Development of Sports Network Analysis: Methodological Considerations

IntroductionCollective behaviour in team sports and the possibilities of match analysisNetworks emerges from the interactions between teammates in the match (Pena & Touchette, 2012). By using some analysis techniques, it is possible to determine the style of play (Clemente et al., 2013a). The information available from the reality of the game may help to characterize the collective processes and also to predict next events (Bartlett, Button, Robins, Dutt-Mazumder, & Kennedy, 2012). Moreover, it is also possible to re-organize the strategy of the team and tactical behaviour of players (Clemente, Couceiro, Martins, & Mendes, 2015), and even optimize the sports training based on the knowledge of strengths and weaknesses of the team and an opponent (Clemente, Couceiro, Martins, Mendes, & Figueiredo, 2013b). Several methods of and different approaches to match analysis can be used to provide information for coaches (Carling, Williams, & Reilly, 2005; Hughes & Franks, 2005). From that data, it is possible to classify such information into categories (Clemente, Couceiro, Martins, Mendes, & Figueiredo, 2014): (i) notational analysis based on individual actions; (ii) tactical analysis based on observational methods; (iii) computational metrics to characterize the spatio-temporal relationship within and between teams; and (iv) observational methods to classify the level of cooperation and patterns within a team. Three main types of observational methods have been used to classify the level of cooperation: (i) temporal patterns (Jonsson et al., 2006); ii) neural network (Grunz, Memmert, & Perl, 2012); and iii) social network analysis based on graph theory (Lusher et al., 2010). The last example, social network analysis, is a very useful and user-friendly method of applying social network metrics to any game and competition level. The method involves observation and codifying of team interaction and processing the data using software. For a better understanding about the concept of social network analysis, the following section presents the global approach and its use in sport sciences.Social Network Analysis and Graph Theory: Concepts and DefinitionsThe Social Network Analysis (SNA) is based on Graph Theory (Barnes & Harary, 1983), a mathematical study of sets of nodes connected by lines. The techniques model pairwise relations between the vertices. Some understood fundamentals of graph theory are directed graphs, undirected graphs, and weighted graphs (digraphs) (Pavlopoulos et al., 2011). In the following presented elementary concepts on Graphs TeoryDefinition 1. (Gross & Yellen, 2004)A graph G=(V,E) can be characterized as two sets V and E, where V is a set of vertices (or nodes), E is a set of edges and each edge has a set of one or two vertices associated to it, which are called its endpoints (or neighbors) and an edge is said to joint its endpoints.Definition 2. (Gross & Yellen, 2004)A graph that has no loops and includes no more than one edge between a pair of nodes is called a simple graph.The Definition 1 represent the class of graphs called of undirected graph.The other broad class are the directed graphs that we show the following in Definition 3.Definition 3. (Gross & Yellen, 2004)A directed graph (or digraph) is a graph each of whose edges is directed shut that a direct edge (or arc) is an edge that linked in the initial node to the terminal node.Definition 4. (Gross & Yellen, 2004). A digraph that has no loops and includes no more than one arc that linked in the initial node to the terminal node is called a simple digraph.Definition 5. (Gross & Yellen, 2004)In the case of a any graph (digraph) with all connections measured between any two nodes is called weighted graph (digraph). Definition 6. The x matrix = M is the adjacency matrix of a graph or digraph such that *'! …