%0 Journal Article %1 paper:schank:2004 %A Schank, Thomas %A Wagner, Dorothea %D 2004 %J Journal of Graph Algorithms and Applications %K 2004 algorithm analysis clustering coefficient graph networks social %N 2 %P 265-275 %T Approximating clustering-coefficient and transitivity %U http://www.ubka.uni-karlsruhe.de/vvv/ira/2004/9/9.pdf %V 9 %X Since its introduction in the year 1998 by Watts and Strogatz, the clustering-coefficient has become a frequently used tool for analyzing graphs. In 2002 the transitivity was proposed by Newman, Strogatz and Watts as an alternative to the clustering-coefficient. However, as we illustrate by several examples both parameters may differ vastly. On the other hand, an extension of the definitions to weighted versions provides the formal relation between them. As many networks considered in complex systems are huge, the efficient computation of such network parameters is crucial. Several algorithms with polynomial running time can be derived from results known in graph theory. The main contribution of this work is a new fast approximation algorithm for the weighted clustering-coefficient which also gives very efficient approximation algorithms for the clustering-coefficient and the transitivity. We namely present an algorithm with running time in $O(1)$ for the clustering-coefficient, respectively with running time in $O(n)$ for the transitivity. By an experimental study we demonstrate the performance of the proposed algorithms on real-world data as well as on generated graphs. These results also support the assumption that normally the values of clustering-coefficient and transitivity differ considerably.

@article{paper:schank:2004, abstract = {Since its introduction in the year 1998 by Watts and Strogatz, the clustering-coefficient has become a frequently used tool for analyzing graphs. In 2002 the transitivity was proposed by Newman, Strogatz and Watts as an alternative to the clustering-coefficient. However, as we illustrate by several examples both parameters may differ vastly. On the other hand, an extension of the definitions to weighted versions provides the formal relation between them. As many networks considered in complex systems are huge, the efficient computation of such network parameters is crucial. Several algorithms with polynomial running time can be derived from results known in graph theory. The main contribution of this work is a new fast approximation algorithm for the weighted clustering-coefficient which also gives very efficient approximation algorithms for the clustering-coefficient and the transitivity. We namely present an algorithm with running time in $O(1)$ for the clustering-coefficient, respectively with running time in $O(n)$ for the transitivity. By an experimental study we demonstrate the performance of the proposed algorithms on real-world data as well as on generated graphs. These results also support the assumption that normally the values of clustering-coefficient and transitivity differ considerably.}, added-at = {2008-07-01T10:18:25.000+0200}, author = {Schank, Thomas and Wagner, Dorothea}, biburl = {https://www.bibsonomy.org/bibtex/2ac57c0828f0fe4c862a795d1aed406de/mschuber}, interhash = {d712fc537e20185cc24c32e75e0ad011}, intrahash = {ac57c0828f0fe4c862a795d1aed406de}, journal = {Journal of Graph Algorithms and Applications}, keywords = {2004 algorithm analysis clustering coefficient graph networks social}, number = 2, pages = {265-275}, timestamp = {2008-09-09T12:53:00.000+0200}, title = {Approximating clustering-coefficient and transitivity}, url = {http://www.ubka.uni-karlsruhe.de/vvv/ira/2004/9/9.pdf}, volume = 9, year = 2004 }