Community structure is a commonly observed feature of real networks. The term refers to the presence in a network of groups of nodes (communities) that feature high internal connectivity, but are poorly connected between each other. Whereas the issue of community detection has been addressed in several works, the problem of validating a partition of nodes as a good community structure for a real network has received considerably less attention and remains an open issue. We propose a set of indices for community structure validation of network partitions that are based on an hypothesis testing procedure that assesses the distribution of links between and within communities. Using both simulations and real data, we illustrate how the proposed indices can be employed to compare the adequacy of different partitions of nodes as community structures in a given network, to assess whether two networks share the same or similar community structures, and to evaluate the performance of different network clustering algorithms.

翻译：社区结构是实际网络中常见的特征。这个术语是指存在于一个网络中,各节点群体(社区)的网络中,这些节点具有高度的内部连通性,但相互之间联系很差。虽然社区探测问题已在若干工作中得到处理,但将节点分割作为真正的网络中良好的社区结构的验证问题却受到的注意要少得多,仍然是一个尚未解决的问题。我们根据一种评估社区之间和社区内部联系分布的假设测试程序,提出了一套网络分区社区结构验证指数。我们用模拟和真实数据来说明如何使用拟议的指数来比较不同节点分布作为特定网络中社区结构的适当性,评估两个网络是否共用相同或类似的社区结构,并评估不同网络组合算法的性能。