Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. The population structure can be expressed as configurations. Such configurations extend scenarios with a single cooperator among defectors to any number of cooperators and any arrangement of cooperators and defectors on the network. For interaction networks modeled as regular graphs and for weak selection, the emergence of cooperation can be assessed by structure coefficients, which can be specified for each configuration and each regular graph. Thus, as a single cooperator can be interpreted as a lone mutant, the configuration-based structure coefficients also describe fixation properties of multiple mutants. We analyze the structure coefficients and particularly show that under certain conditions, the coefficients strongly correlate to the average shortest path length between cooperators on the evolutionary graph. Thus, for multiple cooperators fixation properties on regular evolutionary graphs can be linked to cooperator path lengths.

中文翻译：

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规则图上多个合作者配置的固定属性。

在图上的演化游戏中是否赞成合作取决于交互网络的总体结构和空间特性。种群结构可以表示为构型。这样的配置将在叛逃者之间具有单个合作者的场景扩展到网络上任何数量的合作者以及合作者和叛逃者的任何安排。对于建模为正则图的交互网络以及弱选择，可以通过结构系数来评估合作的出现，该系数可以为每种配置和每个正则图指定。因此，由于单个合作者可以解释为一个孤独的突变体，因此基于构型的结构系数也描述了多个突变体的固定特性。我们分析了结构系数，特别是表明在某些条件下，系数与进化图上合作者之间的平均最短路径长度密切相关。因此，对于多个合作者，可以将规则进化图上的固定属性链接到合作者的路径长度。