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 neighbor. In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of nodes with one or no neighbors to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases.  We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied  .
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 neighbor. In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases. This novel definition 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 URLanisms, relations changed for 58\% of the comparisons when a different definition was applied . Values for the clustering coefficient vary with the ratio of isolated and leaf nodes which is critical for comparing networks. We suggest including ratio and definition in publications to enable comparisons across different studies .
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nodes with one or no neighbors
leafs and isolated nodes
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This novel definition leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated.
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. Values for the clustering coefficient vary with the ratio of isolated and leaf nodes which is critical for comparing networks. We suggest including ratio and definition in publications to enable comparisons across different studies