平均聚类系数：孤立节点和叶对小世界网络聚类测度的作用
Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks
摘要：
许多网络表现出小世界性质的邻域连通性高于可比的随机网络。然而，如果节点有一个或没有邻居，则通常不定义局部邻居聚类的标准度量。在这种情况下，局部聚类传统上被设置为零，并且该值影响全局聚类系数。这样的过程会导致低估稀疏网络中的邻域聚类。我们建议包括$θ$作为叶和孤立节点的比例，以估计这些情况的贡献，并提供一个用于估计聚类系数的公式，从Watts和Strogatz（1998 Nature 393 440-2）的聚类系数定义中排除这些情况。排除叶和孤立的节点导致的值是高达140%，高于传统的观察到的网络的值，表明邻里连接通常被低估。我们发现，在比较不同的网络时，聚类系数的定义有很大的影响。对于43种生物体的代谢网络，当应用不同的定义时，58%的比较关系发生了变化。我们还表明，定义的影响小世界的功能和分类可以从非小世界网络的小世界网络。我们讨论了使用的替代措施，断开D，这是受叶和孤立的节点。
英文摘要：
Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbors. In such cases, local clustering has traditionally been set to zero and this value influenced the global clustering coefficient. Such a procedure leads to underestimation of the neighborhood clustering in sparse networks. We propose to include $θ$ as the proportion of leafs and isolated nodes to estimate the contribution of these cases and provide a formula for estimating a clustering coefficient excluding these cases from the Watts and Strogatz (1998 Nature 393 440-2) definition of the clustering coefficient. Excluding leafs and isolated nodes leads to values which are up to 140% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of 43 organisms, relations changed for 58% of the comparisons when a different definition was applied. We also show that the definition influences small-world features and that the classification can change from non-small-world to small-world network. We discuss the use of an alternative measure, disconnectedness D, which is less influenced by leafs and isolated nodes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
