A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultrasmall-world organization, whereby the graph’s diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the “six degrees of separation” is the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.

中文翻译：

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为什么社交网络中存在六度分离？

大量证据表明，现实世界的网络具有小世界属性，即任意两个节点之间的最大距离与其大小成对数关系而不是线性关系。此外，大多数社交网络的组织方式都使得每个人之间的联系都不超过六个，这种经验规律被称为六度分离。为什么社交网络有这种超小世界组织，图的直径在几个数量级上与网络规模无关，这仍然是未知的。我们表明，“六度分离”是任何网络平衡状态的特征，在这种状态下，个人会在提高中心地位的愿望与建立和维持联系所产生的成本之间进行权衡。此外，我们表明，这种规律性的出现与所有其他特征兼容，例如集群和无标度，这些特征通常是社交网络结构的特征。因此，我们的结果表明，传统上与​​人类合作和利他主义相关的那种简单的进化规则也可以解释社交网络最有趣的属性之一的出现。