Onody Roberto N, de Castro Paulo A
Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, C.P.369, 13560-970 São Carlos-SP, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):037103. doi: 10.1103/PhysRevE.70.037103. Epub 2004 Sep 29.
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 player 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.
尽管足球在许多国家都是一项非常受欢迎的运动，但科学界对其关注甚少。在本文中，我们从复杂网络的角度研究足球。首先，我们考虑一个具有两种顶点或节点的二分网络：足球运动员和俱乐部。实际数据来自巴西足球锦标赛的32个赛季，总共涉及13411名足球运动员和127家俱乐部。我们发现了许多有趣且可能意想不到的结果。一名巴西足球运动员效力于N家俱乐部或参加M场比赛的概率呈指数衰减，而他进G个球的概率则遵循幂律。现在，如果同时在同一俱乐部效力的两名足球运动员通过一条边相连，那么就会出现一种新型网络（完全由足球运动员节点组成）。我们的分析表明，对于这个网络，度分布呈指数衰减。我们确定了聚类系数、 assortativity系数和平均最短路径长度的精确值，并将它们与Erdös-Rényi模型和配置模型的值进行比较。计算了这些量的时间演化，并对相应结果进行了讨论。
