Archive of SID Social Network Analysis of Passes and Communication Graph in Football by mining Frequent Subgraphs Amir Hossein Ahmadi Ahmadi Noori Babak Teimourpour* Master of Information Technology Master of Information Technology Assistant Professor of Information Engineering Engineering Technology Engineering Tarbiat Modares University Tarbiat Modares University Tarbiat Modares University Tehran, Iran Tehran, Iran Tehran, Iran [email protected] [email protected] [email protected] Abstract−Sport is regarded as an inseparable part of Concerning the graph and network analysis, different human life. Currently, a growing trend is observed in people's types of node centrality criteria can be found in a graph, interest in football teams. In general, a successful procedure in which indicate the relative importance of a node in the graph. players’ communication is one of the main factors required for Most centrality concepts were first developed in social the victory of that team. The present study aimed to perform network analysis and consequently, various terms used for analyzes based on the perspective of social and communication measuring the centrality were used as a sociological origin networks (such as player passes and in-game transactions) to [5]. improve team performance. The analysis was performed on data collected from three matches of the Persepolis club in the Regarding the high importance of analyzing the players' first half-season of the Iranian Premier League 2019-20. This cooperation in team matches, several studies have applied research seeks to review this issue from two integral social network analysis to determine relationships between perspectives as follows: 1) evaluating the performance of players in a team [3, 6, 7], as a high degree of coordination in individuals as a part of a social network, 2) investigating the the team leads to better performance. Thus, it can be said that communication network between players. To this aim, we used a team with strong coordination and interaction between the innovative method of recognizing and classifying frequent team players seeks high performance in the games [8]. By subgroups in this analysis. It is worth noting that 20 persen of using the network approach, this study indicates that the these routes were in the defensive line while 31 persen were in crucial role of interaction patterns between players in team the defensive midfielder. However, there were no routes in the performance [3]. attacker line or offensive midfielder, which indicated a form of weakness. On the other hand, various types of node degrees, However, determining the relationship between the points, and n-pass cycles were calculated in other sections. The players in a team is necessary to formulate the passing results revealed the weak performance of the connection process within a team. In the consecutive passes cycle, the bridge between the team's playmakers and the end-players for passing process depends on the connection between the shooting the ball. Although these topics were discussed at a players and the team's collective behavior [9, 10]. The game minor level and only three matches of a team, the results can position of a player is the main limitation on passes be generalized to other issues. distribution and communications between teammates [11, Keywords−Social Network Analysis; Graph Analysis; 12]. Frequent Subgraphs; Reach Centrality; Football Analysis. Note that analyzing the centrality of the pass network is I. INTRODUCTION another important issue that should be considered in this field. The creation of scoring positions during the game and Generally, discovering different ways to score a goal in a the match score to some extent depend on the centrality of football team by using the passes network helps the technical the passing network to different game situations during staff to analyze the match and select players and tactics to be consecutive passes [13]. In 2014, a study was conducted on used in the next matches. So far, a large number of studies the players in the FIFA World Cup (2014), concluding that conducted by using network theory have shown passes midfielders have the highest value of out-of-degree leading to offensive situations as networks, in which nodes centrality, degree centrality, closeness centrality, and indicate players and edges represent passes between players. distance centrality in most teams [14]. Pass network includes various contents such as evaluating the characteristics of players and teams quantitatively [1, 2, On the other hand, some research has studied ball 3]. Another research has only analyzed successful passes, possession and its effect on the result of the match, by including throw-in, goal kicks, corner kick, and free-kick [4]. comparing two possession and direct play styles. In this regard, studies have highlighted the importance and necessity www.SID.ir Archive of SID of evaluating how to use possession style related to effective event. The statistical result of these communication was offensive aspects by teams [15, 16]. For example, a study shown in Table I. reviewed the playing methods of successful and unsuccessful teams in the 1986 World Cup and concluded the high rate of A. Cycle possession in successful teams compared to unsuccessful A cycle or ball circulation cycle is considered from the teams [17]. However, another article obtained a result on first event that Perspolis players possess the ball to the last goals scored in the competition, according to which 80% of event that they lose the ball. These cycles are classified into goals were scored with a sequence of three passes and less two categories of successful and unsuccessful categories, [18]. Specifically, no contradiction exists between these two depending on the result of each cycle. In successful cycles, results and it can be said that the team with the highest possession percentage has scored goals in three passes or the destination of the last communication includes one of less. Another research revealed that successful teams created the nodes of the shoot, on-target shoot, and the like. On the more opportunities by using long consecutive passes, other hand, unsuccessful cycles refer to the cycles whose although the ratio of goals scored by direct style was better last event includes losing the ball and the like. than that of the possession game [19]. In long consecutive pass cycles, the number of shots was significantly higher for B. Communication graph successful teams, compared to short consecutive pass cycles The team's communications network was developed [19]. Another research proved that top European football based on transactions. Nodes include players’ numbers teams use long consecutive passes to score goals when losing or drawing, and short consecutive passes when winning [20]. present on the ground, goal (as Gol), shoot (on goal as Shoot2Darvazeh), shoot, cross (as Santr), throw-in (as Out), By reviewing previous research in this field, it is corner, losing the ball (as Lo), and faults made by Persepolis observed that the highest degree of centrality can be found in and opponents players (as Khata1, Khata2). Fig 1 illustrates offensive players of teams that mainly use direct style, have the network as a directed graph in Gephi visualization [21]. Another research represented that the highest centrality software, as well as an example in this way. was in the wing-back defenders and the defensive midfielders. These values indicate the first step in the pass C. Degrees distribution sequence from the wing-back defenders and the defensive For each node, the sum of the input and output degrees is midfielders. An attempt to create an attacking position starts calculated to obtain the frequency distribution graph of the from the spaces at the back of the ground. They also suggested a play style based on possession and the lack of nodes. The degree of each node indicates the level of the using counterattack [22, 23]. Concerning the teams with play node's involvement in match transactions, which is one of style based on the pass sequence in midfield players, the criteria for measuring the individual performance of midfielders had the most pass received from their teammates, players. Mathematically, G represents the directed graph of and therefore, it is obvious that they were the team’s target the communication and V(G) shows the set of the vertices in players [22]. Despite conducting important studies in this this graph. If , then the vertex v equals the sum of area, few studies have used centrality criteria to identify the edges exited and entered into this vertex. players with an important role in the structure of the team D. Average degrees network graph [21, 24]. This research seeks to analyze the pass and The average node degrees and the graph density level communication network by finding and categorizing frequent were calculated as a criterion for displaying cooperation subgraphs for a football team (Persepolis), aiming to identify between the players. Fig 2 shows the statistics of average and examine team play style patterns, strengths and degrees, average weighted degrees, and graph density weaknesses, critical routes, and strong communication obtained according (1,2,3) from the three matches. The between players. Adopting an attitude different from a social weighted degree of each node is achieved by weighting the network perspective to players can generate different results events in the reach centrality section. In this way, the for team use and increase the quality of matches. TABLE I. STATISTICS OF NODES AND COMMUNICATION IN EACH MATCH ESEARCH ETHOD II. R M Total number of nodes (N) 23 In this study, we examined three matches of a team in Persepolis vs. Gol Gohar Total number of edges (L) 657 the 19th season of the Persian Gulf Pro League (Persepolis F.C. against Gol Gohar Sirjan F.C., Paykan F.C., and Total number of nodes (N) 23 Esteghlal F.C.).