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

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

2008-02-18

arxiv.org/abs/0802.2512v3

Marcus Kaiser 2008 New J. Phys. 10 083042

Physics

Physics and Society

final version of the manuscript

Scientific paper

10.1088/1367-2630/10/8/083042

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 $\theta$ 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.

Affiliated with

Also associated with

No associations

Rating

Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-198086