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Many networks exhibit the small-world property of the neighborhoodconnectivity being higher than in comparable random networks. However, thestandard measure of local neighborhood clustering is typically not defined if anode has one or no neighbors. In such cases, local clustering has traditionallybeen set to zero and this value influenced the global clustering coefficient.Such a procedure leads to underestimation of the neighborhood clustering insparse networks. We propose to include $\theta$ as the proportion of leafs andisolated nodes to estimate the contribution of these cases and provide aformula for estimating a clustering coefficient excluding these cases from theWatts and Strogatz (1998 Nature 393 440-2) definition of the clusteringcoefficient. Excluding leafs and isolated nodes leads to values which are up to140% higher than the traditional values for the observed networks indicatingthat neighborhood connectivity is normally underestimated. We find that thedefinition of the clustering coefficient has a major effect when comparingdifferent networks. For metabolic networks of 43 organisms, relations changedfor 58% of the comparisons when a different definition was applied. We alsoshow that the definition influences small-world features and that theclassification can change from non-small-world to small-world network. Wediscuss the use of an alternative measure, disconnectedness D, which is lessinfluenced by leafs and isolated nodes.

Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks