Complex Network Analysis in Cricket : Community structure, player's role and performance index

Abstract: This paper describes the applications of network methods for understanding interaction within members of sport teams.We analyze the interaction of batsmen in International Cricket matches. We generate batting partnership network (BPN) for different teams and determine the exact values of clustering coefficient, average degree, average shortest path length of the networks and compare them with the Erd\text{\"{o}}s-R\text{\'{e}}nyi model. We observe that the networks display small-world behavior and are disassortative in nature. We find that most connected batsman is not necessarily the most central and most central players are not necessarily the one with high batting averages. We study the community structure of the BPNs and identify each player's role based on inter-community and intra-community links. We observe that {\it Sir DG Bradman}, regarded as the best batsman in Cricket history does not occupy the central position in the network $-$ the so-called connector hub. We extend our analysis to quantify the performance, relative importance and effect of removing a player from the team, based on different centrality scores.