, we develop an innovative hierarchical clustering method to divide a sample of undirected weighted networks into groups. The methodology consists of two phases: The first phase is aimed at putting the single networks in a broader framework by including the characteristics of the population in the data, while the second phase creates a subdivision of the sample on the basis of the similarity between the community structures of the processed networks. Starting from the representation of the team's playing style as a network, we apply the method to group the Italian Serie A teams’ performances and consequently detect the main 15 tactics shown during the 2015–2016 season. The information obtained is used to verify the effect of the styles of play on the number of goals scored, and we prove the key role of one of them by implementing an extension of the Dixon and Coles model.