Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks
| dc.creator | Kaiser, Marcus | |
| dc.date | 2008-02-18 | |
| dc.date | 2008-08-29 | |
| dc.date.accessioned | 2026-07-07T09:59:11Z | |
| dc.date.available | 2026-07-07T09:59:11Z | |
| dc.description | 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. | |
| dc.description | final version of the manuscript | |
| dc.identifier | https://arxiv.org/abs/0802.2512 | |
| dc.identifier | http://arxiv.org/abs/0802.2512 | |
| dc.identifier | Marcus Kaiser 2008 New J. Phys. 10 083042 | |
| dc.identifier | doi:10.1088/1367-2630/10/8/083042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167937 | |
| dc.subject | Physics and Society | |
| dc.subject | Molecular Networks | |
| dc.title | Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks | |
| dc.type | text |